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In this paper, we proposed a novel probability distribution model known as the unit compound Rayleigh distribution, which possesses the distinctive characteristic of defining the range within the bounded interval (0,1). Through an in-depth investigation of this distribution, we analyzed various statistical and structural characteristics including reliability function, risk function, quantile function, moment analysis, order statistics, and entropy measurement. To estimate the unknown parameters of our proposed distribution model, we employed maximum likelihood (ML) estimation and Bayesian estimation. Furthermore, we derived several entropy measures based on ML estimation under the unit compound Rayleigh distribution. To comprehensively evaluate the performance of these entropies, we employed the Monte Carlo simulation method to calculate the average entropy estimate, average entropy bias, corresponding mean square error, and mean relative estimate for assessing the performance of various entropies within the unit compound Rayleigh distribution model. Finally, in order to validate its potential for practical applications, two sets of real data were selected for empirical analysis where fitting and parameter estimation were conducted to demonstrate the advantages of utilizing the unit compound Rayleigh distribution in describing and predicting actual data. This study not only introduces a new probability theory and statistics framework by proposing a novel distribution model but also provides researchers and practitioners in related fields with a powerful analytical tool. [ABSTRACT FROM AUTHOR]

In this paper, we focus on studying the Mixed-Effects State-Space (MESS) models previously introduced by Liu et al. [Liu D, Lu T, Niu X-F, et al. Mixed-effects state-space models for analysis of longitudinal dynamic systems. Biometrics. 2011;67(2):476–485]. We propose an estimation method by combining the auxiliary particle learning and smoothing approach with the Expectation Maximization (EM) algorithm. First, we describe the technical details of the algorithm steps. Then, we evaluate their effectiveness and goodness of fit through a simulation study. Our method requires expressing the posterior distribution for the random effects using a sufficient statistic that can be updated recursively, thus enabling its application to various model formulations including non-Gaussian and nonlinear cases. Finally, we demonstrate the usefulness of our method and its capability to handle the missing data problem through an application to a real dataset. [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]

This paper proposes new algorithms of adaptive Gaussian filters for nonlinear state estimation with maximum one‐step randomly delayed measurements. The unknown random delay is modeled as a Bernoulli random variable with the latency probability known a priori. However, a contingent situation has been considered in this work when the measurement noise statistics remain partially unknown. Due to unavailability of the complete knowledge of measurement noise statistics, the unknown measurement noise covariance matrix is estimated along with states following: (i) variational Bayesian approach, (ii) maximum likelihood estimation. The adaptation algorithms are mathematically derived following both of the above approaches. Subsequently, a general framework for adaptive Gaussian filter is presented with which variants of adaptive nonlinear filters can be formulated using different rules of numerical approximation for Gaussian integrals. This paper presents a few of such filters, viz., adaptive cubature Kalman filter, adaptive cubature quadrature Kalman filter with their higher degree variants, adaptive unscented Kalman filter, and adaptive Gauss–Hermite filter, and demonstrates the comparative performance analysis with the help of a nontrivial Bearing only tracking problem in simulation. Additionally, the paper carries out relative performance comparison between maximum likelihood estimation and variational Bayesian approaches for adaptation using Monte Carlo simulation. The proposed algorithms are also validated with the help of an off‐line harmonics estimation problem with real data. [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]

In this paper, interval estimation of the two-parameter exponential distribution based on constant-stress accelerated life test data under Type-II censoring is studied. The life-stress models of the scale and location parameters are assumed to be log-linear. The maximum likelihood estimators of the model parameters are obtained. The exact and approximate confidence intervals for the parameters in the life-stress model of the scale parameter are developed. The generalized confidence intervals for the parameters in the life-stress model of the location parameter, and mean and reliability function at the designed stress level are derived. The performance of the proposed generalized confidence intervals is assessed by the Monte Carlo simulation. Finally, a real example is used to illustrate our methods. [ABSTRACT FROM AUTHOR]

Comparative life tests of a life product have received considerable attention in the past few years for measuring the relative merits of a product in competing duration. In this paper, we are adopting the problem of estimation and prediction of Rayleigh lifetime distributions under joint Type-I censoring scheme. The point and interval estimation is formulated with maximum likelihood and the Bayes methods for the unknown parameters. Also, Bayesian approach is applied in viewpoint both point and interval prediction. The results of estimation and prediction are discussed through analysis the set of real data and bulding Monte-Carlo simulation studies. Finally, we built a numerical discussion of the most important results and future recommendations. [ABSTRACT FROM AUTHOR]

Analysis of jointly censoring schemes has received considerable attention in the last few years. In this paper, maximum likelihood and Bayes methods of estimation are used to estimate the unknown parameters of two Gompertz populations under a joint progressive Type-II censoring scheme. Bayesian estimations of the unknown parameters are obtained based on squared error loss functions under the assumption of independent gamma priors. We propose to apply the Markov Chain Monte Carlo technique to carry out a Bayes estimation procedure. The approximate, bootstrap, and credible confidence intervals for the unknown parameters are also obtained. Also, reliability and hazard rate function of the two Gompertz populations under joint progressive Type-II censoring scheme is obtained and the corresponding approximate confidence intervals. Finally, all the theoretical results obtained are assessed and compared using two real-world data sets and Monte Carlo simulation studies. [ABSTRACT FROM AUTHOR]

The proportional hazard regression models are widely used statistical tools for analyzing survival data and estimating the effects of covariates on survival times. It is assumed that the effects of the covariates are constant across the time. In this paper, we propose a novel extension of the proportional hazard model by incorporating an exponentiated-Weibull distribution to model the baseline line hazard function. The proposed model offers more flexibility in capturing various shapes of failure rates and accommodates both monotonic and non-monotonic hazard shapes. The performance evaluation of the proposed model and comparison with other commonly used survival models including the generalized log–logistic, Weibull, Gompertz, and exponentiated exponential PH regression models are explored using simulation results. The results demonstrate the ability of the introduced model to capture the baseline hazard shapes and to estimate the effect of covariates on the hazard function accurately. Furthermore, two real survival medical data sets are analyzed to illustrate the practical importance of the proposed model to provide accurate predictions of survival outcomes for individual patients. Finally, the survival data analysis reveal that the model is a powerful tool for analyzing complex survival data. [ABSTRACT FROM AUTHOR]

In this paper, a new bounded distribution is introduced and some distributional properties of the new distribution are discussed. Moreover, the new distribution is implemented in the field of engineering to the Cpc process capability index. Three unknown parameters of the distribution are estimated with several estimators, and the performances of the estimators are evaluated with a Monte Carlo simulation. A new regression model is introduced based on this new distribution as an alternative to beta and Kumaraswamy models. Furthermore, it is considered one of the first studies where regression model parameters are estimated using least squares, weighted least squares, Cramér–von Mises, and maximum product spacing estimators other than the maximum likelihood. The efficiency of the estimators for the parameters of the regression model is further assessed through a simulation. Real datasets are analyzed to demonstrate the applicability of the new distribution and regression model. [ABSTRACT FROM AUTHOR]

In this paper, we consider three sampling methods that are ranked set sampling (RSS), generalized modified ranked set sampling (GMRSS) and extreme ranked set sampling (ERSS). RSS and ERSS are well-known sampling schemes. In GMRSS procedure, a single ranked unit is selected for full measurement. This paper improves estimators based on RSS, GMRSS and ERSS for association parameter of type-I Gumbel's bivariate exponential distribution (GBED-I) by using maximum likelihood (ML) estimation. To determine whether there is a statistically significant association between the components, we investigate likelihood ratio tests based on RSS, MRSS and ERSS. To examine the performances of suggested estimators and tests with respect to their counterparts of simple random sampling (SRS), we provide an extensive Monte Carlo simulation. According to the results, it appears that GMRSS provides a more efficient ML estimator than the other sampling methods when only the maximum ranked units are selected. Also, it is observed that the test statistic based on GMRSS has the highest power among the test statistics when the sample is obtained from the maximum ranked units. Considering that GMRSS can be obtained with less effort than other samples, these results become even more meaningful. [ABSTRACT FROM AUTHOR]

Recently, there has been a lot of interest in comparative life testing for items under jointly censored schemes for products from multiple production lines. The inverse Weibull distribution (IWD) is commonly used in life testing and reliability theory. In this paper, we address the problem of statistical inference from comparative inverse Weibull distributions under joint samples. An adaptive type-II hybrid progressive censoring scheme (HPCS) is used to save the balance between the ideal test time and the number of observed failures. Under the adaptive type-II HPCS, unknown parameters of the inverse Weibull populations are estimated using both maximum likelihood and Bayesian approaches. Asymptotic confidence intervals are established using the observed Fisher information matrix and bootstrap confidence intervals. We suggest using Markov chain Monte Carlo (MCMC) techniques to compute credible intervals under independent gamma priors. Using Monte Carlo simulations, all theoretical conclusions are tested and contrasted. For illustration purposes, an actual sample from comparative populations is analysed. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new cure rate frailty regression model based on a two-parameter weighted Lindley distribution. The weighted Lindley distribution has attractive properties such as flexibility on its probability density function, Laplace transform function on closed-form, among others. An advantage of proposed model is the possibility to jointly model the heterogeneity among patients by their frailties and the presence of a cured fraction of them. To make the model parameters identifiable, we consider a reparameterized version of the weighted Lindley distribution with unit mean as frailty distribution. The proposed model is very flexible in sense that has some traditional cure rate models as special cases. The statistical inference for the model's parameters is discussed in detail using the maximum likelihood estimation under random right-censoring. Further, we present a Monte Carlo simulation study to verify the maximum likelihood estimators' behavior assuming different sample sizes and censoring proportions. Finally, the new model describes the lifetime of 22,148 patients with stomach cancer, obtained from the Fundação Oncocentro de São Paulo, Brazil. [ABSTRACT FROM AUTHOR]

In the multicomponent stress–strength reliability literary work, though assumption of identical stress and strengths components may not be universally true but have been commonly considered. Herein, we consider a multicomponent stress–strength model having k identical strength components, say X i , i = 1 , 2 ,... , k , which are exposed to a common random stress Y, so that Y , X i , i = 1 , 2 ,... , k are independent. Two different generalized cases of estimation are considered; namely, (i) when the strength components follow the proportional hazard rate model and stress component follows the proportional reversed hazard rate model and (ii) when the strength components follow the proportional reversed hazard rate model and stress component follow the proportional hazard rate model. In each case, maximum likelihood and Bayesian approach using Markov Chain Monte Carlo method has been utilized to estimate the reliability of the system. Asymptotic confidence intervals are also constructed for the reliability functions in both the cases. Monte Carlo simulation study is exercised to compare the performance of the aforementioned estimators. A real data example is also explored to examine the utility of the paper. [ABSTRACT FROM AUTHOR]

This paper presents a novel analytical method based on improved Gaussian mixture model (GMM) to solve the probabilistic load flow problem. The proposed method accounts for the uncertainty introduced due to increasing percentages of renewable generation. First, the joint probability density function of several wind farms outputs is derived by using the improved GMM with the estimated parameters obtained by genetic algorithm (GA) in this paper, which could improve the accuracy of the probabilistic model. Next, the analytical expressions between the output power of wind farms and line power of power system are deduced by linearizing load flow equations. And, the joint probability density function and joint cumulative distribution function of line power are obtained from linear load equation and joint probability density function of wind output power. Finally, the proposed method, Monte Carlo simulation (MCS) and traditional GMM based methods are all tested on a modified IEEE 39-bus system and a modified IEEE 118-bus system with multiple wind farms, which demonstrates the feasibility of the proposed method. [ABSTRACT FROM AUTHOR]

This paper deals with measurement extraction, from an optical sensor's Focal Plane Array (FPA), of a streaking target. We use a model that assumes pixels are separated by dead zones and model the streaking target's point spread function (PSF) as a Gaussian PSF that moves during the optical sensor's integration time. We make an assumption that the target has a constant velocity over the sampling interval and parametrize its motion with a starting and ending position. The noise model for a single pixel has variance proportional to its area, consistent with a Poisson model of the number of nontarget originated photons. We develop a maximum likelihood (ML) method of estimating the target motion parameter vector based on the set of pixel measurements from the optical sensor. This paper then derives the Cramer–Rao lower bound (CRLB) on the estimation error of the target motion parameter. We then present a matched filter (MF) based definition of the signal-to-noise ratio (SNR) to use as a basis for comparison of Monte Carlo simulation based location estimates to the calculated CRLB. It is shown that the ML estimator for the starting and ending positions of a streak in the FPA is efficient for MFSNR $\geq 12$  dB. We then provide a test statistic for target detection and propose approximate distributions to set the detection threshold for specific detection ($P_D$) and false alarm probabilities ($P_{\text{FA}}$), which are then verified via simulations. This paper's major contributions are the proposal of an ML/MF method for measurement extraction of streaking targets, confirmation that this method achieves the best accuracy possible for realistic FPA sensors, i.e., it attains the CRLB, the introduction of a statistically supported definition of SNR for these measurements, and an evaluation of the target measurement detection performance. Furthermore, this paper shows that, given our MFSNR definition, the streak length and direction of motion in the FPA have a negligible effect on performance compared to the SNR where we show that with a 4-dB change, the detection performance increases dramatically. [ABSTRACT FROM AUTHOR]

In this paper, we want to promote the influence of randomized arithmetic on the leaks during a code execution. When somebody wants to extract some specific information from these leaks, one can observe different emanations of the device like power consumption. These leaks mostly come from the variations of the Hamming distances of the successive states of the system. This phenomenon is particularly critical for cryptographic devices. Our work evaluates the resilience of randomized moduli in Residue Number System (RNS) against Correlation Power Analysis (CPA), Differential Power Analysis (DPA). Our analysis is illustrated through the evaluation of scalar multiplication on an elliptic curve using the Montgomery Powering Ladder (MPL) algorithm which protects from Simple Power Analysis (SPA). We also propose an evaluation based on the Maximum Likelihood Estimator (MLE), which crosses the information of the whole state vector, instead of analysing only the current state like with CPA or DPA. Furthermore, MLE gives better performance and smooths the results allowing a better evaluation of the behaviour of the leakage. Our experimental evaluation suggests that the number of observations, needed to perform exploitable information leakage, is proportional to the number of possible RNS bases. [ABSTRACT FROM AUTHOR]

The linear exponential distribution is a generalization of the exponential and Rayleigh distributions. This distribution is one of the best models to fit data with increasing failure rate (IFR). But it does not provide a reasonable fit for modeling data with decreasing failure rate (DFR) and bathtub shaped failure rate (BTFR). To overcome this drawback, we propose a new record-based transmuted generalized linear exponential (RTGLE) distribution by using the technique of Balakrishnan and He. The family of RTGLE distributions is more flexible to fit the data sets with IFR, DFR, and BTFR, and also generalizes several well-known models as well as some new record-based transmuted models. This paper aims to study the statistical properties of RTGLE distribution, like, the shape of the probability density function and hazard function, quantile function and its applications, moments and its generating function, order and record statistics, Rényi entropy. The maximum likelihood estimators, least squares and weighted least squares estimators, Anderson-Darling estimators, Cramér-von Mises estimators of the unknown parameters are constructed and their biases and mean squared errors are reported via Monte Carlo simulation study. Finally, the real data sets illustrate the goodness of fit and applicability of the proposed distribution; hence, suitable recommendations are forwarded. [ABSTRACT FROM AUTHOR]

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

Design of efficient test plans to assessing product reliability rapidly, is a critical step to obtain product reliability accurately. In this paper, we are adopted the problem of statistical inference of two generalized inverted exponential populations in a competing duration. To save the balance between the optimal test time and the number of failures needing for statistical inference, joint adaptive type-II hybrid progressive censoring scheme is applied. The model parameters are estimated with classical methods (maximum likelihood and bootstrap) for point estimate and the corresponding confidence intervals. Also, Bayes estimators of model parameters are computed under importance sample technique with the corresponding Bayes credible intervals. A real data sets are analyzed for illustrating purposes. The results are compared and assessed through Monte Carlo simulation study. [ABSTRACT FROM AUTHOR]

This paper discusses inferential approaches for the problem of constant-stress accelerated life testing when the failure data are progressive type-I interval censored. Both frequentist and Bayesian estimations are carried out under the assumption that the log-normal location parameter is nonconstant and follows a log-linear life-stress model. The confidence intervals of unknown parameters are also constructed based on asymptotic theory and Bayesian techniques. An analysis of a real data set is combined with a Monte Carlo simulation to provide a thorough assessment of the proposed methods. [ABSTRACT FROM AUTHOR]

In this paper, estimations of the parameter and acceleration factor of the Burr–Hatke exponential distribution in partially accelerated life tests under progressively type II censoring are investigated. By using typical maximum likelihood methods and the Bayesian method, point estimations of the distribution parameter and the acceleration factor are obtained. Based on the asymptotic normality and Delta method, approximate confidence intervals are established using the Fisher information matrix. The confidence intervals of the percentile bootstrap method are also evaluated. Comprehensive simulation tests are conducted to evaluate the estimations effects. A real dataset is studied by constructing a Burr–Hatke exponential model and analyzing the practicality and utility of parameter estimation. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the newly generated Ristić–Balakrishnan–Topp–Leone–Gompertz-G family of distributions. Statistical and mathematical properties of this new family including moments, moment generating function, incomplete moments, conditional moments, probability weighted moments, distribution of the order statistics, stochastic ordering, and Rényi entropy are derived. The unknown parameters of the family are inferred using the maximum likelihood estimation technique. A Monte Carlo simulation study is performed to investigate the convergence of the maximum likelihood estimation. Three real-life data sets are used to demonstrate the flexibility and capacity of the new family of distributions. [ABSTRACT FROM AUTHOR]

Based on the well-known Poisson (P) distribution and the new generalized Lindley distribution (NGLD) developed by using gamma ( α , θ) and gamma ( α − 1 , θ) distributions, a new compound two-parameter Poisson generalized Lindley (TPPGL) distribution is proposed in this paper and thereon systematically explores the mathematical properties. Closed form expressions are assembled for such properties including the probability generating function, moments, skewness, kurtosis, etc. The likelihood-based method is used for estimating the parameters followed by a broad Monte Carlo simulation study. To further motivate the proposed model, a count regression model and a first order integer valued autoregressive process are constructed based on the novel TPPGL distribution. The empirical importance of the proposed models is confirmed through application to four real datasets. [ABSTRACT FROM AUTHOR]

Adaptive Type-II progressive hybrid censoring scheme has quite popular in a life-testing problem and reliability analysis due to it ensures more efficiency of inference procedures and saves total testing time. In this paper, an adaptive Type-II progressive hybrid censored sampling with random removals is considered, where the removals of the survival units at each stage from a life-test follows a binomial distribution during the execution of the experiment. The classical and Bayesian approaches are used to obtain the point and interval estimates of the unknown parameters of Weibull distribution, when the lifetimes are collected under the proposed censoring scheme. Different Bayesian estimates relative to various balanced type loss functions are obtained. Due to the complexity of the proposed estimators, some numerical techniques are implemented to obtain them. Using Markov chain Monte Carlo methods, the different Bayes estimates and associate credible intervals are developed. Extensive simulation study is performed to examine the efficiency of the proposed estimators. To show the applicability of the proposed methods in a real-life scenario, two real data sets coming from clinical and engineering areas are analysed. [ABSTRACT FROM AUTHOR]

In this paper, it is introduced a new parametric distribution to be used in multivariate lifetime data analysis as an alternative for the use of some existing multivariate parametric models as the popular multivariate normal distribution which is the most widely used model assumed in the analysis of continuous multivariate data. Although the normal multivariate distribution has univariate marginal normal probability distributions and simple interpretations for all their parameters, it may not be well fitted by many data sets, especially in survival data applications, usually considering logarithm transformed data. In many cases the use of parametric multivariate discrete models could be more appropriate for the data analysis. In this paper, it is introduced a generalization of the bivariate Basu-Dhar geometric distribution to a trivariate case applied to count data. Some properties of this trivariate geometric distribution, including its marginal probability distributions, order statistics distributions, the probability generating function and some simulation studies are presented. It is also presented some discussion on an extension of the trivariate case for the multivariate case. Classical and Bayesian inferences are presented assuming censored or uncensored observations. To illustrate the proposed methodology, two applications with real lifetime data are considered as examples. [ABSTRACT FROM AUTHOR]

The use of statistical distributions to model life phenomena has received considerable attention in the literature. Recent studies have shown the potential of statistical distributions in modeling data in applied sciences, especially in environmental sciences. Among them, the Weibull distribution is one of the most well-known models that can be used very effectively for modeling data in the fields of pollution and gas emissions, to name a few. In this paper, we introduce a family of distributions, which we call the modified Alpha-Power Weibull-X family of distributions. Based on the proposed family, we introduce a new model with five parameters, the modified Alpha-Power Weibull–Weibull distribution. Some mathematical properties were determined. Bayesian and maximum likelihood estimates for the model parameters were derived. The MLEs, bootstrap and Bayesian HPD credibility intervals for the unknown parameters were performed. A Monte Carlo simulation study was performed to evaluate the performance of the estimates. A simulation study was performed based on the parameters of the proposed model. An application to the carbon dioxide emissions dataset was performed to predict unique symmetric and asymmetric patterns and illustrate the applicability and potential of the model. For this data set, the proposed model is compared with the modified alpha power Weibull exponential distribution and the two-parameter Weibull distribution. To show which of the competing distributions is the best, we draw on certain analytical tools such as the Kolmogorov–Smirnov test. Based on these analytical measures, we found that the new model outperforms the competing 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]

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]

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This paper analyzes with the cost of a single-server three identical unit cold standby system. Initially one unit is functioning, while the other two are kept in cold standby. The operating system occasionally faces random shocks. As a result of each shock, there is a fixed known probability that (i) the operating unit is unaffected by the random shock,(ii) the operating unit enters into quasi-normal mode whereas its failure rate increases as compared to that when it is functioning in normal mode, (iii) the unit enters into total failure mode. An operating unit can also fail due to its ageing effect that is without being faced to a random shock. The repair is carried out only when all the units fail totally. Failure time distribution of each unit is taken as exponential whereas repair time distribution of all the three units are taken as general. The system model is analyzed by using the supplementary variable technique in order to derive a number of useful measures of system effectiveness. Unknown parameters that are used to evaluate the measures of system effectiveness such as MTSF and Profit function, have been estimated by using maximum likelihood approach and Bayesian approach under different priors. A simulation study at the end exhibits the behavior of such a system. Monte Carlo simulation is used to derive the posterior distribution for the mean time to system failure and Profit function. [ABSTRACT FROM AUTHOR]

This paper proposes a bias-corrected expression for maximum likelihood estimators using the sequential number-theoretic method for optimization (SNTO) to improve the efficiency and accuracy of the estimators in three extreme value distributions (EVDs). It is well known that the widely used maximum likelihood estimation (MLE) could be often biased for small-size samples in EVDs. Meanwhile, numerical simulation results reveal that maximum likelihood estimators are suffered from high variance when the sample size is small and the impact is non-negligible. A comprehensive comparison study which includes classical bias-corrected methods and more recent ones is presented. Based on the simulation studies, the bias-correction estimator via SNTO is highly recommended to reduce the bias and variance of estimators. In addition, a real data set is illustrated to employ different techniques. [ABSTRACT FROM AUTHOR]

Generally, the analysis of a lifetime data to quantify the life characteristics of the product done under normal conditions. The engineers for some reasons may be needed to obtain the reliability results more quickly then, accelerated life tests are applied. In this paper, we adopted partially step-stress accelerated life tests model of product has the generalized half-logistic lifetime distribution. This model is applied on a solar lighting device and the stress factor consider to be temperature. Also, to save the minimum and maximum ideal test time, we applied the generalized type-II hybrid censoring scheme. The parameters of the proposed model are estimated by maximum likelihood and Bayes methods for point and corresponding interval estimators. The validity of results is tested under formulation Monte-Carlo simulation study. The proposed model is applied on analysis data obtained from solar lighting device as real data set for illustrative purposes. [ABSTRACT FROM AUTHOR]

Lomax distribution has been widely used in economics, business and actuarial sciences. Due to its importance, we consider the statistical inference of this model under joint type-II censoring scenario. In order to estimate the parameters, we derive the Newton-Raphson(NR) procedure and we observe that most of the times in the simulation NR algorithm does not converge. Consequently, we make use of the expectation-maximization (EM) algorithm. Moreover, Bayesian estimations are also provided based on squared error, linear-exponential and generalized entropy loss functions together with the importance sampling method due to the structure of posterior density function. In the sequel, we perform a Monte Carlo simulation experiment to compare the performances of the listed methods. Mean squared error values, averages of estimated values as well as coverage probabilities and average interval lengths are considered to compare the performances of different methods. The approximate confidence intervals, bootstrap-p and bootstrap-t confidence intervals are computed for EM estimations. Also, Bayesian coverage probabilities and credible intervals are obtained. Finally, we consider the Bladder Cancer data to illustrate the applicability of the methods covered in the paper. [ABSTRACT FROM AUTHOR]

Probability distributions perform a very significant role in the field of applied sciences, particularly in the field of reliability engineering. Engineering data sets are either negatively or positively skewed and/or symmetrical. Therefore, a flexible distribution is required that can handle such data sets. In this paper, we propose a new family of lifetime distributions to model the aforementioned data sets. This proposed family is known as a "New Modified Exponent Power Alpha Family of distributions" or in short NMEPA. The proposed family is obtained by applying the well-known T-X approach together with the exponential distribution. A three-parameter-specific sub-model of the proposed method termed a "new Modified Exponent Power Alpha Weibull distribution" (NMEPA-Wei for short), is discussed in detail. The various mathematical properties including hazard rate function, ordinary moments, moment generating function, and order statistics are also discussed. In addition, we adopted the method of maximum likelihood estimation (MLE) for estimating the unknown model parameters. A brief Monte Carlo simulation study is conducted to evaluate the performance of the MLE based on bias and mean square errors. A comprehensive study is also provided to assess the proposed family of distributions by analyzing two real-life data sets from reliability engineering. The analytical goodness of fit measures of the proposed distribution are compared with well-known distributions including (i) APT-Wei (alpha power transformed Weibull), (ii) Ex-Wei (exponentiated-Weibull), (iii) classical two-parameter Weibull, (iv) Mod-Wei (modified Weibull), and (v) Kumar-Wei (Kumaraswamy–Weibull) distributions. The proposed class of distributions is expected to produce many more new distributions for fitting monotonic and non-monotonic data in the field of reliability analysis and survival analysis. [ABSTRACT FROM AUTHOR]

In this paper, a dependent competing risks model is considered and investigated by utilizing the copula approach which flexibly constructs dependent relationships between marginal distributions of several competing risk factors, and the closeness of the dependency can be determined by the copula parameters. Samples are collected from the step-stress accelerated life test combined with generalized progressive hybrid censoring, where the test duration is controlled within acceptable limits and a sufficient number of samples are guaranteed. From a classical frequency perspective, the maximum likelihood estimates are derived, then the relevant confidence intervals are provided based on the Fisher information matrix. Furthermore, the bias-corrected accelerated bootstrap method is employed to obtain the interval estimation of parameters. Under the Bayesian framework, Bayesian point estimates and the corresponding credible intervals are also explored, and their results are achieved by Markov Chain Monte Carlo technique. Finally, numerical simulation experiments and real data analysis are developed to more intuitively present the constructed model and the performance of the above-mentioned methods. [ABSTRACT FROM AUTHOR]

As the essential component of prognostic and health management (PHM), life prediction for equipment plays a more and more significant role in recent years. However, current studies cannot fully consider the influence of imperfect maintenance activities that the equipment may experience on the degradation process and prognostic result. In this paper, we propose a degradation model subjected to the influence of imperfect maintenance for life prediction. Firstly, the multi-stage Wiener process is employed to characterize the influence of imperfect maintenance activities on the degradation level and degradation rate. Then, the theoretical expression of life probability distribution is derived under the concept of first hitting time using the convolution operation, and the approximate expression of life probability distribution is evaluated by the Monte Carlo simulation algorithm. Furthermore, we utilize the maximum likelihood estimation (MLE) to estimate unknown parameters in the concerned model. Finally, a numerical example and a practical case study are provided to substantiate the practicality and effectiveness of the newly proposed life prediction method. The results indicate that the proposed model can guarantee that the relative error (RE) is almost below 5%. [ABSTRACT FROM AUTHOR]

Discrete-valued time series modeling has witnessed numerous bivariate first-order integer-valued autoregressive process or BINAR(1) processes based on binomial thinning and different innovation distributions. These BINAR(1) processes are mainly focused on over-dispersion. This paper aims to propose new bivariate distributions and processes based on a recently proposed over-dispersed distribution: the Poisson 2S-Lindley distribution. The new bivariate distributions, denoted by the abbreviations BP2S-L(I) and BP2S-L(II), are then used as innovation distributions for the BINAR(1) process. Properties are investigated for both distributions as well as for the BINAR(1) processes. The distribution parameters are estimated using the maximum likelihood method, and the BINAR(1)BP2S-L(I) and BINAR(1)BP2S-L(II) process parameters are estimated using the conditional least squares and conditional maximum likelihood methods. Monte Carlo simulation experiments are conducted to study large and small sample performances and for the comparison of the estimation methods. The Pittsburgh crime series and candy sales datasets are then used to compare the new BINAR(1) processes to some other existing BINAR(1) processes in the literature. [ABSTRACT FROM AUTHOR]

The moment estimates and maximum likelihood estimates of the truncation points in the truncated normal distribution are given, as well as the interval estimates for large samples. The estimation method of truncation point is applied to the assembly of DNA sequencing data, and moment estimation, maximum likelihood estimation and interval estimation of gap length are obtained. Monte Carlo simulations show that the experimental results are very close to the theoretical estimates. When the estimation method given in this paper is applied to a real DNA sequencing dataset, ideal estimation results are also obtained. [ABSTRACT FROM AUTHOR]

On the basis of a Type-II censored sample, Barakat et al. (Predicting future lifetimes of mixture exponential distribution, Commun Stat Simul Comput https://doi.org/10.1080/03610918.2020.1715434, 2020) considered the problem of predicting the unobserved censored units from a mixture exponential distribution with known parameters. They then discussed how to use the pivotal quantity for obtaining prediction intervals for non-random and random sample size when all parameters are known. In this work, we consider the same problem of prediction where the model parameters involving the scale parameters as well as the mixing proportion parameter are all unknown. Further, we propose different prediction methods for obtaining prediction intervals of future lifetimes including likelihood, highest conditional median, and parametric bootstrap methods. In this set-up, two cases are considered. In the first case, we assume that the sample size is non-random, while in the second case, the sample size is assumed to be random number. It is shown from our numerical results that the parametric bootstrap-based prediction intervals are comparable in terms of coverage probability and very competitive in terms of average length when compared to all other prediction intervals considered in this paper. [ABSTRACT FROM AUTHOR]

In this paper, the estimation of the unknown parameters of the inverted modified Lindley distribution using the concept of dual generalized order statistics is investigated from both classical and Bayesian viewpoints. Based on this considered distribution, first, the maximum likelihood estimator and approximate confidence interval of the model parameter are obtained using order statistics and lower record values. Next, we consider Bayes estimation under the symmetric loss function using a gamma prior. We also derived the highest posterior density credible interval based on the Metropolis–Hastings algorithm. Moreover, the results for single and product moments based on dual generalized order statistics using this distribution are derived. Based on order statistics and lower record values, Monte Carlo simulations are carried out to examine the enforcement of the proposed estimators, and a dataset is investigated for both order statistics and lower record values for illustrative purposes. [ABSTRACT FROM AUTHOR]

This paper investigates the quasi-maximum likelihood estimation of short dynamic panel data models. We consider their estimation on both fixed effects and random effects specifications and propose a Hausman test when exogenous variables are present. For a dynamic panel model, initial conditions play important roles in model structure and estimation, and they give rise to a between equation under the random effects framework. With the between equation properly defined, we show that the random effects model can be decomposed into a within equation and a between equation; hence, the random effects estimate is a pooling of the within and between estimates. Thus, our paper extends the pooling in the static panel data model (Maddala, 1971a) to the setting of dynamic panel data. This decomposition of a dynamic panel data model is revealing and valuable for estimation and the formulation of a Hausman test to test the possible correlation of individual effects with included regressors. Monte Carlo experiments are conducted to investigate the finite sample performance of estimators and the Hausman test. An empirical application of growth convergence in OECD countries is provided. [ABSTRACT FROM AUTHOR]

In this paper, when the stress and strength are two independent Kumaraswamy random variables, we derive the point and interval estimate of the stress–strength parameter, from both frequentist and Bayesian viewpoints, under the Type-II hybrid progressive censoring scheme. In fact, the problem is solved in two cases. First, with the assumption that the stress and strength have different first shape parameters and the common second shape parameter, we attain maximum likelihood estimate (MLE), approximation MLE, and two Bayesian approximation estimates, Lindley's approximation and the Markov chain Monte Carlo (MCMC) method, due to lack of closed forms. Also, the asymptotic confidence interval of $R$ is constructed by asymptotic distribution of it. Moreover, by using the MCMC method, we achieve the highest posterior density credible intervals. Second, with the assumption that the common shape parameter is known, we attain the MLE, the exact Bayes estimate, and the uniformly minimum-variance unbiased estimate of $R$. Also, we construct the asymptotic and Bayesian intervals for the stress–strength parameter. Furthermore, to compare the performance of various methods, we apply the Monte Carlo simulation. Finally, one real dataset is analyzed for demonstrative aims. [ABSTRACT FROM AUTHOR]

Here in this paper, we consider the progressive Type-II censoring Gompertz data under competing risks model with binomial removals. The maximum likelihood estimators of the model parameters involved are obtained by applying numerical methods and the asymptotic variance-covariance matrix of the estimates is also derived. Bayesian estimates based on importance sampling procedure are developed under squared error, LINEX and general entropy loss functions. The confidence intervals using the asymptotic normality and Bayesian approaches are also developed. Finally, a Monte Carlo simulation is conducted to evaluate the performance of the so proposed estimators under all these different estimation methods. [ABSTRACT FROM AUTHOR]

This paper explores statistical inferences when the lifetime of product follows the inverse Nakagami distribution using progressive Type-II censored data. Likelihood-based and maximum product of spacing (MPS)-based methods are considered for estimating the parameters of the model. In addition, approximate confidence intervals are constructed via the asymptotic theory using both likelihood and product spacing functions. Based on traditional likelihood and the product of spacing functions, Bayesian estimates are also considered under a squared error loss function using non-informative priors, and Gibbs sampling based on the MCMC algorithm is proposed to approximate the Bayes estimates, where the highest posterior density credible intervals of the parameters are obtained. Numerical studies are presented to compare the proposed estimators using Monte Carlo simulations. To demonstrate the proposed methodology in a real-life scenario, a well-known data set on agricultural machine elevators with high defect rates is also analyzed for illustration. [ABSTRACT FROM AUTHOR]

The Truncated Cauchy Power Weibull-G class is presented as a new family of distributions. Unique models for this family are presented in this paper. The statistical aspects of the family are explored, including the expansion of the density function, moments, incomplete moments (IMOs), residual life and reversed residual life functions, and entropy. The maximum likelihood (ML) and Bayesian estimations are developed based on the Type-II censored sample. The properties of Bayes estimators of the parameters are studied under different loss functions (squared error loss function and LINEX loss function). To create Markov-chain Monte Carlo samples from the posterior density, the Metropolis–Hasting technique was used with posterior density. Using non-informative and informative priors, a full simulation technique was carried out. The maximum likelihood estimator was compared to the Bayesian estimators using Monte Carlo simulation. To compare the performances of the suggested estimators, a simulation study was carried out. Real-world data sets, such as strength measured in GPA for single carbon fibers and impregnated 1000-carbon fiber tows, maximum stress per cycle at 31,000 psi, and COVID-19 data were used to demonstrate the relevance and flexibility of the suggested method. The suggested models are then compared to comparable models such as the Marshall–Olkin alpha power exponential, the extended odd Weibull exponential, the Weibull–Rayleigh, the Weibull–Lomax, and the exponential Lomax distributions. [ABSTRACT FROM AUTHOR]

In this paper, we study the statistical inference of the generalized inverted exponential distribution with the same scale parameter and various shape parameters based on joint progressively type-II censored data. The expectation maximization (EM) algorithm is applied to calculate the maximum likelihood estimates (MLEs) of the parameters. We obtain the observed information matrix based on the missing value principle. Interval estimations are computed by the bootstrap method. We provide Bayesian inference for the informative prior and the non-informative prior. The importance sampling technique is performed to derive the Bayesian estimates and credible intervals under the squared error loss function and the linex loss function, respectively. Eventually, we conduct the Monte Carlo simulation and real data analysis. Moreover, we consider the parameters that have order restrictions and provide the maximum likelihood estimates and Bayesian inference. [ABSTRACT FROM AUTHOR]

In this paper, a five-parameter distribution, Khalil's new generalized Weibull distribution, is defined and studied in detail. Some mathematical and statistical functions are studied. The effects of shape parameters on skewness and kurtosis are studied. Extensions for density and distribution functions are provided. Estimation of the intended model parameters based on ranked samples is investigated. The behavior of the maximum likelihood estimators is examined using a Monte Carlo simulation. In order to predict unique symmetric and asymmetric patterns and illustrate the applicability and potential of the intended distribution, a COVID-19 dataset is analyzed. The goodness-of-fit results of the new generalized Weibull model of Khalil are compared with some other models. Finally, we make some concluding remarks. [ABSTRACT FROM AUTHOR]

Asymptotic distribution theory for maximum likelihood estimators under fixed alternative hypotheses is reported in the literature even though the power of any realistic test converges to one under fixed alternatives. Under fixed alternatives, authors have established that nuisance parameter estimates are inconsistent when sample size re-estimation (SSR) follows blinded randomization. These results have helped to inhibit the use of SSR. In this paper, we argue for local alternatives to be used instead of fixed alternatives. We treat unavailable treatment assignments in blinded experiments as missing data and rely on single imputation from marginal distributions to fill in for missing data. With local alternatives, it is sufficient to proceed only with the first step of the EM algorithm mimicking imputation under the null hypothesis. Then, we show that blinded and unblinded estimates of the nuisance parameter σ θ 2 are consistent, and re-estimated sample sizes converge to their locally asymptotically optimal values. This theoretical finding is confirmed through Monte-Carlo simulation studies. Practical utility is illustrated through a multiple logistic regression example. We conclude that, for hypothesis testing with a predetermined minimally clinically relevant local effect size, both blinded and unblinded SSR procedures lead to similar sample sizes and power. [ABSTRACT FROM AUTHOR]