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In this paper, we present a statistical approach to evaluate the relationship between variables observed in a two-factors experiment. We consider a three-level model with covariance structure Σ ⊗ Ψ 1 ⊗ Ψ 2 , where Σ is an arbitrary positive definite covariance matrix, and Ψ 1 and Ψ 2 are both correlation matrices with a compound symmetric structure corresponding to two different factors. The Rao's score test is used to test the hypotheses that observations grouped by one or two factors are uncorrelated. We analyze a fermentation process to illustrate the results. Supplementary materials accompanying this paper appear online. [ABSTRACT FROM AUTHOR]

In this paper, the stress–strength reliability $ R_{s,k} $ R s , k of a multicomponent s-out-of-k system for exponentiated Gumbel distribution is considered. An s-out-of-k system means a system with total k components and the system can survive only when atleast s of the total components function properly. The ability of the system to overcome the experiencing stress with its strength is termed as its stress–strengh reliability. The maximum likelihood estimator and Bayes estimator for $ R_{s,k} $ R s , k are obtained. The Bayes estimators are obtained using Markov chain Monte Carlo(MCMC) method under both symmetric and asymmetric loss functions. The loss functions we considered are squared error loss function, LINEX loss function and entropy loss function. The asymptotic, bootstrap and highest posterior density(HPD) confidence intervals for $ R_{s,k} $ R s , k are also obtained. A simulation study is conducted for evaluating the efficiency of the estimators derived in this paper. Real data sets are also considered for illustration. [ABSTRACT FROM AUTHOR]

In this paper, we have considered the classical and Bayesian inference of the unknown parameters of the lifetime distribution based on the observations obtained from a simple step‐stress life‐testing (SSLT) experiment and when more than one cause of failures are observed. We have used the Tampered Random Variable (TRV) approach. The main advantage of the TRV approach is that it can be easily extended to a multiple step‐stress model as well as for different lifetime distributions. In this paper, it is assumed that the lifetime of the experimental units at each stress level follows Weibull distribution with the same shape parameter and different scale parameters. Further, we have introduced different tempering co‐efficient for different causes of failures. The maximum likelihood estimators and the associated asymptotic confidence intervals are obtained based on Type‐II censored observations. Further, we have considered the Bayesian inference of the unknown model parameters based on a fairly general class prior distributions. An extensive simulation study is performed to examine the performances of the proposed method, and the analysis of a real data set has been provided to show how the method can be used in practice. We have compared the TRV model with some of the other existing models, and the TRV model provides a better fit in terms of information theoretic criteria. We have also provided some optimality criteria, to determine the optimal stress change time and some sensitivity analyses have been performed. Most of the methods can be extended for other lifetime distributions also. [ABSTRACT FROM AUTHOR]

In this paper, we propose a method for the three-dimensional (3D) image visualization of objects under photon-starved conditions using multiple observations and statistical estimation. To visualize 3D objects under these conditions, photon counting integral imaging was used, which can extract photons from 3D objects using the Poisson random process. However, this process may not reconstruct 3D images under severely photon-starved conditions due to a lack of photons. Therefore, to solve this problem, in this paper, we propose N-observation photon-counting integral imaging with statistical estimation. Since photons are extracted randomly using the Poisson distribution, increasing the samples of photons can improve the accuracy of photon extraction. In addition, by using a statistical estimation method, such as maximum likelihood estimation, 3D images can be reconstructed. To prove our proposed method, we implemented the optical experiment and calculated its performance metrics, which included the peak signal-to-noise ratio (PSNR), structural similarity (SSIM), peak-to-correlation energy (PCE), and the peak sidelobe ratio (PSR). [ABSTRACT FROM AUTHOR]

The record values data have received the attention of researchers in statistics for over seven decades. Through these decades the records have played a significant and widely utilized role for statistical inference in parameter estimation, predicting future values, hypothesis tests, as well as stressstrength tests, and characterizing distributions. In this paper, the types of record values, some distributional properties, and statistical inferences of record values and their applications are reviewed. The purpose of this paper is to shed light on the role of record values in statistical inference. Therefore, we will examine this issue from two perspectives, the first perspective being estimation and the second perspective being prediction. These are through some of the most important lifetime distributions are Exponential, Weibull, Gumbel, Geometric, Pareto, Generalized exponential, Rayleigh, Lomax, and Nadarajah-Haghighi distributions. I hope that the findings of this paper will be useful for researchers in various fields and lead to further enhancement of research in record values theory and its applications. [ABSTRACT FROM AUTHOR]

This paper introduces a novel probability distribution known as the Ejaz distribution (ED), which is characterized by two parameters. The study offers a comprehensive analysis of this distribution, including an examination of key properties such as moments, moment-generating functions, order statistics, and reliability functions. Additionally, the paper explores the graphical representation of essential functions like the probability density function, cumulative distribution function, and hazard rate function, enhancing our visual understanding of their behavior. The distribution's parameters are estimated using the widely accepted method of maximum likelihood estimation. Through real-world examples, the paper highlights the practical applicability of the Ejaz distribution, demonstrating its performance and relevance in diverse scenarios. [ABSTRACT FROM AUTHOR]

In this paper, we formulate mean and dispersion submodels for the class of Bell-Touchard regression models, and so we introduce the Bell-Touchard regression model with varying precision for count response variables. This regression model is, in some aspects, similar to the double generalized linear model framework, allowing for parameter interpretation in terms of the response variable in its original scale. We also provide an iterative process to estimate the regression coefficients in the mean and dispersion submodels, and develop diagnostic measures for this class of regression models. The methods developed are applied in a real data set for illustrative purposes. • Univariate count data modeling. • Two-parameter Bell-Touchard family of distributions. • Regression model for count variables with varying precision. • Overdispersion. [ABSTRACT FROM AUTHOR]

Thermal spray coating is a critical process in many industries, involving the application of coatings to surfaces to enhance their functionality. This paper proposes a framework for modelling and predicting critical target variables in thermal spray coating processes, based on the application of statistical design of experiments (DoE) and the modelling of the data using generalized linear models (GLMs) with a particular emphasis on gamma regression. Experimental data obtained from thermal spray coating trials are used to validate the presented approach, demonstrating that it is able to accurately model and predict critical target variables. As such, the framework has significant potential for the optimization of thermal spray coating processes, and can contribute to the development of more efficient and effective coating technologies in various industries. [ABSTRACT FROM AUTHOR]

This paper introduces a new four-parameter additive model, named xgamma-Burr XII distribution, by considering two competing risks: the former has the xgamma distribution and the latter has the Burr XII distribution. A graphical description of the xgamma-Burr XII distribution is presented, including plots of the probability density function, hazard rate and reversed hazard rate functions. The xgamma-Burr XII density has different shapes such as decreasing, unimodal, approximately symmetric and decreasing-unimodal. The main statistical properties of the proposed model are studied. The unknown model parameters, reliability, hazard rate and reversed hazard rate functions are estimated via the maximum likelihood method. The asymptotic confidence intervals of the parameters, reliability function, hazard rate function and reversed hazard rate function are also obtained. A simulation study is carried out to evaluate the performance of the maximum likelihood estimates. In addition, three real data are applied to show the superiority of the xgamma-Burr XII distribution over some known distributions in real-life applications. [ABSTRACT FROM AUTHOR]

This paper explores the inference for a constant-stress accelerated life test under a ranked set sampling scenario. When the lifetime of products follows the Fréchet distribution, and the failure times are collected under a maximum ranked set sampling with unequal samples, classical and Bayesian approaches are proposed, respectively. Maximum likelihood estimators along with the existence and uniqueness of model parameters are established, and the corresponding asymptotic confidence intervals are constructed based on asymptotic theory. Under squared error loss, Bayesian estimation and highest posterior density confidence intervals are provided, and an associated Monte-Carlo sampling algorithm is proposed for complex posterior computation. Finally, extensive simulation studies are conducted to demonstrate the performance of different methods, and a real-data example is also presented for applications. [ABSTRACT FROM AUTHOR]

This paper sets up a small open new Keynesian economy model with constrained households and incomplete markets to address the driving forces of business cycles in Korea. It shows that there exists a substantial fraction of constrained households who cannot have access to financial market. Furthermore, the estimated model reveals that a TANK model is better than a RANK model in explaining business cycles in Korea. The effect of domestic productivity shock on Korean economy has dominated in the variations of output, while the contribution of the foreign productivity shock to the variations of output and inflation has increased after the Asian financial crisis. The monetary policy shock has dominated the variation of inflation at short and medium horizons. [ABSTRACT FROM AUTHOR]

The use of structural durability analysis technology can effectively improve the economic efficiency of aircraft structures while ensuring their reliability. This paper utilizes the structural durability analysis technique to study the initial fatigue quality (IFQ) of a typical fatigue structure of 7B04-T651 high-strength aluminum alloy under the action of flight load spectrum of a certain type of aircraft. Firstly, the maximum likelihood estimation method is applied to the parameter estimation problem of crack initiation time distribution based on three-parameter Weibull distribution. The Monte Carlo method is used to verify the correctness of this approach. Secondly, fatigue tests under three different stress levels are carried out on the flight load spectrum. The logarithmic sample moment approach is proposed to process the equivalent initial flaw size distribution to obtain its general model. In addition, the initial fatigue quality model describing the typical structure is established, which verifies that the equivalent initial flaw size (EIFS) is less than the allowable 0.125 mm. By analyzing the initial fatigue quality of the typical structure, the correctness and practicability of the generalization method is demonstrated, and the life estimation model of this typical structure is built under different stress zones, different specified crack sizes and different reliability levels. [ABSTRACT FROM AUTHOR]

Ranked set sampling (RSS) has been proved to be an efficient sampling design for parametric and nonparametric inference. This paper explores inference for a maximum RSS procedure with unequal samples (MRSSU) with multiple dependent failure causes. When the lifetimes of units are characterized by a proposed complementary competing risks model, classical likelihood and Bayesian approaches are discussed for parameters and reliability estimation. Maximum likelihood estimators of model parameters and associated existence and uniqueness are established, and approximate confidence intervals are constructed using asymptotic theory and delta methods. With respect to general flexible priors, Bayesian estimates of interested quantities are also performed and a Monte Carlo sampling algorithm is proposed for complex posterior computation. Additionally, when extra historical information between the competing risks parameters is available, likelihood and Bayesian estimation are also studied under an order restriction case. Different methods are compared based on extensive simulation studies, and another real data example is demonstrated for application propose. [ABSTRACT FROM AUTHOR]

Survival data analysis often uses the Cox proportional hazards (PH) model. This model is widely applied due to its straightforward interpretation of the hazard ratio under the assumption that the hazard rates for two subjects remain constant over time. However, in several randomized clinical trials with long-term survival data comparing two new treatments, it is frequently observed that Kaplan-Meier plots exhibit crossing survival curves. This violation of the PH assumption of the Cox PH model can not be applied to evaluate the treatment's effect on survival. This paper introduces a novel long-term survival model with non-PH that incorporates a frailty term into the hazard function. This model allows us to examine the effect of prognostic factors on survival and quantify the degree of unobservable heterogeneity. The model parameters are estimated using the maximum likelihood estimation procedure, and we evaluate the performance of the proposed models through simulation studies. Additionally, we demonstrate the applicability of our approach by fitting the models to a real skin cancer dataset. [ABSTRACT FROM AUTHOR]

Symmetrical as well as asymmetrical statistical models play a prominent role in describing and predicting the real-world phenomena of nature. Among other fields, these models are very useful for modeling data in the sector of civil engineering. Due to the applicability of the statistical models in civil engineering and other related sectors, this paper offers a statistical methodology to improve the distributional flexibility of traditional models. The suggested method/approach is called the extended-X family of distributions. The proposed method has the ability to generate symmetrical and asymmetrical probability distributions. Based on the extended-X family approach, an updated version of the Weibull model, namely, the extended Weibull model, is studied. The proposed model is very flexible and has the ability to capture the symmetrical and asymmetrical shapes of its density function. For the extended-X method, the estimation of parameters, a simulation study, and some mathematical properties are derived. Finally, the practical illustration/usefulness of the suggested model is shown by analyzing two data sets taken from the field of engineering. Both data sets represent the fracture toughness of alumina (Al2O3). [ABSTRACT FROM AUTHOR]

In this paper, we focus on Bayesian estimation of the parameters in the geometric process (GP) in which the first occurrence time of an event is assumed to have Weibull distribution. The Bayesian estimators are derived based on both symmetric (Squared Error) and asymmetric (General Entropy, LINEX) loss functions. Since the Bayesian estimators of unknown parameters cannot be obtained analytically, Lindley's approximation and the Markov Chain Monte Carlo (MCMC) methods are applied to compute the Bayesian estimates. Furthermore, by using the MCMC methods, credible intervals of the parameters are constructed. Maximum likelihood (ML) estimators are also derived for unknown parameters. The confidence intervals of the parameters are obtained based on an asymptotic distribution of ML estimators. Moreover, the performances of the proposed Bayesian estimators are compared with the corresponding ML, modified moment and modified maximum likelihood estimators through an extensive simulation study. Finally, analyses of two different real data sets are presented for illustrative purposes. [ABSTRACT FROM AUTHOR]

In this paper, we consider a transformation in a random variable which follows a bimodal Birnbaum-Saunders distribution. We propose the unit-bimodal Birnbaum-Saunders (UBBS) distribution and investigate some of its important properties, like cumulative distribution function, moments, survival function and risk function. We apply the UBBS distribution to censored data inflated at zero and one. We used the maximum likelihood approach for parameter estimation and to compare the models. Given the flexibility in UBBS distribution modes, our proposal performs best in beta regression models with zero and/or one excess. [ABSTRACT FROM AUTHOR]

A recent paper introduced the interpolating family (IF) of distributions, and they also derived various mathematical properties of the family. Some of the most important properties discussed were the integer order moments of the IF distributions. The moments were expressed as an integral (which were not evaluated) or as finite sums of the beta function. In this paper, more general expressions for moments of any integer order or any real order are derived. Apart from being more general, our expressions converge for a wider range of parameter values. The expressions for entropies are also derived, the maximum likelihood estimation is considered and the finite sample performance of maximum likelihood estimates is investigated. [ABSTRACT FROM AUTHOR]

This paper aims to introduce a novel family of probability distributions by the well-known method of the T–X family of distributions. The proposed family is called a "Novel Generalized Exponent Power X Family" of distributions. A three-parameters special sub-model of the proposed method is derived and named a "Novel Generalized Exponent Power Weibull" distribution (NGEP-Wei for short). For the proposed family, some statistical properties are derived including the hazard rate function, moments, moment generating function, order statistics, residual life, and reverse residual life. The well-known method of estimation, the maximum likelihood estimation method is used for estimating the model parameters. Besides, a comprehensive Monte Carlo simulation study is conducted to assess the efficacy of this estimation method. Finally, the model selection criterion such as Akaike information criterion (AINC), the correct information criterion (CINC), the Bayesian information criterion (BINC), the Hannan–Quinn information criterion (HQINC), the Cramer–von-Misses (CRMI), and the ANDA (Anderson–Darling) are used for comparison purpose. The comparison of the NGEP-Wei with other rival distributions is made by Two COVID-19 data sets. In terms of performance, we show that the proposed method outperforms the other competing methods included in this study. [ABSTRACT FROM AUTHOR]

In this paper, we have introduced the concept of a new multicomponent reliability function ρk(t).${\rho }_k( t ).$ Estimation procedures are developed for ρk(t)${\rho }_k( t )$ under progressive type II censoring scheme, which is subsequently used to develop the estimation procedures for the multicomponent stress‐strength reliability function ρs,k${\rho }_{s,\ k}$. Herein, we consider a system having k statistically independent and identically distributed strength components, Xi,i=1,2,…,k${X}_i,\ i = 1,2,\ldots,k$, say, which are exposed to a common random stress Y. Both strength and stress variables are independent and follow different scaled proportional hazard rate family of distributions with common scale parameter. The reliability functions ρk(t)${\rho }_k( t )$ and ρs,k${\rho }_{s,\ k}$ are estimated by using maximum likelihood and Bayesian methods of estimation. The performances of these estimators are studied on the basis of their mean squared errors through Monte Carlo simulation technique. Finally, the utility of the proposed estimators is examined and explained through two different real data sets. [ABSTRACT FROM AUTHOR]

In this paper, we consider one-parameter regularly varying discrete distribution generated by Levy probability (RDLP). Some useful plots of the models are illustrated. Mathematically, to propose the RDLP model as a discrete distribution in bioinformatics, some common statistical facts such as unimodality, skewness to the right, upward/downward convexity, regular variation at infinity, and asymptotically constant slowly varying component are established for the model. Based on the Monte Carlo method and limited-memory Broyden–Fletcher–Goldfarb–Shanno for bound-constrained optimization, simulation studies are done to estimate bias, mean square error, and maximum likelihood estimation for the unknown parameter of the model. Some asymptotic properties and asymptotic expansions are given for useful functions. Moreover, we shall attempt to examine the RDLP model with a real count data set to show its application, and also compare it with two rival models. [ABSTRACT FROM AUTHOR]

The noterate is a tool for predicting home mortgage rates, it is often skewed and has missing information. The noterate could be affected by incomplete or inaccurate data, thus leading to inaccurate predictions. Financial organizations including mortgage companies or banks need to consider the risk of uncertainty carefully and make a more accurate prediction based on some suitable models. To deal with this situation, in this paper we compared six computational statistical methods, including the ordinary least square model, maximum likelihood estimation, maximum a posterior, bootstrapping, Metropolis-Hastings, and Gibbs sampling method on a mortgage dataset. Based on the k fold cross-validation technique and four metrics including mean absolute error (MAE), mean squared error (MSE), root mean squared error (RMSE), and mean absolute percentage error (MAPE), the bootstrapping method outperforms other methods. In practice, this method is recommended for predicting noterate. [ABSTRACT FROM AUTHOR]

Ground-Based Synthetic Aperture Radar (GB-SAR), due to its high precision, high resolution, and real-time capabilities, is widely used in the detection of slope deformations. However, the weak scattering coefficient in low-coherence areas poses a great challenge to the observation point selection accuracy. This paper introduces a selection process for reliable observation points that integrates phase and spatial information. First, for various observation points with differentiated stability, we propose to utilize maximum likelihood estimation (MLE) methods to achieve stability assessment. Second, a phase correction approach is proposed to address unwrapped phase errors encountered at less stable points. Third, adaptive filtering for deformation information at observation points is achieved using estimated variance combined with wavelet filtering thresholds. Finally, in dealing with unknown deformation trends, we propose utilizing a clustering method to accurately identify these trends, thereby enhancing the precision in identifying reliable observation points (ROPs). The experimental results demonstrate that this method enhances the accuracy of observation point selection in low-coherence areas, providing a broader observational field for deformation detection. [ABSTRACT FROM AUTHOR]

AbstractThe main objective of this paper is to propose a new general family of distributions, namely compound truncated Poisson log-normal distribution of which log-normal distribution is a special case. The proposed model has three unknown parameters, and it can take variety of shapes. It can be used effectively in analyzing maximum precipitation data during a particular period of time obtained from different stations. It is assumed that the number of stations operate follows a zero-truncated Poisson random variables, and the daily precipitation follows a log-normal random variable. The maximum likelihood estimators can be obtained quite conveniently using Expectation-Maximization (EM) algorithm. Approximate maximum likelihood estimators are also derived. The associated confidence intervals can also be obtained from the observed Fisher information matrix. Simulation results have been performed to check the performance of the EM algorithm, and it is observed that the EM algorithm works quite well in this case. When we analyze the precipitation data set using the proposed model it is observed that the proposed model provides better fit than some of the existing models. [ABSTRACT FROM AUTHOR]

This paper considers the problem of making inference for a multicomponent stress–strength (MSS) model under Type-II censoring. It is assumed that stress–strength components of the multicomponent system follow unit generalized Rayleigh (UGR) distributions. Inferences are derived when the strength and stress have a common unknown UGR parameters. We derive maximum likelihood estimator of MSS reliability based on observed censored data. In sequel, interval estimator is evaluated using delta method and asymptotic normality property. Pivotal quantities based inference upon MSS reliability are derived as well. In addition, we further consider the case when all the parameters of stress–strength model are unknown and obtain various inferences for the reliability. Equivalence of model parameters is considered based on likelihood ratio test. Assessment of different methods is evaluated from Monte Carlo simulations and remarks are presented for further discussion. Three numerical examples including a petroleum reservoirs data are analyzed for illustration purposes. [ABSTRACT FROM AUTHOR]

This paper proposed a novel distribution parameterized by four parameters. This is achieved by compounding the potentials properties of the Type I half logistic topp-leone generalized distribution family with the properties of the inverse lomax distribution to form the novel Type I half logistic topp-leone inverse lomax distribution. The novel distribution is potentially capable of extending classical inverse lomax distribution. The potentiality of the shape of the probability density function of the novel distribution is worth recognizing since it produces right skewed, approximately normal, left skewed and a reverted J-shaped. Decreasing life failure shape is also observed. Distinctive features of the novel distribution such as moments, entropy, moment generating function, reliability and hazard function were derived. The estimation method explored in this study is maximum likelihood estimation. It is adopted to estimate the novel distribution unknown parameters. Real life data set was adopted to investigate the potentiality and applicability of the novel model. The type I half logistic topp-leone inverse lomax distribution outperform the recent models. [ABSTRACT FROM AUTHOR]

Tolerance intervals from quality attribute measurements are used to establish specification limits for drug products. Some attribute measurements may be below the reporting limits, that is, left‐censored data. When data has a long, right‐skew tail, a gamma distribution may be applicable. This paper compares maximum likelihood estimation (MLE) and Bayesian methods to estimate shape and scale parameters of censored gamma distributions and to calculate tolerance intervals under varying sample sizes and extents of censoring. The noninformative reference prior and the maximal data information prior (MDIP) are used to compare the impact of prior choice. Metrics used are bias and root mean square error for the parameter estimation and average length and confidence coefficient for the tolerance interval evaluation. It will be shown that Bayesian method using a reference prior overall performs better than MLE for the scenarios evaluated. When sample size is small, the Bayesian method using MDIP yields conservatively too wide tolerance intervals that are unsuitable basis for specification setting. The metrics for all methods worsened with increasing extent of censoring but improved with increasing sample size, as expected. This study demonstrates that although MLE is relatively simple and available in user‐friendly statistical software, it falls short in accurately and precisely producing tolerance limits that maintain the stated confidence depending on the scenario. The Bayesian method using noninformative prior, even though computationally intensive and requires considerable statistical programming, produces tolerance limits which are practically useful for specification setting. Real‐world examples are provided to illustrate the findings from the simulation study. [ABSTRACT FROM AUTHOR]

People living with HIV on antiretroviral therapy often have undetectable virus levels by standard assays, but "latent" HIV still persists in viral reservoirs. Eliminating these reservoirs is the goal of HIV cure research. The quantitative viral outgrowth assay (QVOA) is commonly used to estimate the reservoir size, that is, the infectious units per million (IUPM) of HIV-persistent resting CD4+ T cells. A new variation of the QVOA, the ultra deep sequencing assay of the outgrowth virus (UDSA), was recently developed that further quantifies the number of viral lineages within a subset of infected wells. Performing the UDSA on a subset of wells provides additional information that can improve IUPM estimation. This paper considers statistical inference about the IUPM from combined dilution assay (QVOA) and deep viral sequencing (UDSA) data, even when some deep sequencing data are missing. Methods are proposed to accommodate assays with wells sequenced at multiple dilution levels and with imperfect sensitivity and specificity, and a novel bias-corrected estimator is included for small samples. The proposed methods are evaluated in a simulation study, applied to data from the University of North Carolina HIV Cure Center, and implemented in the open-source R package SLDeepAssay. [ABSTRACT FROM AUTHOR]

Gompertz distribution is a significant and commonly used lifetime distribution, which plays an important role in reliability engineering. In this paper, we study the statistical inference of Gompertz distribution based on adaptive Type-II hybrid progressive censored schemes. From the perspective of frequentist, we derive the point estimations through the method of maximum likelihood estimation (MLE) and the existence of MLE is proved. Besides MLE, we propose the stochastic EM algorithm to reduce complexity and simplify computing. We also apply the method of Bootstraps (Bootstrap-p and Bootstrap-t) to construct confidence intervals. From Bayesian aspect, the Bayes estimates of the unknown parameters are evaluated by applying the MCMC method, the average length and coverage rate of credible intervals are also carried out. The Bayes inference is based on the squared error loss function and LINEX loss function. Furthermore, a numerical simulation is conducted to assess the performance of the proposed methods. Finally, a real-life example is considered to illustrate the application and development of the inference methods. In summary, the Bayesian method seems to perform the best among all approaches, while other approaches also present different advantages. [ABSTRACT FROM AUTHOR]

Progressive type-II (Prog-II) censoring schemes are gaining traction in estimating the parameters, and reliability characteristics of lifetime distributions. The focus of this paper is to enhance the accuracy and reliability of such estimations for the inverse power exponentiated Pareto (IPEP) distribution, a flexible extension of the exponentiated Pareto distribution suitable for modeling engineering and medical data. We aim to develop novel statistical inference methods applicable under Prog-II censoring, leading to a deeper understanding of failure time behavior, improved decision-making, and enhanced overall model reliability. Our investigation employs both classical and Bayesian approaches. The classical technique involves constructing maximum likelihood estimators of the model parameters and their bootstrap covariance intervals. Using the Gibbs process constructed by the Metropolis–Hasting sampler technique, the Markov chain Monte Carlo method provides Bayesian estimates of the unknown parameters. In addition, an actual data analysis is carried out to examine the estimation process's performance under this ideal scheme. [ABSTRACT FROM AUTHOR]

The paper describes a two parameter model and its relationship to the widely used Weibull model. Mathematical properties of the distribution like survival and hazard functions, moments, harmonic and geometric means, Shannon entropy and mean residual life are derived. Different methods of estimation are discussed and a simulation study is performed to verify the efficiency of estimation methods. Applications of our distribution in different scenarios observed in real life are illustrated. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the inference for the competing risks model when the failure times follow Chen distribution. With assumption of two causes of failures, which are partially observed, are considered as independent. The existence and uniqueness of maximum likelihood estimates for model parameters are obtained under generalized progressive hybrid censoring. Also, we discussed the classical and Bayesian inferences of the model parameters under the assumption of restricted and nonrestricted parameters. Performance of classical point and interval estimators are compared with Bayesian point and interval estimators by conducting extensive simulation study. In addition to that, for illustration purpose, a real life example is discussed. Finally, some concluding remarks, regarding the presented model, are made. [ABSTRACT FROM AUTHOR]

In order to explore the widespread applications of Odd Log-Logistic Generalized Gompertz （OLLGG） distribution in fields such as biology, sociology, computer science and marketing, this paper studies a multi-parameter regression model for OLLGG distribution under left-truncated and right-censored data, and estimates the parameters using maximum likelihood thinking. Through numerical simulation, the effectiveness of the estimation method is verified, and the Akaike information criterion is used to select the appropriate distribution form. Finally, the regression model proposed in this article is applied to the channing house dataset to demonstrate its good fitting performance. [ABSTRACT FROM AUTHOR]

In this paper, the Bayesian and non-Bayesian estimation of $$\psi = P(X \gt Y)$$ ψ = P (X > Y) based on the progressively first-failure censored data is considered. The $$X$$ X and $$Y$$ Y are strength and stress random variables and follow the Topp-Leone distributions, respectively. The maximum likelihood and Bayes estimators of $$\psi $$ ψ are derived. The Bayes estimators under generalized entropy loss function are computed using Lindley's approximation and Gibbs sampling methods. Different interval estimates like asymptotic, bootstrap confidence, Bayesian credible, and highest posterior density credible intervals of $$\psi $$ ψ are constructed. Furthermore, a Monte Carlo numerical study is conducted to check the performance of various estimators developed. Finally, an application of algorithm real data is considered for illustrative purposes. [ABSTRACT FROM AUTHOR]

Gompertz distribution is a significant and practical continuous lifetime distribution, which plays an important role in reliability engineering. A Gompertz distribution competing risks model is discussed and studied under general progressive censoring in this paper. When the lifetime model fails for different latent reasons, the maximum likelihood estimates are given for the unknown parameters. The approximate confidence intervals through Fisher information matrix and bootstrap confidence intervals are established, containing bootstrap-p and bootstrap-t techniques. In addition, the Bayes estimation of unknown parameters is investigated under the condition of squared error loss. Moreover, the Bayes credible interval is derived. Finally, a numerical simulation is conducted to evaluate the performances of the proposed methods and real-life data is analyzed by applying the proposed inference methods. [ABSTRACT FROM AUTHOR]

This paper proposes a new robust method for accurately and reliably estimating remote bus frequencies in a power system. Two different measurement sources for the remote bus frequency are considered, that is, the ideal Frequency Divider (FD) and the Synchronous Reference Frame Phase Locked Loops (SRF‐PLLs). Each measurement signal encounters different uncertainties and data quality issues. In this paper, both data sources are employed and fused together to better estimate the remote bus frequencies. To this end, the model structure of the power system is selected and an Unscented Kalman Filter (UKF) is utilized together with a fusion covariance intersection method to enhance the accuracy of the estimated bus frequency. Since the fusion estimation method fails in case of quality issues on both channels, a robust Generalized Maximum‐likelihood UKF (GM‐UKF) using a novel outlier detection criteria is developed. The impact of the resulting robust fusion filter on the estimation of the remote bus frequencies and on the performance of WAPSS, which makes use of the estimated frequencies as the feedback signal, is examined via simulations. The results demonstrate the excellent performance and reliability of the proposed method in dealing with noise filtering and outlier suppression while ensuring a high statistical efficiency. [ABSTRACT FROM AUTHOR]

In this paper, paired comparison models with stochastic background are investigated. We focus on the models that allow three options for choice and the parameters are estimated by maximum likelihood method. The existence and uniqueness of the estimator are key issues of the evaluation. In the case of two options, a necessary and sufficient condition is given by Ford in the Bradley–Terry model. We generalize this statement for the set of strictly log-concave distribution. Although in the case of three options the necessary and sufficient condition is not known, there are two different sufficient conditions that are formulated in the literature. In this paper, we generalize them; moreover, we compare these conditions. Their capacities to indicate the existence of the maximum were analyzed using a large number of computer simulations. These simulations support that the new condition indicates the existence of the maximum much more frequently than the previously known ones. [ABSTRACT FROM AUTHOR]

The competing risks model plays an important role in the statistical analysis of engineering, econometric, biological and other fields. A tested product may fail from different causes. Therefore, these failure causes as if competing with each other to bring about the failure of tested products (an experimental unit). Hence, in the statistical literature, this is known as the competing risk problem and it has been studied quite extensively by several researchers when the lifetime of the product is the latent failure time of the first failure cause among all the possible failure causes. In this paper, a competing risks model based on a generalized progressive hybrid type-I (GPH type-I) censoring is considered when the latent lifetime distributions of failure causes are inverse Weibull (IW) distributed and partially observed. We established various estimation methods including Maximum likelihood estimates (MLEs) and Bayes estimates (BEs). MLEs with the corresponding asymptotic confidence intervals are obtained. Bayes estimates of the parameters are obtained based on squared error loss (SEL) function under the assumption of independent gamma priors. Furthermore, we applied Markov Chain Monte Carlo (MCMC) techniques to compute BEs and to calculate the credible intervals. Finally, simulation studies and real data set are used for illustrative purpose. [ABSTRACT FROM AUTHOR]

In this paper we describe a methodology for parameter estimation of multivariate distributions defined as normal mean-variance mixture where the mixing random variable is rapidly decreasing tempered stable distributed. We address some numerical issues resulting from the use of the characteristic function for density approximation. We focus our attention on the practical implementation of numerical methods involving the use of these multivariate distributions in the field of finance and we empirical assess the proposed algorithm through an analysis on a five-dimensional series of stock index log-returns. [ABSTRACT FROM AUTHOR]

In this paper we study the joint determination of source and background flux for point sources as observed by digital array detectors. We explicitly compute the two-dimensional Cramér–Rao absolute lower bound (CRLB) as well as the performance bounds for high-dimensional implicit estimators from a generalized Taylor expansion. This later approach allows us to obtain computable prescriptions for the bias and variance of the joint estimators. We compare these prescriptions with empirical results from numerical simulations in the case of the weighted least squares estimator (introducing an improved version, denoted stochastic weighted least-squares) as well as with the maximum likelihood estimator, finding excellent agreement. We demonstrate that these estimators provide quasi-unbiased joint estimations of the flux and background, with a variance that approaches the CRLB very tightly and are, hence, optimal, unlike the case of sequential estimation used commonly in astronomical photometry which is sub-optimal. We compare our predictions with numerical simulations of realistic observations, as well as with observations of a bona fide non-variable stellar source observed with TESS, and compare it to the results from the sequential estimation of background and flux, confirming our theoretical expectations. Our practical estimators can be used as benchmarks for general photometric pipelines, or for applications that require maximum precision and accuracy in absolute photometry. [ABSTRACT FROM AUTHOR]

In this paper, we first develop exact likelihood inference for Laplace distribution based on a generalized Type-I hybrid censored sample (Type-I HCS). We derive explicit expressions for the maximum likelihood estimators (MLEs) of the location and scale parameters. We then derive the joint moment generating function (MGF) of the MLEs, and use it to obtain the exact distributions and moments of the MLEs. Using an analogous approach, we extend the results to a generalized Type-II hybrid censored sample (Type-II HCS) next. Finally, we present a numerical example to illustrate all the results established here. [ABSTRACT FROM AUTHOR]

In this paper, the unit Garima distribution is introduced. It is used for analysing proportional data. Some statistical properties of the proposed distribution are investigated, including survival and hazard functions, order statistics, quantile function, and stress-strength reliability measures. A new family of continuous distributions, called the unit Garima-generated family of distributions, is also provided. It used the unit Garima distribution as the main generator. Some sub-models of the unit Garima-generated family of distributions are provided, such as the unit Garima-beta, unit Garima-Weibull, and unit Garima-normal distributions. The method of maximum likelihood is used to estimate the model parameters. A Monte Carlo simulation is used to illustrate the performance of the percentile confidence interval construction for each parameter of the proposed distributions. Finally, the developed distributions are applied to eight real data sets. [ABSTRACT FROM AUTHOR]

This paper introduces a new cubic transmutation of the inverse Weibull distribution, known as a cubic transmuted inverse Weibull distribution. The model is thought to be useful for the analysis of complex life data, modeling failure times, accessing product reliability, and many other fields like economics, hydrology, biology, and engineering. Some statistical features of the proposed distribution are explored. These include moments, generating functions, quantile functions, reliability functions, and hazard rate functions. The distribution of order statistics for the proposed cubic transmuted inverse Weibull distribution is also studied. The maximum likelihood estimation approach is used to estimate the model parameters. The effectiveness of the estimation is investigated through extensive simulation study. The suitability of the proposed distribution has been studied by using five real-life datasets. It is found that the proposed distribution is the most suitable fit for the used data sets. [ABSTRACT FROM AUTHOR]

This paper proposes a new three-parameter inverse Weibull-type distribution via a similar way of constructing a skew normal distribution. The additional shape parameter increases the distribution's modelling capability as other three-parameter inverse Weibull-type distributions. The mathematical properties of this inverse extended Weibull distribution are studied and proven. In the empirical study of four insurance datasets from Australia, Denmark and the USA, we show that the proposed distribution performs very well compared with other three-parameter competitors. [ABSTRACT FROM AUTHOR]

In this paper, a new extension of the standard Rayleigh distribution called the Power Rayleigh distribution (PRD) is investigated for the accelerated life test (ALT) using the geometric process (GP) under Type-I censored data. Point estimates of the formulated model parameters are obtained via the likelihood estimation approach. In addition, interval estimates are obtained based on the asymptotic normality of the derived estimators. To evaluate the performance of the obtained estimates, a simulation study of 4, 5 and 6 levels of stress is conducted for ALT in different combinations of sample sizes and censored times. Simulation results indicated that point estimates are very close to their initial true values, have small relative errors, are robust and are efficient for estimating the model parameters. Similarly, the interval estimates have small lengths and their coverage probabilities are almost converging to their 95% nominated significance level. The estimation procedure is also improved by the approach of finding optimum values of the acceleration factor to have optimum values for the reliability function at the specified design stress level. This work confirms that PRD has the superiority to model the lifetimes in ALT using GP under any censoring scheme and can be effectively used in reliability and survival analysis. [ABSTRACT FROM AUTHOR]

A popular way to estimate the parameters of a hidden Markov model (HMM) is direct numerical maximization (DNM) of the (log-)likelihood function. The advantages of employing the TMB [Kristensen K, Nielsen A, Berg C, et al. TMB: automatic differentiation and Laplace approximation. J Stat Softw Articles. 2016;70(5):1–21] framework in R for this purpose were illustrated recently [Bacri T, Berentsen GD, Bulla J, et al. A gentle tutorial on accelerated parameter and confidence interval estimation for hidden Markov models using template model builder. Biom J. 2022 Oct;64(7):1260–1288]. In this paper, we present extensions of these results in two directions. First, we present a practical way to obtain uncertainty estimates in form of confidence intervals (CIs) for the so-called smoothing probabilities at moderate computational and programming effort via TMB. Our approach thus permits to avoid computer-intensive bootstrap methods. By means of several examples, we illustrate patterns present for the derived CIs. Secondly, we investigate the performance of popular optimizers available in R when estimating HMMs via DNM. Hereby, our focus lies on the potential benefits of employing TMB. Investigated criteria via a number of simulation studies are convergence speed, accuracy, and the impact of (poor) initial values. Our findings suggest that all optimizers considered benefit in terms of speed from using the gradient supplied by TMB. When supplying both gradient and Hessian from TMB, the number of iterations reduces, suggesting a more efficient convergence to the maximum of the log-likelihood. Last, we briefly point out potential advantages of a hybrid approach. [ABSTRACT FROM AUTHOR]

In this paper, we consider the estimation of a multicomponent stress–strength reliability when stress and strength variables follow unit Bur XII distribution. In estimation procedure, the maximum likelihood and Bayesian methods are used. The maximum likelihood estimator is obtained via iterative methods. The asymptotic confidence interval is constructed using asymptotic properties of the corresponding estimator. In addition, two bootstrap confidence intervals are constructed. Bayesian estimator is obtained using three different approximation methods: Lindley's approximation, Tierney–Kadane approximation and Markov Chain Monte Carlo method. The interval estimation based on Bayesian method is studied. The simulation study is conducted to investigate and compare the performance of the considered methods. Finally, an original data set, general dam occupancy rate of Istanbul, Turkey obtained from Istanbul Statistic Office, is analysed in the concept of multicomponent stress–strength reliability. [ABSTRACT FROM AUTHOR]

A multivariate folded normal distribution is a distribution of the absolute value of a Gaussian random vector. In this paper, we provide the marginal and conditional distributions of the multivariate folded normal distribution, and also prove that independence and non-correlation are equivalent for it. In addition, we provide a numerical approach using the R language to fit a multivariate folded normal distribution. The accuracy of the estimated mean and variance parameters is then examined. Finally, a real data application to body mass index data are presented. [ABSTRACT FROM AUTHOR]

Gradient-enhanced Kriging (GE-Kriging) is a well-established surrogate modeling technique for approximating expensive computational models. However, it tends to get impractical for high-dimensional problems due to the size of the inherent correlation matrix and the associated high-dimensional hyperparameter tuning problem. To address these issues, a new method, called sliced GE-Kriging (SGE-Kriging), is developed in this paper for reducing both the size of the correlation matrix and the number of hyperparameters. We first split the training sample set into multiple slices, and invoke Bayes' theorem to approximate the full likelihood function via a sliced likelihood function, in which multiple small correlation matrices are utilized to describe the correlation of the sample set rather than one large one. Then, we replace the original high-dimensional hyperparameter tuning problem with a low-dimensional counterpart by learning the relationship between the hyperparameters and the derivative-based global sensitivity indices. The performance of SGE-kriging is finally validated by means of numerical experiments with several benchmarks and a high-dimensional aerodynamic modeling problem. The results show that the SGE-Kriging model features an accuracy and robustness that is comparable to the standard one but comes at much less training costs. The benefits are most evident for high-dimensional problems with tens of variables. [ABSTRACT FROM AUTHOR]

In this paper we present the symbolic neutrosophic and plithogenic Marshall-Olkin type I class of distributions. We derive the formal form of the cumulative distribution function and probability density function of neutrosophic and plithogenic Marshall-Olkin Type I class of distributions. As a special case of the mentioned class of distributions we study the generalized uniform distribution in both neutrosophic and plithogenic forms, we derive its PDF and CDF then present an algorithm of random numbers generation according to it, then we estimate its parameters using maximum likelihood estimation and support the results with a simulation study to show the efficiency of the calculated parameters and study its asymptotic properties including unbiasedness and consistency. [ABSTRACT FROM AUTHOR]