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Motivated by the papers of Mladenović and Piterbarg (2006), Krajka (2011), and Pereira and Tan (2017), we study the limit properties for the maxima from non stationary random fields subject to missing observations and obtain the weakly convergence and almost sure convergence results for these maxima. Some examples such as Gaussian random fields, chi-random fields, and Gaussian order statistics fields are given to illustrate the obtained results. [ABSTRACT FROM AUTHOR]

This paper considers parallel and series systems with heterogeneous components having dependent exponential lifetimes. The underlying dependence is assumed to be Archimedean and the component lifetimes are supposed to be connected according to an Archimedean copula. Sufficient conditions are found to dominate a parallel system with heterogenous exponential components, with respect to the dispersive order, by another parallel system with homogenous exponential components where the dependence structure between lifetimes of components is the same. We also compare two series systems (and two parallel systems) with general one-parameter dependent components and with respect to the usual stochastic ordering. Examples are given to illustrate the theoretical findings. [ABSTRACT FROM AUTHOR]

Being inspired by the biological eye, event camera is a novel asynchronous technology that poses a paradigm shift in acquisition of visual information. This paradigm enables event cameras to capture pixel-size fast motions much more naturally compared to classical cameras.In this paper, we present a new asynchronous event-driven algorithm for detection of high-frequency pixel-size periodic signals using an event camera. Development of such new algorithms to efficiently process the asynchronous information of event cameras is essential to utilize its special properties and potential, and being a main challenge in the research community.It turns out that this algorithm, which was developed in order to satisfy the new paradigm, is related to an untreated theoretical problem in probability: Let 0 ≤ τ1 ≤ τ2 ≤⋯ ≤ τm ≤ 1 originated from an unknown distribution. Let also 휖,δ ∈ ℝ, and d ∈ ℕ. What can be said about the probability Φ(m,d) of having more than d adjacent τi-s pairs that the distance between them is δ, up to an error 휖? This problem, which reminds the area of order statistic, shows how the new visualization paradigm is also an opportunity to develop new areas and problems in mathematics. [ABSTRACT FROM AUTHOR]

This paper presents the exponentiated alpha-power log-logistic (EAPLL) distribution, which extends the log-logistic distribution. The EAPLL distribution emphasizes its suitability for survival data modeling by providing analytical simplicity and accommodating both monotone and non-monotone failure rates. We derive some of its mathematical properties and test eight estimation methods using an extensive simulation study. To determine the best estimation approach, we rank mean estimates, mean square errors, and average absolute biases on a partial and overall ranking. Furthermore, we use the EAPLL distribution to examine three real-life survival data sets, demonstrating its superior performance over competing log-logistic distributions. This study adds vital insights to survival analysis methodology and provides a solid framework for modeling various survival data scenarios. [ABSTRACT FROM AUTHOR]

This paper presents several nonparametric estimators for the Sharma–Taneja–Mittal entropy measure of a continuous random variable with known support, utilizing spacing, a local linear model, and a kernel function. The properties of these estimators are discussed. Their performance was also examined through real data analysis and Monte Carlo simulations. In the Monte Carlo experiments, the proposed Sharma–Taneja–Mittal entropy estimators were employed to create a test of goodness-of-fit under the standard uniform distribution. The suggested test statistics demonstrate strong performance, as evidenced by a comparison of their power with that of other tests for uniformity. Finally, we examine a classification issue in the recognition of patterns to underscore the significance of these measures. [ABSTRACT FROM AUTHOR]

We propose a new threshold selection method for nonparametric estimation of the extremal index of stochastic processes. The discrepancy method was proposed as a data-driven smoothing tool for estimation of a probability density function. Now it is modified to select a threshold parameter of an extremal index estimator. A modification of the discrepancy statistic based on the Cramér–von Mises–Smirnov statistic $ \omega ^2 $ ω 2 is calculated by k largest order statistics instead of an entire sample. Its asymptotic distribution as $ k\to \infty $ k → ∞ is proved to coincide with the $ \omega ^2 $ ω 2 -distribution. Its quantiles are used as discrepancy values. The convergence rate of an extremal index estimate coupled with the discrepancy method is derived. The discrepancy method is used as an automatic threshold selection for the intervals and K-gaps estimators. It may be applied to other estimators of the extremal index. The performance of our method is evaluated by simulated and real data examples. [ABSTRACT FROM AUTHOR]

Abstract–The Weibull distribution is the most applied model in reliability field for lifetime analysis. The Weibull location parameter, characterizing the minimum possible life, plays a significant role in engineering applications. In this paper, we consider the interval estimation on the location parameter when the product's lifetime follows the three-parameter Weibull distribution with a known shape parameter. A novel approach based on the relationship between the minimum order statistics, the location parameter, and the sample size is developed to construct confidence intervals for the Weibull location parameter. Thereafter, we compare it with other two interval estimation approaches by the performances of the coverage probability and the average length via simulations and a real application. The results show that the proposed method outperforms the pivot quantity (PQ) method and the bias-corrected and accelerated (Bca) bootstrap method in small and medium samples in terms of coverage probability. [ABSTRACT FROM AUTHOR]

We establish a novel family of Kumaraswamy-X probability distributions in the present investigation. We discussed the KumaraswamyExponential univariate probability distribution. The new distribution with three parameters possesses density function with unimodal and reverse J-shape and hazard rate function of bathtub shaped. We study various statistical properties for it and derive the expressions for its density function, distribution function, survival and hazard rate function, Probability weighted Moments, lth moment, moment generating function, quantile function and Shannon entropy. For the derived distribution order statistics is also discussed. The parameters are estimated using the maximum likelihood estimation approach, and the performance of the estimators was evaluated using a Monte Carlo simulation. Through extensive Monte Carlo simulations and comparative analyses, we assess the performance of the Kumaraswamy-X distribution against other common probability distributions used in engineering contexts. When we apply it to real datasets, it offers a more suitable fit than other existing distributions. We explore the characteristics and potential applications of the Kumaraswamy-X distribution in the context of engineering problems through a comprehensive simulation-based investigation. [ABSTRACT FROM AUTHOR]

We adopt extreme value theory to estimate the upper limit of the next record‐breaking magnitudes of induced seismic events. The methodology is based on order statistics and does not rely on knowledge of the state of the subsurface reservoir or injection strategy. The estimation depends on the history of record‐breaking events produced by the anthropogenic activities. We apply the methodology to three different types of industrial operations: natural gas production, saltwater disposal and hydraulic fracturing. We show that the upper limit estimate provides a reliable and realistic upper bound for magnitudes of the record‐breaking events in investigated datasets including 15 publicly available datasets. The predicted magnitudes do not overestimate the observed magnitudes by more than 1.0 magnitude unit and underestimation is rare, probably resulting from insufficient sampling of the statistical distribution of the induced seismicity. The richest dataset, sourced from downhole and surface monitoring of the Preston New Road hydraulic fracturing, provides reliable estimates of the magnitudes over three orders of magnitudes with only slight underprediction of the largest observed event. While the detection of weaker events improves the performance of the method, we show that it can be applied even with a few observed record‐breaking events to provide reliable estimates of magnitudes. However, care must be taken to ensure that event catalogues are estimated consistently across a range of magnitudes. [ABSTRACT FROM AUTHOR]

As one of data-driven approaches to computational mechanics in elasticity, this paper presents a method finding a bound for structural response, taking uncertainty in a material data set into account. For construction of an uncertainty set, we adopt the segmented least squares so that a data set that is not fitted well by the linear regression model can be dealt with. Since the obtained uncertainty set is nonconvex, the optimization problem solved for the uncertainty analysis is nonconvex. We recast this optimization problem as a mixed-integer programming problem to find a global optimal solution. This global optimality, together with a fundamental property of the order statistics, guarantees that the obtained bound for the structural response is conservative, in the sense that, at least a specified confidence level, probability that the structural response is in this bound is no smaller than a specified target value. We present numerical examples for three different types of skeletal structures. [ABSTRACT FROM AUTHOR]

AbstractIn the context of actuarial science, the second largest claim amount is crucial to insurance analysis since they provide useful information for determining annual premium. In this article, we provide sufficient conditions of the second largest claim amounts arising from two sets of dependent and heterogeneous individual risk models according to various stochastic orders. It is first shown that the reversed hazard order between the occurrence probabilities vectors implies the reversed hazard order of the second largest claim amounts under certain conditions. Second, sufficient conditions are established for the usual stochastic ordering of the second largest claim amounts arising from heterogeneous dependent individual risk models under copula dependence. Finally, several examples illustrating the theoretical results are presented as well. [ABSTRACT FROM AUTHOR]

We consider the Bayesian estimation of the parameters of a finite mixture model from independent order statistics arising from imperfect ranked set sampling designs. As a cost‐effective method, ranked set sampling enables us to incorporate easily attainable characteristics, as ranking information, into data collection and Bayesian estimation. To handle the special structure of the ranked set samples, we develop a Bayesian estimation approach exploiting the Expectation‐Maximization (EM) algorithm in estimating the ranking parameters and Metropolis within Gibbs Sampling to estimate the parameters of the underlying mixture model. Our findings show that the proposed RSS‐based Bayesian estimation method outperforms the commonly used Bayesian counterpart using simple random sampling. The developed method is finally applied to estimate the bone disorder status of women aged 50 and older. [ABSTRACT FROM AUTHOR]

AbstractGeneralized weighted cumulative residual entropies and generalized weighted cumulative entropies are represented by means of weighted sums of moments of upper and lower order statistics, respectively. A variety of examples is shown by specifying the weight function. [ABSTRACT FROM AUTHOR]

Abstract.In industrial, environmental, and ecological investigations, ranked set sampling is a sample method that enables the experimenter to use the whole range of population values. The ranked set sampling process can be modified in two extremely helpful ways: maximum ranked set sampling with unequal samples and minimum ranked set sampling with unequal samples. They permit an increase in set size without too many ranking errors being introduced. In this article, we are defining general weighted extropy (GWJ) of minimum and maximum ranked set samples when samples are of unequal size (minRSSU and maxRSSU, respectively). Stochastic comparison and monotone properties have been studied under different situations. Additionally, we compare the extropy of these two sampling data with that of ranked set sampling data and simple random sampling data. Bounds of GWJ of minRSSU and maxRSSU have been obtained. Finally, we investigate the weighted discrimination information between simple random sampling, ranked set sampling, and minimum and maximum ranked set sampling with unequal sample sizes. Some results for equality of GWJ of minRSSU and maxRSSU under symmetric assumption are also obtained. [ABSTRACT FROM AUTHOR]

The largest magnitude earthquake in a sequence is often used as a proxy for hazard estimates, as consequences are often predominately from this single event (in small seismic zones). In this article, the concept of order statistics is adapted to infer the maximum magnitude (MMAX) of an earthquake catalogue. A suite tools developed here can discern MMAX influences through hypothesis testing, quantify MMAX through maximum likelihood estimation (MLE) or select the best MMAX prediction amongst several models. The efficacy of these tools is benchmarked against synthetic and real-data tests, demonstrating their utility. Ultimately, 13 cases of induced seismicity spanning wastewater disposal, hydraulic fracturing and enhanced geothermal systems are tested for volume-based MMAX. I find that there is no evidence of volume-based processes influencing any of these cases. On the contrary, all these cases are adequately explained by an unbounded magnitude distribution. This is significant because it suggests that induced earthquake hazards should also be treated as unbounded. On the other hand, if bounded cases exist, then the tools developed here will be able to discern them, potentially changing how an operator mitigates these hazards. Overall, this suite of tools will be important for better-understanding earthquakes and managing their risks. This article is part of the theme issue 'Induced seismicity in coupled subsurface systems'. [ABSTRACT FROM AUTHOR]

High placebo responses in clinical trial could reduce the treatment effect leading to the failure of a promising drug. Several strategies have been developed to minimize high placebo responses, including the sequential parallel comparison design (SPCD). For a study with binary outcome, the existing statistical methods to test the drug effectiveness always rely on the asymptotic limiting distribution. When a study's sample size is small to medium, the asymptotic approaches do not have satisfactory performance with regard to type I error rate and statistical power. For that reason, we propose utilizing exact conditional approach to calculate sample size based on the existing test statistics to order the sample space. The proposed method controls the type I error rate under the unconditional framework. We compare the proposed exact sample sizes using different test statistics and the sample size for a randomized parallel study. We would recommend using exact sample sizes for the SPCD with small- to medium sample sizes and the SPCD with extreme response rates. [ABSTRACT FROM AUTHOR]

Let a stick be broken at random at n – 1 points to form n pieces. We consider three problems on forming k-gons with k out of these n pieces, 3≤ k ≤ n, and show how a statistical approach, through a linear transformation of variables, yields simple solutions that also allow fast computation. [ABSTRACT FROM AUTHOR]

Bandwidth selection is key for kernel quantile estimators (KQEs), which estimate quantiles by averaging all of the order statistics with appropriate kernel-weighting functions. This paper provides a new data-driven bandwidth selection method for KQEs, named the exact bootstrap-based bandwidth selection (EBS) rule. By relying on the exact analytic expressions for the bootstrap mean and variance of KQEs, the error due to bootstrap resampling is eliminated, and thus the optimal bandwidth can be obtained by minimizing the mean squared error (MSE) estimate. The effectiveness of this EBS rule is confirmed by numerical experiments. First, the bandwidth selection performance of the EBS method is compared to that of a benchmark approach. Simulation studies show that the EBS method performs well, especially in selecting bandwidths for extreme quantiles and when applied to small sample sizes with skewed distributions and relatively large variances. Second, KQEs with a bandwidth determined by our EBS rule is compared with five other state-of-the-art quantile estimators over six typical distributions. The results further validate the efficiency of the EBS method. Third, the results of simulations of controlling actual type-I error rates that occur when two independent groups are compared through quantiles further demonstrate the precision of our EBS-based KQEs. [ABSTRACT FROM AUTHOR]

Statistical moments of the turbulent circulation are complex geometry-dependent functionals of closed oriented contours and present a hard challenge for theoretical understanding. Conveniently defined circulation moment ratios, however, are empirically known to have appreciable geometric dependency only at lower moment orders and for contours that are sized near the bottom of the inertial range, in the situation where they span minimal surfaces of equivalent areas. Resorting to ideas addressed in the framework of the vortex gas model of circulation statistics, which integrates structural and multifractal aspects of the turbulent velocity field, we are able to reproduce, with reasonable accuracy, the observed contour shape dependency of circulation moment ratios, up to high order statistics. A key phenomenological point in our discussion is the assumption that the energy dissipation field, closely related to the local density of thin vortex tubes, is sharply bounded from above at finite Reynolds numbers. [ABSTRACT FROM AUTHOR]

In this research, we studied the concomitants of generalized order statistics from the bivariate generalized Weibull distribution. We derived probability density functions and moments of concomitants of generalized order statistics from the bivariate generalized Weibull distribution. Moreover, utilizing the ranked set sample obtained from this distribution, we computed the best linear unbiased (BLU) estimator of the parameter connected with the study variable (variable of primary interest). Also, a real data application was presented. [ABSTRACT FROM AUTHOR]

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In this article, we improve the behavior of nonparametric Shewhart-type control charts, which employ order statistics and multiple runs-type rules. The proposed class of monitoring schemes includes some existing control charts. In addition, new distribution-free monitoring schemes that pertain to the class, are set up and examined extensively. Explicit expressions for determining the variability and the mean of the run length distribution for the enhanced control charts are additionally delivered. As an example, a real-life managerial application is considered, where the proposed framework is implemented in order to enhance the provided services of a company under a supply chain management environment. Based on numerical comparisons, we draw the conclusion that the new charts outperform their competitors in identifying potential changes in the fundamental distribution in almost all cases considered. [ABSTRACT FROM AUTHOR]

Quantile regression predictions are considered for generalized order statistics which extend results previously established for record values and order statistics. In order to derive the results, some (univariate and bivariate) distortion representations of generalized order statistics are established. In particular, prediction of the sth generalized order statistic $ X_{(s)}^* $ X(s)∗ based on F given a single (generalized) order statistic $ X_{(r)}^* $ X(r)∗ with r<s will be addressed. The presentation includes results for both known and unknown baseline distributions. In the latter case, we consider exponential distributions with unknown mean as well as the proportional hazards model. Using unimodality properties of the marginal density functions (pdf) of generalized order statistics, we find a simple representation of the maximum likelihood prediction of $ X_{(s)}^* $ X(s)∗ given $ X_{(r)}^* $ X(r)∗. [ABSTRACT FROM AUTHOR]

This study compares two different series systems under various scenarios for which the components are assumed to be heterogeneous and follow Gompertz-G distributions. In the first scheme, the components of the systems are supposed to be independently distributed. In the second, we compared two series systems in the case that the independent components also experience random shocks. In the last scenario, we considered a case where the components of the systems have dependent structure sharing Archimedean copula. However, in all scenarios, the comparisons are performed based on the concepts of usual stochastic, the hazard rate, and the likelihood ratio orders through the majorization of the Gompertz-G parameters. [ABSTRACT FROM AUTHOR]

Nashaat [25] introduced the powered inverse Rayleigh (PIR) distribution. It provides a better fit other than (inverse Rayleigh, Rayleigh, and Weibull) distributions. The moments of order statistics and recurrence relations for the single and double moments have been established. The computation of the means and variances are enumerated. These computations can be truly interesting and applied in numerous domains of study. Moreover, cumulative entropy (C.E.) and actuarial measures (A.M.) are also calculated to address the uncertainty in portfolio optimization. The usages of C. E. and A.M. are widespread in many real-word applications specifically in physical sciences and insurance science. [ABSTRACT FROM AUTHOR]

In this article, we discuss sufficient conditions for the hazard rate order on smallest order statistics for variables with Archimedean survival copula and having modified proportional hazard rates (modified scale) model. We also establish the reversed hazard rate order on largest order statistics from variables with Archimedean copula and having modified proportional reversed hazard rates model. The results established here extend the recent results of Li and Li (2019). [ABSTRACT FROM AUTHOR]

This article introduces an innovative sampling scheme, the median sampling (MS), utilizing individual observations over time to efficiently estimate the mean of a process characterized by a symmetric (non-uniform) probability distribution. The mean estimator based on MS is not only unbiased but also boasts enhanced precision compared to its simple random sampling-based counterpart. Moreover, a new EWMA chart based on the mean estimator within the MS scheme is proposed. The performance of the EWMA charts, derived from both simple random sampling (SRS) and MS schemes, is evaluated using the metrics of steady-state average run-length and average number of items-to-signal. The findings underscore the superiority of the EWMA-MS chart over the EWMA-SRS chart. Additionally, as the magnitude of ranking errors escalates, the behavior of the EWMA-MS chart converges toward that of the EWMA-SRS chart. The practical implementation of the newly introduced EWMA chart is demonstrated through an illustrative example. [ABSTRACT FROM AUTHOR]

Mobile communications systems are affected by what is known as fading, which is a well-known problem largely studied for decades. The direct consequence of fading is the complete loss of signal (or a large decrease of the received power). Rayleigh fading is a reasonable model for wireless channels although, Nakagami-m distribution seems better suited to fitting experimental data. In this paper we obtain the Nakagami-m distribution as a composite (mixture) of the Rayleigh distribution, a result which as far as we know it has not been shown in the literature. This representation of the Nakagami-m distribution facilitates computations of the average BER (Bit Error Rate) for DPSK (Differential Phase Shift Keying) and MSK (Minimum-Shift Keying) modulations for this distribution and higher moments of them, which is of great applicability to modeling wireless fading channels. Furthermore, a simple, not depending on any special function, apart of the Gamma function, bivariate version of the Nakagami-m distribution is also proposed as a special case of the multivariate version which is also presented. The proposed composite distribution is simulated through the standard procedure of summation of phasors, and results for the new closed-form measures for the MSK modulation are also shown. From that it is clear that the alternative formulation of the Nakagami-m distribution allows for easier modeling of fading fading-shadowing wireless channels through the new explicit second order statistics metrics. is well suited for modelling fading-shadowing wireless channels. [ABSTRACT FROM AUTHOR]

The study introduces a new generalised family of distributions for cancer data modelling using a generalisation of the gamma function and a Topp-Leone-G distribution called the Gamma-Odd Topp-Leone-G (GOTL-G). Cancer data is normally characterised by complex heterogeneous properties like skewness, kurtosis, and presence of extreme values which makes it difficult to model using classical distributions. We derived multiple statistical properties including the linear representation, Re«yi entropy, quantile functions, distribution of order statistics, and maximum likelihood estimates which normally guarantees a positive effect on the generalisability of cancer data. Interestingly, we observed that these derived statistical properties make it possible for the generalisation of different models which are useful in the analysis, control, insurance, and survival of cancer patients. Our results show that this new family of distributions can be applied to a variety of data sets such as bladder and breast cancer data which exhibited high level of skewness and kurtosis as well as symmetric attributes. Therefore, we can conclude that the GOTL-G family of distributions can be extremely useful in capturing distinct complex heterogeneous properties normally exhibited by cancer patients. We recommend that this new family of distributions can be useful in modelling complex real-life applications including cancer data. [ABSTRACT FROM AUTHOR]

We propose a new family of distributions called the Zografos-Balakrishnan type-I heavy-tailed-G (ZBTIHT-G) distributions. A special model of the proposed family, namely Zografos-Balakrishnan type-I heavy-tailed-Weibull (ZBTIHT-W) model is thoroughly studied. Statistical properties of the new family of distributions including, among others, the hazard rate function, quantile function, moments, distribution of order statistics and Rényi entropy are presented. The maximum likelihood method of estimation is used for estimating the model parameters and Monte Carlo simulation is conducted to examine the performance of the estimators of the model parameters. The flexibility and importance of the new family of distributions are demonstrated by means of applications to real data sets. [ABSTRACT FROM AUTHOR]

In this study, we focused on investigating the properties of residual Tsallis entropy for order statistics. The reliability of engineering systems is highly influenced by order statistics, for example, when modeling the lifetime of a series system and the lifetime of a parallel system. The residual Tsallis entropy of the ith order statistic from a continuous distribution function and its deviation from the residual Tsallis entropy of the ith order statistics from a uniform distribution were investigated. In the mathematical framework, a method was provided to represent the residual Tsallis entropy of the ith order statistic in the continuous case with respect to the case where the distribution was uniform. This approach can provide insight into the behavior and properties of the residual Tsallis entropy for order statistics. We also investigated the monotonicity of the new uncertainty measure under different conditions. An investigation of these properties leads to a deeper understanding of the relationship between the position of the order statistics and the resulting Tsallis entropy. Finally, we presented the computational results and proposed estimators for estimating the residual Tsallis entropy of an exponential distribution. For this purpose, we derived a maximum likelihood estimator. [ABSTRACT FROM AUTHOR]

Under the influence of strong noise, period fault features of rolling bearing are not obvious, which increases the difficulty of accurately extracting period fault features. An autonomous weak period fault extraction method under strong noise named Ramanujan-gram is proposed in this paper. The greatest advantage of Ramanujan-gram is that it uses the Ramanujan feature extraction technique to reconstruct the components in each frequency band, which can overcome the weakness of the weak noise robustness of the filter methods used by the traditional kurtogram methods and improve the accuracy of period fault feature extraction. Meanwhile, the adaptive frequency band segmentation method based on the order statistical filter is used for adaptive frequency band segmentation, which overcomes the defect that the binary tree structure of fixed frequency band segmentation may destroy the optimal demodulated frequency band. Considering that kurtosis index is difficult to accurately evaluate period fault information in components, Ramanujan-gram adopts adaptive square envelope spectrum weighted kurtosis index to improve the evaluation accuracy of period fault information. The test signals of rolling bearing verify that Ramanujan-gram has strong noise robustness and is an effective method for weak period fault extraction under strong noise. [ABSTRACT FROM AUTHOR]

This paper is concerned with some recurrence relations for single and product moments of doubly truncated power linear hazard rate distribution via generalized order statistics. Some deductions and related results are also considered. The characterization result is provided at the end [ABSTRACT FROM AUTHOR]

A new family of distributions called the Marshall-Olkin-Topp-Leone-Gompertz-G (MO-TL-Gom-G) distribution is developed and studied in detail. Some mathematical and statistical properties of the new family of distributions are explored. Statistical properties of the new family of distributions considered are the quantile function, moments and generating function, probability weighted moments, distribution of the order statistics and Renyi entropy. The maximum ´ likelihood technique is used for estimating the model parameters and Monte Carlo simulation is conducted to examine the performance of the model. Finally, we give examples of real-life data applications to show the usefulness of the above mentioned Topp-Leone-Gompertz generalization. [ABSTRACT FROM AUTHOR]

This article introduces the generalized Kumaraswamy power Lindley (GKPL) distribution, a novel probabilistic model derived by combining the generalized Kumaraswamy (GK-G) family with the power Lindley (PL) distribution. The GKPL distribution encompasses a wide range of distributions, including Kumaraswamy power Lindley, Kumaraswamy Lindley, generalized power Lindley, generalized Lindley, power Lindley, and the well-known Lindley, as special cases. Fundamental properties are derived, such as the hazard rate function, survival function, quantile function, reverse hazard function, moments, mean residual life function, entropy, and order statistics. To determine the parameters of the GKPL distribution, four estimation methods, including maximum likelihood, least squares, Cramer-von Mises, and AndersonDarling methods, are used to estimate the parameters of the GKPL distribution. The effectiveness of the estimation techniques is assessed by employing Monte Carlo simulations. The adaptability and validity of the proposed GKPL distribution are compared with alternative models, including the Kumaraswamy power Lindley (KPL), Extended Kumaraswamy power Lindley (EKPL), type II generalized Topp Leone-power Lindley (TIIGTLPL), exponentiated generalized power Lindley (EGPL), generalized Kumaraswamy Weibull (GKW), generalized Kumaraswamy log-logistic (GKLLo), and generalized Kumaraswamy generalized power Gompertz (GKGPGo) distributions, through analyses of three real datasets. [ABSTRACT FROM AUTHOR]

In this article, we introduced the truncated versions (lower, upper and double) of xgamma distribution (Sen et al. 2016). In particular, different structural and distributional properties such as moments, popular entropy measures, order statistics and survival characteristics of the upper truncated xgamma distribution are discussed in detail. We briefly describe different estimation methods, namely the maximum likelihood, ordinary least squares, weighted least square and L-Moments. Monte Carlo simulation experiments are performed for comparing the performances of the proposed methods of estimation for both small and large samples under the lower, upper and double versions. Two applications are provided, the first one comparing estimation methods and the other for illustrating the applicability of the new model. [ABSTRACT FROM AUTHOR]

Abstract This paper presents the exponentiated alpha-power log-logistic (EAPLL) distribution, which extends the log-logistic distribution. The EAPLL distribution emphasizes its suitability for survival data modeling by providing analytical simplicity and accommodating both monotone and non-monotone failure rates. We derive some of its mathematical properties and test eight estimation methods using an extensive simulation study. To determine the best estimation approach, we rank mean estimates, mean square errors, and average absolute biases on a partial and overall ranking. Furthermore, we use the EAPLL distribution to examine three real-life survival data sets, demonstrating its superior performance over competing log-logistic distributions. This study adds vital insights to survival analysis methodology and provides a solid framework for modeling various survival data scenarios.

In this article, we improve the behavior of nonparametric Shewhart-type control charts, which employ order statistics and multiple runs-type rules. The proposed class of monitoring schemes includes some existing control charts. In addition, new distribution-free monitoring schemes that pertain to the class, are set up and examined extensively. Explicit expressions for determining the variability and the mean of the run length distribution for the enhanced control charts are additionally delivered. As an example, a real-life managerial application is considered, where the proposed framework is implemented in order to enhance the provided services of a company under a supply chain management environment. Based on numerical comparisons, we draw the conclusion that the new charts outperform their competitors in identifying potential changes in the fundamental distribution in almost all cases considered.

In this study, we focused on investigating the properties of residual Tsallis entropy for order statistics. The reliability of engineering systems is highly influenced by order statistics, for example, when modeling the lifetime of a series system and the lifetime of a parallel system. The residual Tsallis entropy of the ith order statistic from a continuous distribution function and its deviation from the residual Tsallis entropy of the ith order statistics from a uniform distribution were investigated. In the mathematical framework, a method was provided to represent the residual Tsallis entropy of the ith order statistic in the continuous case with respect to the case where the distribution was uniform. This approach can provide insight into the behavior and properties of the residual Tsallis entropy for order statistics. We also investigated the monotonicity of the new uncertainty measure under different conditions. An investigation of these properties leads to a deeper understanding of the relationship between the position of the order statistics and the resulting Tsallis entropy. Finally, we presented the computational results and proposed estimators for estimating the residual Tsallis entropy of an exponential distribution. For this purpose, we derived a maximum likelihood estimator.

Abstract This paper proposes a new Topp-Leone Exponentiated Pareto (TLEtP) distribution. The new distribution family is derived by expanding the Topp Leone-G family of distributions with additional positive shape parameters. The corresponding density and distribution functions are derived and shown. Some of the derived mathematical properties of the distribution include quantile function, ordinary and incomplete moments generating function (mgf), hazard function, survival function, odd function, probability weighted moment, and distribution of order statistic. The parameters of the distribution are estimated using Maximum Likelihood method. The proposed distribution’s validity is demonstrated by fitting two sets of real data and comparing the results with two existing same-family distributions, the Topp-Leone Pareto type I(TLPI) and Pareto (P), with the Akaike Information Criteria (AIC) and Bayesian Information Criteria (BIC), respectively. The comparison of the proposed Topp-Leone Exponentiated Pareto (TLEtP) to the Topp-Leone Pareto type I(TLPI) and Pareto (P) distribution demonstrate that the TLEtP distribution offers a better fit for the data sets than the other two distributions.

In this paper, we present some results to make inference about the parameters of lower truncated proportional hazard rate models with the same baseline distributions based on three independent generalized order statistics samples. Then, especially by considering the results of the diagnostic tests for the non-diseased, early-diseased stage and fully diseased populations, we make inference about sensitivity to the early disease stage parameter. The maximum likelihood estimator, a generalized pivotal estimator and some Bayes estimators are obtained for different structures of prior distributions. The percentile bootstrap confidence interval, a generalized pivotal confidence interval and some Bayesian credible intervals are also presented. A Monte Carlo simulation study is used to evaluate the performances of the obtained point estimators and confidence/credible intervals and two competitors. We use two real datasets to illustrate the proposed methods. [ABSTRACT FROM AUTHOR]

AbstractThe two-parameter standard two-sided power family of distributions on (0, 1) is considered in this article. We propose bootstrap standard errors for the maximum likelihood estimators, as well as bootstrap confidence intervals for its parameters, once these important statistical measures of accuracy cannot be computed based on first-order asymptotic theory. We consider Monte Carlo simulation experiments to verify the performance of the bootstrap methods, and the numerical results are quite promising. Applications to real data are also considered to illustrate the proposed methodology in practice. [ABSTRACT FROM AUTHOR]

We show that the distribution of bulk spacings between pairs of adjacent eigenvalue real parts of a random matrix drawn from the complex elliptic Ginibre ensemble is asymptotically given by a generalization of the Gaudin-Mehta distribution, in the limit of weak non-Hermiticity. The same generalization is expressed in terms of an integro-differential Painlevé function and it is shown that the generalized Gaudin-Mehta distribution describes the crossover, with increasing degree of non-Hermiticity, from Gaudin-Mehta nearest-neighbor bulk statistics in the Gaussian Unitary Ensemble to Poisson gap statistics for eigenvalue real parts in the bulk of the Complex Ginibre Ensemble. [ABSTRACT FROM AUTHOR]

The class of log-symmetric distributions is a generalization of log-normal distribution and includes some well-known distributions such as log-normal, log-logistic, log-Laplace, log-Cauchy, log-power-exponential, log-student-t, log-slash, and Birnbaum-Saunders distributions. In this paper, several characterization results are obtained for log-symmetric distributions based on moments of some functions of the parent distribution and also on the basis of some properties of order statistics. Specifically, when X is identical in distribution with a decreasing continuous function $ h(X) $ h (X) , then a relationship is established between upper and lower order statistics which is then utilized to construct characterization results for log-symmetric distributions in terms of functions of order statistics. The established results can be used for constructing a goodness-of-fit test for log-symmetric distributions. [ABSTRACT FROM AUTHOR]

This study proposes a new approach to estimate the parameters of the two-parameter Weibull distribution in the case of complete (uncensored) or doubly Type II censored samples. The proposed estimators have closed forms and can be adapted to Type II right or Type II left censored samples. The new estimators are strongly consistent and the new shape estimator follows asymptotically a normal and the new scale estimator a lognormal distribution. Bias, mean square and efficiency performance of the new estimators are investigated through simulations and compared to some known estimation methods such as maximum likelihood estimation, method of moments, quantile estimation, maximum goodness of fit estimation, L-moments, U-statistics and bias-corrected maximum likelihood. According to the simulations, the newly proposed estimators seem to have good efficiency performance in comparison to the other methods, particularly in small samples. Furthermore, two real data sets are used to illustrate the new estimators. [ABSTRACT FROM AUTHOR]

In many industries, the reliability of a product is often determined by a quantile of a distribution of a product's characteristics meeting a specified requirement. A typical approach to address this is to assume a parametric model and compute a one‐sided confidence bound on the quantile. However, this can become difficult if the sample size is too small to reliably estimate such a parametric model. Linear interpolation between order statistics is a viable nonparametric alternative if the sample size is sufficiently large. In most cases, linear extrapolation from the extreme order statistics can be used, but can result in inconsistent coverage. In this work, we perform an empirical study to generate robust weights for linear extrapolation that greatly improves the accuracy of the coverage across a feasible range of distribution families with positive support. Our method is applied to two industrial datasets. [ABSTRACT FROM AUTHOR]

Moments of order statistics (OSs) characterize the Weibull–geometric and half-logistic families of distributions, of which the extended exponential–geometric (EEG) distribution is a particular case. The EEG distribution is used to create the log-extended exponential–geometric (LEEG) distribution, which is bounded in the unit interval (0, 1). In addition to the generalized Stirling numbers of the first kind, a few years ago, the polylogarithm function and the Lerch transcendent function were used to determine the moments of order statistics of the LEEG distributions. As an application based on the L-moments, we expand the features of the LEEG distribution in this work. In terms of the Gauss hypergeometric function, this work presents the precise equations and recurrence relations for the single moments of OSs from the LEEG distribution. Along with recurrence relations between the expectations of function of two OSs from the LEEG distribution, it also displays the truncated and conditional distribution of the OSs. Additionally, we use the L-moments to estimate the parameters of the LEEG distribution. We further fit the LEEG distribution on three practical data sets from medical and environmental sciences areas. It is seen that the estimated parameters through L-moments of the OSs give a superior fit. We finally determine the correspondence between the entropies and the OSs. [ABSTRACT FROM AUTHOR]