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ABSTRACT The positive predictive value (PPV) and negative predictive value (NPV) can be expressed as functions of disease prevalence (ρ$$ \rho $$) and the ratios of two binomial proportions (ϕ$$ \phi $$), where ϕppv=1−specificitysensitivity$$ {\phi}_{ppv}=\frac{1- specificity}{sensitivity} $$ and ϕnpv=1−sensitivityspecificity$$ {\phi}_{npv}=\frac{1- sensitivity}{specificity} $$. In prospective studies, where the proportion of subjects with the disease in the study cohort is an unbiased estimate of the disease prevalence, the confidence intervals (CIs) of PPV and NPV can be estimated using established methods for single proportion. However, in enrichment studies, such as case–control studies, where the proportion of diseased subjects significantly differs from disease prevalence, estimating CIs for PPV and NPV remains a challenge in terms of skewness and overall coverage, especially under extreme conditions (e.g., NPV=1$$ \mathrm{NPV}=1 $$). In this article, we extend the method adopted by Li, where CIs for PPV and NPV were derived from those of ϕ$$ \phi $$. We explored additional CI methods for ϕ$$ \phi $$, including those by Gart & Nam (GN), MoverJ, and Walter and convert their corresponding CIs for PPV and NPV. Through simulations, we compared these methods with established CI methods, Fieller, Pepe, and Delta in terms of skewness and overall coverage. While no method proves universally optimal, GN and MoverJ methods generally emerge as recommended choices. [ABSTRACT FROM AUTHOR]

AbstractPrivacy protection methods, such as differentially private mechanisms, introduce noise into resulting statistics which often produces complex and intractable sampling distributions. In this paper, we propose a simulation-based “repro sample” approach to produce statistically valid confidence intervals and hypothesis tests, which builds on the work of Xie and Wang (2022). We show that this methodology is applicable to a wide variety of private inference problems, appropriately accounts for biases introduced by privacy mechanisms (such as by clamping), and improves over other state-of-the-art inference methods such as the parametric bootstrap in terms of the coverage and type I error of the private inference. We also develop significant improvements and extensions for the repro sample methodology for general models (not necessarily related to privacy), including 1) modifying the procedure to ensure guaranteed coverage and type I errors, even accounting for Monte Carlo error, and 2) proposing efficient numerical algorithms to implement the confidence intervals and p-values. [ABSTRACT FROM AUTHOR]

When a researcher proposes an SEM model to explain the dynamics among some latent variables, the real question in model evaluation is the fit of the model's structural part. A composite index that lumps the fit of the structural part and measurement part does not directly address that question. The need for more attention to structural-level fit has been noted for a long time, but the literature has been limited to conceptual issues such as how to define the structural-level RMSEA or CFI. How to estimate those structural-level fit indices, however, have been overlooked. Traditional estimation methods for composite-fit RMSEA and CFI are not applicable to structural-level fit indices, even if data are complete and normally distributed. In this article, we give correct point estimators and confidence intervals for structural-level RMSEA and CFI. Simulation results suggest that the new methods have satisfactory performance in realistic situations. [ABSTRACT FROM AUTHOR]

In this paper, we propose an estimator of power spot volatility of order p through Edgeworth expansion. We provide a precise description of how to compute the expansion and the first four cumulants are given in an explicit form. We also construct feasible confidence intervals (one-sided and two-sided) for the pth power spot volatility estimator by using Edgeworth expansion. A Monte Carlo simulation study shows that the confidence intervals and probability density curve based on Edgeworth expansion perform better than the conventional case based on Normal approximation. [ABSTRACT FROM AUTHOR]

A sufficient number of participants should be included to adequately address the research interest in the surveys with sensitive questions. In this paper, sample size formulas/iterative algorithms are developed from the perspective of controlling the confidence interval width of the prevalence of a sensitive attribute under four non‐randomized response models: the crosswise model, parallel model, Poisson item count technique model and negative binomial item count technique model. In contrast to the conventional approach for sample size determination, our sample size formulas/algorithms explicitly incorporate an assurance probability of controlling the width of a confidence interval within the pre‐specified range. The performance of the proposed methods is evaluated with respect to the empirical coverage probability, empirical assurance probability and confidence width. Simulation results show that all formulas/algorithms are effective and hence are recommended for practical applications. A real example is used to illustrate the proposed methods. [ABSTRACT FROM AUTHOR]

Asymmetrical probability models are helpful for analyzing skewed data sets since they allow you to describe the form of the distribution and anticipate the chance of extreme events. This article defines a novel approach to continuous moment exponential distribution called the exponentiated generalized moment exponential model. The extension has two additional parameters accounting for the distribution's shape. We extend this distribution probability density, cumulative distribution, hazard rate, and survival functions and establish different key statistical properties. Parameter estimation is obtained using different procedures, notably maximum likelihood estimation, least square, and Bayesian methods. A Monte Carlo simulation experiment is conducted to assess parameter performance and indicator risk measures. This article examines two distinct actual data sets in order to highlight the significance of the proposed model as well as its application in a variety of settings. The new model is compared to a large number of well-known extensions that were developed by other businesses. [ABSTRACT FROM AUTHOR]

Confidence interval performance is typically assessed in terms of two criteria: coverage probability and interval width (or margin of error). In this article, we assess the performance of four common proportion interval estimators: the Wald, Clopper-Pearson (exact), Wilson and Agresti-Coull, in the context of rare-event probabilities. We define the interval precision in terms of a relative margin of error which ensures consistency with the magnitude of the proportion. Thus, confidence interval estimators are assessed in terms of achieving a desired coverage probability whilst simultaneously satisfying the specified relative margin of error. We illustrate the importance of considering both coverage probability and relative margin of error when estimating rare-event proportions, and show that within this framework, all four interval estimators perform somewhat similarly for a given sample size and confidence level. We identify relative margin of error values that result in satisfactory coverage while being conservative in terms of sample size requirements, and hence suggest a range of values that can be adopted in practice. The proposed relative margin of error scheme is evaluated analytically, by simulation, and by application to a number of recent studies from the literature. [ABSTRACT FROM AUTHOR]

AbstractThis paper proposes a novel method for determining confidence intervals in non-probabilistic survey samples, addressing the challenge of statistically quantifying uncertainty in such samples. The method utilizes combinatorial calculations to assess the myriad combinations possible in the unsampled population, applying the symmetric property of binomial coefficients to optimize computational efficiency. The proposed approach offers a practical solution, making it feasible to calculate confidence intervals even with large sample sizes. This methodology represents a significant advancement in survey research, providing a tool to evaluate and generalize non-probabilistic data, particularly in contexts where probabilistic sampling is not viable. The paper also validates the method using extensive testing, demonstrating its applicability and effectiveness in real-world scenarios. [ABSTRACT FROM AUTHOR]

AbstractDuring the dry season, the northern region of Thailand consistently grapples with compromised air quality, notably an excessive level of particulate matter with a diameter of less than 2.5 microns (PM2.5), which poses implications for public health. Wind speed emerges as the primary factor that diminishes the concentration of PM2.5, making the evaluation of wind speed changes crucial in understanding and potentially mitigating the impact of air pollution on public health in the region. The wind speed data contain zero and positive values. This can be estimated through the confidence intervals of the difference and ratio between two means of delta-Birnbaum-Saunders distributions using various methods, including the generalized confidence interval (GCI), bootstrap confidence interval (BCI), and generalized fiducial confidence interval (GFCI). These methods rely on variance stabilizing transformations (VST), the Wilson and Hannig methods. According to the simulation, for small sample sizes, the GCI based on the VST and Hannig was the most effective method in terms of coverage probabilities and average lengths. For medium sample sizes, it was found that the performance of GFCI based on the VST method was superior to other methods. Additionally, when confronted with a large sample size, the BCI based on the VST method becomes relevant and will be introduced. To demonstrate the efficacy of our proposed methods, we applied them to wind speed data gathered from Chiang Mai Airport station in Thailand from January to February in both 2022 and 2023. [ABSTRACT FROM AUTHOR]

Wind curtailment, caused by wind power uncertainty, has become a prominent issue with the large-scale grid connection of wind power. To fully account for the uncertainty of wind power output, a short-term hydro-wind-thermal operation method based on a wind power confidence interval is proposed. By utilizing the flexible start-stop and efficient ramp-up of cascade hydropower plants to smooth fluctuations in wind power output, a multi-objective optimal scheduling model that minimizes the cost of power generation and maximizes the consumption of clean energy is constructed. To reduce the solution's complexity, we chunk the model according to the energy type using a hierarchical solution. The overall solution framework, which integrates a nonparametric method, a heuristic algorithm, and an improved particle swarm algorithm, is constructed to solve the model rapidly. The simulation results of a regional power grid show that the proposed method can attain an efficient solution in 83.5 seconds. Furthermore, the proposed method achieves an additional 455,600 kWh of hydropower and a reduction of ¥233,300 in the cost of coal consumption. These findings suggest that the proposed method is a good reference for the short-term operation of a hydro-wind-thermal combination in large-scale wind power access areas. [ABSTRACT FROM AUTHOR]

Researchers can use many statistical tools to fit data, either simple or complex, based on the likelihood. However, more parameters usually provide a smooth resolution, due to the order of likelihood increases, however, the main issue is to use special tools to estimate parameters. For example, we are used the process capability indices (C L) for measuring the performance of a process with, lower specification limit L). The article adopts a method of C L when the unit's lifetime has two parameters generalised half-logistic lifetime population. The real-world dataset is collected with respected to Type-I generalised hybrid censoring scheme. The scale parameter is specified under data transformation technology. The Bayes and maximum likelihood estimators are formulated using the conjugate form of the prior and examined using the squared error loss procedure. The developed estimators construct credible and confidence intervals for C L. Real world examples in this article illustrate the pattern of the estimate value of confidence interval for the parameter C L and the interval estimations of C L are assessed by a Monte Carlo simulation studies. [ABSTRACT FROM AUTHOR]

Under the assumption of missing response data, empirical likelihood inference is studied via composite quantile regression. Firstly, three empirical likelihood ratios of composite quantile regression are given and proved to be asymptotically χ 2 . Secondly, without an estimation of the asymptotic covariance, confidence intervals are constructed for the regression coefficients. Thirdly, three estimators are presented for the regression parameters to obtain its asymptotic distribution. The finite sample performance is assessed through simulation studies, and the symmetry confidence intervals of the parametric are constructed. Finally, the effectiveness of the proposed methods is illustrated by analyzing a real-world data set. [ABSTRACT FROM AUTHOR]

Context: Development of high-yielding potato cultivars represents the most efficient and sustainable strategy to secure global food and nutrition. In the past decades, numerous quantitative trait loci (QTL) mapping studies have identified various QTLs associated with morphological traits in potato. However, the varying genetic backgrounds of germplasm and the diverse QTL analysis algorithms restrict the utility of identified QTLs for research. Aims: One of the primary objectives of breeders is to identify consistent chromosomal regions linked to economically significant quantitative traits associated with yield through QTL analysis. To achieve this, an investigation was conducted to pinpoint the most stable QTLs for traits such as maturity, harvest index, plant height, stem diameter, tuber starch content, sprouting, and flesh colour. Methods: In order to detect stable QTLs for major agronomic traits, metaQTL analysis was performed using 294 QTLs from 14 publications. Key results: A total of 10 metaQTLs were found to be associated with seven morphological traits. Meta-analysis was considerably refined as compared to the initial QTLs and provided the closest flanking markers for investigated traits and reduce confidence interval mainly to five folds as compared to the mean confidence interval of initial QTLs. The metaQTLs of morphological traits juxtaposed along Chromosomes II, III, IV, and V from independent studies were considered the most stable QTLs over different field trails and genetic background. Conclusions: Ten metaQTLs were identified that contain major consensus QTLs for various morphological traits in potato. Implications: This study will enable the integration of QTLs to create new cultivars with targeted quantitative traits, thereby accelerating breeding initiatives. For decades, potato breeding has been hindered by high diversity and genetic complexity. We identified the individual locations of genes that contribute to potato yield, by analysing data from 14 prior studies. This knowledge will accelerate breeding programmes. This article belongs to the Collection Plant breeding- and genetics-based tools for food security under changing climate. [ABSTRACT FROM AUTHOR]

Thailand is currently grappling with a severe problem of air pollution, especially from small particulate matter (PM), which poses considerable threats to public health. The speed of the wind is pivotal in spreading these harmful particles across the atmosphere. Given the inherently unpredictable wind speed behavior, our focus lies in establishing the confidence interval (CI) for the variance of wind speed data. To achieve this, we will employ the delta-Birnbaum-Saunders (delta-BirSau) distribution. This statistical model allows for analyzing wind speed data and offers valuable insights into its variability and potential implications for air quality. The intervals are derived from ten different methods: generalized confidence interval (GCI), bootstrap confidence interval (BCI), generalized fiducial confidence interval (GFCI), and normal approximation (NA). Specifically, we apply GCI, BCI, and GFCI while considering the estimation of the proportion of zeros using the variance stabilized transformation (VST), Wilson, and Hannig methods. To evaluate the performance of these methods, we conduct a simulation study using Monte Carlo simulations in the R statistical software. The study assesses the coverage probabilities and average widths of the proposed confidence intervals. The simulation results reveal that GFCI based on the Wilson method is optimal for small sample sizes, GFCI based on the Hannig method excels for medium sample sizes, and GFCI based on the VST method stands out for large sample sizes. To further validate the practical application of these methods, we employ daily wind speed data from an industrial area in Prachin Buri and Rayong provinces, Thailand. [ABSTRACT FROM AUTHOR]

High placebo responses could significantly reduce the treatment effect in a parallel randomized trial. To combat that challenge, several approaches were developed, including the sequential parallel comparison design (SPCD) that was shown to increase the statistical power as compared to the traditional randomized trial. A linear combination of the response rate differences from two phases per the SPCD is commonly used to measure the overall treatment effect size. The traditional approach to calculate the confidence interval for the overall rate difference is based on the delta method using the variance–covariance matrix of all outcomes. As outcomes from a multinomial distribution are correlated, we suggest utilizing a constrained variance–covariance matrix in the delta method. In the observation of anti-conservative coverages from asymptotic intervals, we further propose using importance sampling to develop accurate intervals. Simulation studies show that accurate intervals have better coverage probabilities than others and the interval width of accurate intervals is similar to the interval width of others. Two real trials to treat major depressive disorder are used to illustrate the application of the proposed intervals. [ABSTRACT FROM AUTHOR]

Due to the significant impact of occupant behavior uncertainty on building performance, robustness indicators are crucial for assessing and predicting building energy consumption. This study evaluates the robustness of building performance under occupant behavior uncertainty using various robustness indicators such as Maximax, Maximin, Hurwicz, and Laplace. Benchmark values (0.635) and coefficients of variation (0.544) from statistics were introduced to quantify the relative performance of each indicator and the relative dispersion of the data, allowing for fair comparisons across different magnitudes of indicators. "Variance", "Starr's Domain", "Kurtosis", and "Maximin" were identified as key indicators for assessing the robustness of energy consumption and load data. Based on these indicators and statistical principles, assuming the data follows a normal distribution, energy consumption and loads were predicted, showing that the optimized outcomes demonstrate good robustness. [ABSTRACT FROM AUTHOR]

To obtain a profile empirical likelihood ratio statistic is essentially to address a constrained maximization problem. However, when sample size is small, the optimal function may have no numerical solution, as the convex hull of the sample points may not contain the zero vector 0 as its interior point. The adjusted empirical likelihood (AEL) method introduced by Chen, Variyath, and Abraham (2008) is very useful to solve this problem. The innovation of this article is that we extend the AEL method to probability density functions (p.d.f.) under dependent samples, as there are few literatures using this method under dependent samples. It is shown that the AEL ratio statistic for a p.d.f. is asymptotically χ 2 -type distributed under a mixing sample, which is used to obtain an AEL-based confidence interval for the p.d.f. Our simulations show that the AEL is faster to compute than unadjusted empirical likelihood and the coverage probability based on the AEL method is superior to the other two usual methods, namely the unadjusted empirical likelihood and the normal approximation methods, particularly under small sample sizes. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new confidence interval (CI) for the population mean μ based on robust estimators, which involves the application of the winsorized modified one-step M-estimator (WMOM) and winsorized standard deviation (WSD). The proposed method is modified for the Student's t confidence interval CI under the non-normal distribution. The performances of the proposed confidence interval were evaluated via a Monte-Carlo simulation study by considering the coverage ratio (CR) and the average length (AL) as performance criteria. The simulation study results show the superior performance of the proposed confidence interval (CI) over the classical parametric Student's t for data from a non-normal distribution. Two real data sets were analyzed, and the results agree to some extent with those of the simulation study. The results confirm the suitability of the proposed CI estimator for both normally and non-normally distributed data. [ABSTRACT FROM AUTHOR]

Background: Parametric regression analysis is widely used in methods comparisons and more recently in checking the concordance of test results following receipt of new reagent lots. The greater frequency of reagent-lot evaluations increases pressure to detect bias with smallest possible sample sizes (i.e. smallest consumption of time and resources). This study revisits bias detection using the joint slope, intercept confidence region as an alternative to slope and intercept confidence intervals. Methods: Four cases were considered representing constant errors, proportional errors (constant CV) and two more complicated error patterns typical of immunoassays. Maximum:minimum range ratios varied from 2:1 to 2000:1. After setting a maximum tolerable difference a series of slope, intercept combinations, each of which predicted the critical difference, were systematically evaluated in simulations which determined the minimum sample size required to detect the difference, firstly using slope, intercept confidence intervals and secondly using the joint slope, intercept confidence region. Results: At small to moderate range ratios, bias detection by joint confidence region required greatly reduced sample sizes to the extent that it should encourage reagent-lot evaluations or, alternatively, transform those already routinely performed into considerably less costly exercises. Conclusions: While some software is available to calculate joint confidence regions in real-life analyses, shifting this testing method into the mainstream will require a greater number of software developers incorporating the necessary code into their regression programs. The computer program used to conduct this study is freely available and can be used to model any laboratory test. [ABSTRACT FROM AUTHOR]

Evaluating the performance of city construction not only helps optimize city functions and improve city quality, but it also contributes to the development of sustainable cities. However, most of the scoring rules for evaluating the performance of city construction are overly cumbersome and demand very high data integrity. Moreover, the properties, change scale, and scope of different evaluation indicators of city construction often lead to uncertain and ambiguous results. In this study, a hybrid fuzzy method is proposed to conduct the performance evaluation of city construction in two phases. Firstly, a city performance index (CPI) was developed by combining the means and standard deviations of indicators of city construction to address the volatility of historical statistical data as well as different types of data. Considering the sampling errors in data analysis, the parameter estimation method was used to derive the 100% × (1 − α) confidence interval of the CPI. Buckley's fuzzy approach was then adopted to extend the statistical estimators from the CPI into fuzzy estimators, after which a fuzzy CPI was proposed. To identify the specific improvement directions for city construction, the fuzzy axiom design (fuzzy AD) method was applied to explore the relationship between the targets set by city managers and actual performance. Finally, an example of six cities in China is provided to illustrate the effectiveness and practicality of the proposed method. The results show that the performance of Chongqing on several evaluation indicators is lower than that of other cities. The proposed method takes into account the issues of uniformity and diversity in the performance evaluation of city construction. It can enable a quantitative assessment of the city construction level in all cities and provide theoretical support and a decision-making basis for relevant government departments to optimize city construction planning and scientifically formulate city construction policies. [ABSTRACT FROM AUTHOR]

We consider a general regression model, either without a scale parameter or with a known scale parameter. We construct a confidence interval for a scalar parameter of interest that utilizes the uncertain prior information that a distinct scalar parameter takes a specified value. This confidence interval has excellent coverage properties. It also has local scaled expected length, where the scaling is with respect to the usual confidence interval, that (a) is substantially less than 1 when the prior information is correct, (b) has a maximum value that is not too large, and (c) is close to 1 when the data and prior information are highly discordant. An important practical application of this confidence interval is to a quantal bioassay carried out to compare two similar compounds. In this context, the uncertain prior information is that the hypothesis of "parallelism" holds. We provide extensive numerical results that illustrate the attractive properties of this confidence interval in this context. [ABSTRACT FROM AUTHOR]

While the Taguchi capability index developed by Chan (J Qual Technol 20(3):162–175, 1988) takes the process targeting issue into consideration, it fails to account for processes with asymmetric tolerances, which are common in practice. Thus, Chen (Int J Reliab Qual Saf Eng 6(4):383–398) modified this index to include processes with asymmetric tolerances. This index is an important tool for the assessment of quality characteristics with asymmetric tolerances, which are common in practice. As the probability density function of the index is complex, statistical inference can be fairly difficult for quality or process engineers. Furthermore, sample sizes are often small in practice to increase decision-making efficiency, but this can decrease assessment accuracy. To address this issue, we employed a mathematical programming approach to make it more convenient for quality or process engineers to derive the upper confidence limit of the index. We also adopted the suggestion put forward by previous studies to incorporate historical data or expert experience in confidence-interval-based fuzzy testing. The proposed approach therefore has increased assessment accuracy, is convenient to apply in practice, and meets the need for swift responses. [ABSTRACT FROM AUTHOR]

Being the parent distribution in Romania, the Pearson III distribution (PE3) is one of the statistical distributions that is most frequently used in flood frequency analysis (FFA). All the components required for the simple implementation of PE3 distribution in FFA are presented in this manuscript. The estimated methods and exact and approximate relationships for estimating the parameters and frequency factors particular to the distribution are described. All of these factors are used to identify maximum flows with various annual exceedance probabilities, using data collected at the 6 rivers with different morphometric characteristics and different lengths of data series. Five parameter estimation techniques are used in this comparative analysis, i.e. the method of ordinary moments (MOM), the method of linear moments (L-moments), the high-order linear moments method (LH-moments), the method of maximum likelihood (MLE) and the method of least squares (LSM). Given the results, it can be assumed that the L-moments approach is more reliable, stable, robust and less sensitive to variations in recorded data lengths, as well as to the presence of outliers. [ABSTRACT FROM AUTHOR]

Monte Carlo simulations are widely used in analysis of interference between radiocommunication systems. The method performs n random experiments, each called an event, snapshot, or trial, to estimate the statistics of some parameter of the problem (for instance, the interference level). There is no formalization about the number of events necessary to run a simulation. In practice, this is often done based on the intuition of the analyst about the model. In this paper, we propose how to choose a number of events for Monte Carlo simulations. We address this issue by understanding that the protection criteria for radiocommunication systems are usually related to a quantile of the result, and then calculating the number of events for which it is also possible to estimate a confidence interval for it. Results show that, for a confidence level of 99.9%, it is possible to estimate confidence intervals for p-quantiles for p up to 99.89% with 10 000 events. [ABSTRACT FROM AUTHOR]

Asymmetrical probability models are helpful for analyzing skewed data sets since they allow you to describe the form of the distribution and anticipate the chance of extreme events. This article defines a novel approach to continuous moment exponential distribution called the exponentiated generalized moment exponential model. The extension has two additional parameters accounting for the distribution’s shape. We extend this distribution probability density, cumulative distribution, hazard rate, and survival functions and establish different key statistical properties. Parameter estimation is obtained using different procedures, notably maximum likelihood estimation, least square, and Bayesian methods. A Monte Carlo simulation experiment is conducted to assess parameter performance and indicator risk measures. This article examines two distinct actual data sets in order to highlight the significance of the proposed model as well as its application in a variety of settings. The new model is compared to a large number of well-known extensions that were developed by other businesses.

Researchers can use many statistical tools to fit data, either simple or complex, based on the likelihood. However, more parameters usually provide a smooth resolution, due to the order of likelihood increases, however, the main issue is to use special tools to estimate parameters. For example, we are used the process capability indices (CL) for measuring the performance of a process with, lower specification limit L). The article adopts a method of CL when the unit’s lifetime has two parameters generalised half-logistic lifetime population. The real-world dataset is collected with respected to Type-I generalised hybrid censoring scheme. The scale parameter is specified under data transformation technology. The Bayes and maximum likelihood estimators are formulated using the conjugate form of the prior and examined using the squared error loss procedure. The developed estimators construct credible and confidence intervals for CL. Real world examples in this article illustrate the pattern of the estimate value of confidence interval for the parameter CL and the interval estimations of CL are assessed by a Monte Carlo simulation studies.

Estimating a common parameter is the most essential and quite fascinating task across various probability distributions. This article addresses the challenge of estimating this parameter through the application of Maximum Likelihood Estimation (MLE). Numeric determination of common parameters is conducted for several distributions, including the Lomax distribution, Gamma distribution, Rayleigh distribution, and Weibull distribution. In cases where distributions lack a closed-form solution, estimation of MLEs is achieved using the Newton-Raphson technique. Furthermore, asymptotic confidence intervals are computed utilizing the Fisher information matrix tailored to each distribution. The performance evaluation of these estimators centers on the assessment of bias and mean squared error. To enable a numerical comparison of these estimators, the Monte Carlo simulation method is employed. Finally, these techniques are applied to real-time rainfall data to assess parameter estimates for each distribution.

BACKGROUND: Perfusion index (PI) and CRIB (Clinical risk index of babies) Score II both are minimally invasive tools for prediction of mortality and morbidity in sick neonates. This study aims to know the predictive values of both PI and CRIB Score II in assessment of severity of illness in preterm neonates of 28 to 32 weeks and their correlation. METHODS: PI and CRIB II Score of 125 sick preterm neonates admitted in NICU were assessed within 12 hours of admission. Severity noted in form of outcome. Correlation between PI and CRIB Score II were observed. RESULTS: Receiver operating characteristic (ROC) curve were plotted for PI and CIRB Score II with outcome (discharged vs expired). Area under curve for perfusion index was 0.776 at 95% confidence interval. Optimum cutoff point based on ROC curve was 1.65 with sensitivity of 84%., specificity of 37.2% with positive predictive value of 70% and negative predictive value of 57%. Area under curve for CRIB Score II was 0.622 (p value < 0.028), optimum cut off point based on ROC curve for CRIB II score was 3.5 with sensitivity 79.10% of specificity of 40% positive predictive value is 43.03% and negative predictive value of 76.9%. Spearman's correlation coefficient between PI and CRIB II score was –0.272 and p value is 0.002. CONCLUSION: This study concluded that perfusion index (p < 0.001) is better for predicting the severity compared to CRIB II score (p < 0.028). A weak negative correlation exists between PI and CRIB II score (r = –0.272). [ABSTRACT FROM AUTHOR]

In this article we consider the meta‐analysis of stage life testing experiments. We propose a method to combine the data obtained from s$s$ number of independent stage life testing experiments. We have assumed that there are only two stress levels for each stage life testing experiment and lifetime of the experimental units follows Weibull distribution at each stress level. The distributions under two stress levels are connected through Khamis–Higgings model assumption. We assume that the shape parameters of Weibull distribution are same for all the samples; however, the scale parameters are different. We provide the maximum likelihood estimation and the asymptotic confidence intervals of the model parameters. We also provide the Bayesian inference of the model parameters. The Bayes estimates and the associated credible intervals are obtained using Gibbs sampling technique since the explicit forms of the Bayes estimates do not exist. We have performed an extensive simulation study to see the performances of the different estimators, and the analyses of two data sets for illustrative purpose. The results are quite satisfactory. [ABSTRACT FROM AUTHOR]

Sports science as an empirical science produces study results that are to be interpreted hypothesis-oriented. The validity of the interpretation of statistically and practically significant results depends on the one hand on the theoretical foundation of the research question and on the other hand on the concrete methodological procedure in intervention studies. Considering hypotheses at the empirical-content and statistical level, recurring interpretation difficulties arise when numbers are translated into words or recommendations for action. On the basis of two examples, a discussion in the scientific community is to be initiated, which could be continued in this journal in case of corresponding interest in methodological issues. [ABSTRACT FROM AUTHOR]

In the literature, modifying the baseline distributions and proposing novel approach of the existing probability models play an important role in the analysis of real-world phenomena as well as the development of new distributions essentially stems from the need to adequately characterize environmental and lifetime events. In this paper, we introduce a new model by applying maximum compound technique to the baseline distributions for modeling more types data used in different case of studies including symmetric, asymmetric, skewed and complex data sets. The proposed model called univariate maximum Harris extended Rayleigh distribution and three parameters characterize it, and it is regarded as strong competitor for widely applied symmetrical and non symmetrical models. The paper offers varied fundamental distributional and mathematical properties of the suggested distribution, such as conditional probability and its expectation, as well as quantile and moment-generating functions. The model’s parameters are estimated by applying numerous procedures including maximum likelihood estimation, Expectation–Maximization iterative method and Bayesian approach. Bayesian estimation is performed via various loss functions such as square error, Linex and general entropy functions. As well as, approximate and Bootstrap methods are used to construct the confidence interval for the unknown parameters of the proposed model. Additionally, we illustrated different extensive simulation experiments to see the potential of the suggested estimation methods which give satisfactory performance results. In the end, we applied two real data sets for illustrative purposes. In our illustration, we have compared the practicality of the recommended model with several well-known competing distributions.

Timely understanding of surrounding rock pressure bolting is crucial to enhance the service life of drilling rigs and ensure coal mine production safety. However, delayed feedback of drilling pressure, nonlinear distribution of coal and rock hardness,and inapplicability of existing methods in bolt support are common problems. To address these issues, a prediction method of drilling pressure in bolt support is proposed based on the optimal kernel function and historical points of Gaussian process time series regression. This is a machine learning method that is highly adaptabile to nonlinear problems and provides probabilistic output. It utilizes Gaussian stochastic process, kernel function, and Bayesian theory to predict the sequence coal rock pressure during bolt support. The optimal kernel function and historical points for the proposed prediction method were selected based on drilling pressure test data obtained during roadway excavation where the drill box was drilled 1000 mm. The parameters included 10 types of kernel functions (E, SE, RQ, Maten3/2, Maten5/2, ARDE, ARDSE, ARDRQ, ARDMatern3/2, ARDMatern5/2) and 7 different historical points (8, 10, 12, 14, 16, 18, 20). The optimal hyperparameter were adaptively determined through the negative logarithmic edge likelihood function as the minimization objective function. A total of 70 numerical calculations were performed using a single-step extrapolation method with a 7:3 ratio for the training and testing sets on the selected samples. Based on the evaluation indicators, such as determinability coefficient (R2), root mean square error (RMSE), and the average absolute error (MAE) of the test set, the optimal kernel function and optimal combination of duration points for four bolt support drilling pressure prediction strategies were identified. The optimal combination includes Matern5/2 with historical points 10, ARDMatern5/2 with historical points 10, SE with historical points 18, and RQ with historical points 18. The optimal kernel function was selected as Matern5/2 and the optimal number of historical points was chosen as 10, considering the minimization of computational complexity. Drilling pressure test data obtained from drilling the drill box at 1200 mm, 2400 mm and 3000 mm during the tunnel excavation process were used for numerical calculations The predicted distribution of the drilling pressure supported by the anchor rod was given with a 95% confidence interval. The proposed method achieved an R2 of 0.61317 and an MAE of 0.026957 for drilling pressure during drilling with a 1200 mm drill box, with an average width percentage of the interval of 3.072%. For the drilling pressure of 2400 mm drill box, the proposed method achieved an R2 of 0.93118 and an MAE of 0.010895, with an average width percentage of the interval of 0.581%. For the drilling pressure of 3000 mm drill box, the proposed method achieved an R2 of 0.99647 and an MAE of 0.0091847, with an average width percentage of the interval of 0.614%. The final conclusion found that the combination of different kernel functions and historical points has a significant difference in prediction performance,which is two important factors that cannot be ignored.The prediction results were excellent for the data bands with a uniform hardness distribution of the surrounding rock and acceptable for the data bands with abrupt hardness changes.

The event of a student dropping out from an academic program depends on several factors namely course content, change in interest, financial problems among many others. These factors vary interdependently with different phases of the academic program. We assume that the factors put different amount of academic stresses on a student in different phases of the program. We formulate and analyze such an accumulated-stress model under the assumption that the attrition time at each phase follows the Kumaraswamy distribution. A hazard-rate based approach is used to model the accumulated stress through different phases. At each phase the stress levels vary. Accordingly, we estimate the model parameters based on the frequentist approach. Extensive simulation experiments indicate satisfactory performance of the estimators. A synthetic dataset related to students' dropout has been analyzed for illustrative purpose. [ABSTRACT FROM AUTHOR]

In the literature, modifying the baseline distributions and proposing novel approach of the existing probability models play an important role in the analysis of real-world phenomena as well as the development of new distributions essentially stems from the need to adequately characterize environmental and lifetime events. In this paper, we introduce a new model by applying maximum compound technique to the baseline distributions for modeling more types data used in different case of studies including symmetric, asymmetric, skewed and complex data sets. The proposed model called univariate maximum Harris extended Rayleigh distribution and three parameters characterize it, and it is regarded as strong competitor for widely applied symmetrical and non symmetrical models. The paper offers varied fundamental distributional and mathematical properties of the suggested distribution, such as conditional probability and its expectation, as well as quantile and moment-generating functions. The model's parameters are estimated by applying numerous procedures including maximum likelihood estimation, Expectation–Maximization iterative method and Bayesian approach. Bayesian estimation is performed via various loss functions such as square error, Linex and general entropy functions. As well as, approximate and Bootstrap methods are used to construct the confidence interval for the unknown parameters of the proposed model. Additionally, we illustrated different extensive simulation experiments to see the potential of the suggested estimation methods which give satisfactory performance results. In the end, we applied two real data sets for illustrative purposes. In our illustration, we have compared the practicality of the recommended model with several well-known competing distributions. [ABSTRACT FROM AUTHOR]

Background Addressing aggressive behavior in adolescence is a key step toward preventing violence and associated social and economic costs in adulthood. This study examined the secondary effects of the personality-targeted substance use preventive program Preventure on aggressive behavior from ages 13 to 20. Methods In total, 339 young people from nine independent schools (M age = 13.03 years, s.d. = 0.47, range = 12–15) who rated highly on one of the four personality traits associated with increased substance use and other emotional/behavioral symptoms (i.e. impulsivity, anxiety sensitivity, sensation seeking, and negative thinking) were included in the analyses (n = 145 in Preventure, n = 194 in control). Self-report assessments were administered at baseline and follow-up (6 months, 1, 2, 3, 5.5, and 7 years). Overall aggression and subtypes of aggressive behaviors (proactive, reactive) were examined using multilevel mixed-effects analysis accounting for school-level clustering. Results Across the 7-year follow-up period, the average yearly reduction in the frequency of aggressive behaviors (b = −0.42; 95% confidence interval [CI] −0.64 to −0.20; p < 0.001), reactive aggression (b = −0.22; 95% CI 0.35 to −0.10; p = 0.001), and proactive aggression (b = −0.14; 95% CI −0.23 to −0.05; p = 0.002) was greater for the Preventure group compared to the control group. Conclusions The study suggests a brief personality-targeted intervention may have long-term impacts on aggression among young people; however, this interpretation is limited by imbalance of sex ratios between study groups. [ABSTRACT FROM AUTHOR]

Background Problematic drinking frequently co-occurs with depression among young adults, but often remains unaddressed in depression treatment. Evidence is insufficient on whether digital alcohol interventions can be effective in this young comorbid population. In a randomized controlled trial, we examined the effectiveness of Beating the Booze (BtB), an add-on digital alcohol intervention to complement depression treatment for young adults. Methods Participants were randomized to BtB + depression treatment as usual (BTB + TAU, n = 81) or TAU (n = 82). The primary outcome was treatment response, a combined measure for alcohol and depression after 6-month follow-up. Secondary outcomes were number of weekly drinks (Timeline Follow-back) and depressive symptoms (Center for Epidemiologic Studies Depression scale). Treatment response was analyzed using generalized linear modeling and secondary outcomes using robust linear mixed modeling. Results Low treatment response was found due to lower than expected depression remission rates. No statistically significant between-group effect was found for treatment response after 6-month follow-up (odds ratio 2.86, p = 0.089, 95% confidence interval [CI] 0.85–9.63). For our secondary outcomes, statistically significant larger reductions in weekly drinks were found in the intervention group after 3-month (B = −4.00, p = 0.009, 95% CI −6.97 to −1.02, d = 0.27) and 6-month follow-up (B = −3.20, p = 0.032, 95% CI −6.13 to −0.27, d = 0.23). We found no statistically significant between-group differences on depressive symptoms after 3-month (B = −0.57, p = 0.732, 95% CI −3.83 to 2.69) nor after 6-month follow-up (B = −0.44, p = 0.793, 95% CI −3.69 to 2.82). Conclusions The add-on digital alcohol intervention was effective in reducing alcohol use, but not in reducing depressive symptoms and treatment response among young adults with co-occurring depressive disorders and problematic alcohol use. Trial registration: Pre-registered on October 29, 2019 in the Overview of Medical Research in the Netherlands (OMON), formerly the Dutch Trial Register(https://onderzoekmetmensen.nl/en/trial/49219). [ABSTRACT FROM AUTHOR]

Although free-floating thrombus (FFT) poses a significant risk of stroke or transient ischemic attack (TIA), optimal management strategies are uncertain. To determine the state-of-the-art of medical interventions for FFT, we conducted a systematic review of the efficacy of various medical interventions and factors influencing FFT resolution and recurrence. A comprehensive search of Embase, PubMed, and ScienceDirect identified 61 studies encompassing 179 patients with FFT-related stroke or TIA treated with anticoagulants, antiplatelets, or their combinations. Primary outcomes assessed were stroke recurrence and thrombus resolution. Statistical analyses (Fisher's exact test, chi-square test, Mann–Whitney test, and Kruskal–Wallis test) utilized significance set at p < 0.05. Over a median follow-up of 7 months, thrombus resolution occurred in 65% of patients, while 11.2% experienced recurrence, primarily as TIAs. Cardioembolism was significantly less common in resolved cases (p = 0.025). Combination therapy (antiplatelets, anticoagulants, and statins) significantly enhanced clot resolution (OR 11.4; 95% CI 1.436–91.91; p = 0.021) compared to monotherapies. Ulcerated plaque was a significant predictor of recurrence (OR 8.2; 95% CI 1.02–66.07; p = 0.048). These findings underscore the superiority of combination therapy in FFT management and highlight the need for targeted interventions in patients with ulcerated plaques to mitigate recurrence risk. [ABSTRACT FROM AUTHOR]

In the presence of fixed threshold effects, the least squares (LS) estimator of the threshold parameter poses challenges for statistical inference due to its nonstandard limiting distribution, which also presents challenges for bootstrap methods. To address this issue, we propose a novel estimator: a two-step smoothed gradient least squares (SGLS) estimator. Our proposed method achieves a normal limiting distribution for the threshold parameter with minimal efficiency loss compared to the LS estimator. Furthermore, our modified bootstrap method significantly enhances computational efficiency, leading to improved bootstrap confidence intervals (CIs) for the threshold parameter compared to asymptotic CIs. Our method is validated through a small Monte Carlo study and demonstrated with an empirical application. [ABSTRACT FROM AUTHOR]

In the actor-partner interdependence model (APIM), various dyadic patterns between an actor and partner can be examined. One widely used approach is the parameter k method, which tests whether the ratio of the partner effect to the actor effect (p/a) is significantly different from pattern values such as −1 (contrast), 0 (actor-only or partner-only), and 1 (couple). Although using a phantom variable was a useful method for estimating the k ratio, it is no longer necessary due to the availability of statistical packages that allow for a direct estimation of the k ratio without the inclusion of the phantom variable. Moreover, it is possible to examine the patterns by testing new variables defined in different forms from the k or using the χ2 difference test. To date, no previous studies have evaluated and compared the various approaches for detecting the dyadic patterns in APIM. This study aims to assess and compare the performance of four different methods for detecting dyadic patterns: (1) phantom variable approach, (2) direct estimation of the parameter k, (3) new-variable approach, and (4) χ2 difference test. The first two methods frequently included multiple pattern values in there confidence interval. Furthermore, the phantom variable approach was prone to convergence issues. The other two alternatives performed better in detecting the dyadic patterns without convergence problems. Given the findings of the study, we suggest a novel procedure for examining dyadic patterns in APIM. [ABSTRACT FROM AUTHOR]

Drones are a promising technology performing various functions, ranging from aerial photography to emergency response, requiring swift fault diagnosis methods to sustain operational continuity and minimise downtime. This optimises resources, reduces maintenance costs, and boosts mission success rates. Among these methods, traditional approaches such as visual inspection or manual testing have long been utilised. However, in recent years, data representation methods, such as deep learning systems, have achieved significant success. These methods learn patterns and relationships, enhancing fault diagnosis, but also face challenges with data complexity, uncertainties, and modelling complexities. This paper tackles these specific challenges by introducing an efficient representation learning method denoted Multiverse Augmented Recurrent Expansion (MVA-REX), allowing for an iterative understanding of both learning representations and model behaviours and gaining a better understanding of data dependencies. Additionally, this approach involves Uncertainty Bayesian Optimisation (UBO) under Extreme Learning Machine (ELM), a lighter neural network training tool, to tackle both uncertainties in data and reduce modelling complexities. Three main realistic datasets recorded based on acoustic emissions are involved in tackling propeller and motor failures in drones under realistic conditions. The UBO-MVA Extreme REX (UBO-MVA-EREX) is evaluated under many, error metrics, confusion matrix metrics, computational cost metrics, and uncertainty quantification based on both confidence and prediction interval features. Application compared to the well-known long-short term memory (LSTM), under Bayesian optimisation of the approximation error, demonstrates performances, certainty, and cost efficiency of the proposed scheme. More specifically, the accuracy obtained by UBO-MVA-EREX, ~0.9960, exceeds the accuracy of LSTM, ~0.9158, by ~8.75%. Besides, the search time for UBO-MVA-EREX is ~0.0912 s, which is ~98.15% faster than LSTM, ~4.9287 s, making it highly applicable for such challenging tasks of fault diagnosis-based acoustic emission signals of drones. [ABSTRACT FROM AUTHOR]

The size of the effect of the difference in two groups with respect to a variable of interest may be estimated by the classical Cohen's d. A recently proposed generalized estimator allows conditioning on further independent variables within the framework of a linear regression model. In this note, it is demonstrated how unbiased estimation of the effect size parameter together with a corresponding standard error may be obtained based on the non-central t distribution. The portrayed estimator may be considered as a natural generalization of the unbiased Hedges' g. In addition, confidence interval estimation for the unknown parameter is demonstrated by applying the so-called inversion confidence interval principle. The regarded properties collapse to already known ones in case of absence of any additional independent variables. The stated remarks are illustrated with a publicly available data set. [ABSTRACT FROM AUTHOR]

The bootstrap method relies on resampling from the empirical distribution to provide inferences about the population with a distribution F. The empirical distribution serves as an approximation to the population. It is possible, however, to resample from another approximating distribution of F to conduct simulation-based inferences. In this paper, we utilize representative points to form an alternative approximating distribution of F for resampling. The representative points in terms of minimum mean squared error from F have been widely applied to numerical integration, simulation, and the problems of grouping, quantization, and classification. The method of resampling via representative points can be used to estimate the sampling distribution of a statistic of interest. A basic theory for the proposed method is established. We prove the convergence of higher-order moments of the new approximating distribution of F, and establish the consistency of sampling distribution approximation in the cases of the sample mean and sample variance under the Kolmogorov metric and Mallows–Wasserstein metric. Based on some numerical studies, it has been shown that the proposed resampling method improves the nonparametric bootstrap in terms of confidence intervals for mean and variance. [ABSTRACT FROM AUTHOR]

In clinical trials studying paired parts of a subject with binary outcomes, it is expected to collect measurements bilaterally. However, there are cases where subjects contribute measurements for only one part. By utilizing combined data, it is possible to gain additional information compared to using bilateral or unilateral data alone. With the combined data, this article investigates homogeneity tests of risk differences with the presence of stratification effects and proposes interval estimations of a common risk difference if stratification does not introduce underlying dissimilarities. Under Dallal's model (Biometrics 44:253–257, 1988), we propose three test statistics and evaluate their performances regarding type I error controls and powers. Confidence intervals of a common risk difference with satisfactory coverage probabilities and interval length are constructed. Our simulation results show that the score test is the most robust and the profile likelihood confidence interval outperforms other methods proposed. Data from a study of acute otitis media is used to illustrate our proposed procedures. [ABSTRACT FROM AUTHOR]

Powdery mildew (PM), caused by Blumeria graminis f. sp. tritici, poses a significant threat to wheat production, necessitating the development of genetically resistant varieties for long-term control. Therefore, exploring genetic architecture of PM in wheat to uncover important genomic regions is an important area of wheat research. In recent years, the utilization of meta-QTL (MQTL) analysis has gained prominence as an essential tool for unraveling the complex genetic architecture underlying complex quantitative traits. The aim of this research was to conduct a QTL meta-analysis to pinpoint the specific genomic regions in wheat responsible for governing PM resistance. This study integrated 222 QTLs from 33 linkage-based studies using a consensus map with 54,672 markers. The analysis revealed 39 MQTLs, refined to 9 high-confidence MQTLs (hcMQTLs) with confidence intervals of 0.49 to 12.94 cM. The MQTLs had an average physical interval of 41.00 Mb, ranging from 0.000048 Mb to 380.71 Mb per MQTL. Importantly, 18 MQTLs co-localized with known resistance genes like Pm2, Pm3, Pm8, Pm21, Pm38, and Pm41. The study identified 256 gene models within hcMQTLs, providing potential targets for marker-assisted breeding and genomic prediction programs to enhance PM resistance. These MQTLs would serve as a foundation for fine mapping, gene isolation, and functional genomics studies, facilitating a deeper understanding of molecular mechanisms. The identification of candidate genes opens up exciting possibilities for the development of PM-resistant wheat varieties after validation. [ABSTRACT FROM AUTHOR]

ABSTRACT In practice, we often encounter binary classification problems where both main classes consist of multiple subclasses. For example, in an ovarian cancer study where biomarkers were evaluated for their accuracy of distinguishing noncancer cases from cancer cases, the noncancer class consists of healthy subjects and benign cases, while the cancer class consists of subjects at both early and late stages. This article aims to provide a large number of optimal cut‐point selection methods for such setting. Furthermore, we also study confidence interval estimation of the optimal cut‐points. Simulation studies are carried out to explore the performance of the proposed cut‐point selection methods as well as confidence interval estimation methods. A real ovarian cancer data set is analyzed using the proposed methods. [ABSTRACT FROM AUTHOR]

Researchers are often interested in comparing predictors, a practice commonly done via informal comparisons of standardized regression slopes. However, formal interval-based approaches offer advantages over informal comparison. Specifically, this article examines a delta-method-based confidence interval for the difference between two standardized regression coefficients, building upon previous work on confidence intervals for single coefficients. Using Monte Carlo simulation studies, the proposed approach is evaluated at finite sample sizes with respect to coverage rate, interval width, Type I error rate, and statistical power under a variety of conditions, and is shown to outperform an alternative approach that uses the standard covariance matrix found in regression textbooks. Additional simulations evaluate current software implementations, small sample performance, and multiple comparison procedures for simultaneously testing multiple differences of interest. Guidance on sample size planning for narrow confidence intervals, an R function to conduct the proposed method, and two empirical demonstrations are provided. The goal is to offer researchers a different tool in their toolbox for when comparisons among standardized coefficients are desired, as a supplement to, rather than a replacement for, other potentially useful analyses. [ABSTRACT FROM AUTHOR]

The problems of constructing confidence intervals (CIs) for the mean of a gamma distribution containing zero values are considered. Three different methods for constructing such CIs based on Parametric Bootstrap (PB) method, fiducial inference and the method of variance of estimates recovery (MOVER) are developed. The performances of the proposed CIs are evaluated by Monte Carlo simulation and compared with a published method, asymptotic normal (AN) method. The simulation studies indicate that the proposed methods perform better than the existing method (AN) according to coverage probabilities (CPs), tail error rates, robustness and time comparison. All the methods are illustrated using a dataset for HIV risk behavior in adolescent girls and a dataset for the immunologic response to combination therapy for HIV children. Recommendations are made at the end of the articles. [ABSTRACT FROM AUTHOR]

This paper deals with statistical inference for lifetime data in presence of imperfect maintenance. For the maintenance model, the Sheu and Griffith model is considered. The lifetime distribution belongs to exponential distribution class. The maximum likelihood estimation procedure of the model parameters is discussed, and confidence intervals are provided using the asymptotic likelihood theory and bootstrap approach. Based on conjugate and discrete priors, Bayesian estimators of the model parameters are developed under symmetric and asymmetric loss functions. The proposed methodologies are applied to simulated data and sensitivity analysis to different parameters and data characteristics is carried out. The effect of model misspecification is also assessed within this class of distributions through a Monte Carlo simulation study. Finally, two datasets are analyzed for demonstrative aims. [ABSTRACT FROM AUTHOR]

The process capability index (PCI), C pk , one of the widely used tools for assessing the capability of a manufacturing process, expresses the deviation of the process mean from the midpoint of the specification limits. The C pk is known to perform well under the general assumption that the experimental data are normally distributed without contamination. Under this assumption, the sample mean and sample standard deviation are used for the estimation of the PCI. However, the sample mean and sample standard deviation are quite sensitive to data contamination and this will result in underperformance of C pk . Therefore, in this article, we propose alternatives to the conventional method by replacing the sample mean and sample standard deviation with robust location and scale estimators. We also propose a method for constructing a robust PCI C pk confidence interval which lends itself to robust statistical hypothesis testing. The robust hypothesis testing methods based on this confidence interval are shown to be quite efficient when the data are normally distributed yet also outperform the conventional method when data contamination exists. [ABSTRACT FROM AUTHOR]

Estimating a common parameter is the most essential and quite fascinating task across various probability distributions. This article addresses the challenge of estimating this parameter through the application of Maximum Likelihood Estimation (MLE). Numeric determination of common parameters is conducted for several distributions, including the Lomax distribution, Gamma distribution, Rayleigh distribution, and Weibull distribution. In cases where distributions lack a closed-form solution, estimation of MLEs is achieved using the Newton-Raphson technique. Furthermore, asymptotic confidence intervals are computed utilizing the Fisher information matrix tailored to each distribution. The performance evaluation of these estimators centers on the assessment of bias and mean squared error. To enable a numerical comparison of these estimators, the Monte Carlo simulation method is employed. Finally, these techniques are applied to real-time rainfall data to assess parameter estimates for each distribution. [ABSTRACT FROM AUTHOR]