Search

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]

The two-parameter Rayleigh distribution, as an extended distribution of the Rayleigh distribution, has been widely applied in reliability analysis. With the introduction of the location parameter, two-parameter Rayleigh distribution becomes more flexible in fitting real-data. In this paper, based on generalized progressively hybrid censored(GPHC) sample from the two-parameter Rayleigh distribution, Classical and Bayesian inferences are discussed. The Newton-Raphson(NR) and Expectation-Maximization(EM) algorithms are used to compute the maximum likelihood estimates(MLEs). As well as the asymptotic confidence interval(ACI) estimation is obtained through the asymptotic distribution theory of maximum likelihood estimation(MLE) and computation of the observed Fisher information matrix. In Bayesian frame, the estimation of unknown parameters and prediction of future observable are taken into consideration. Due to Bayesian estimation is challenging to compute precisely and for the purpose of comparison, the Lindley's approximation, the Tierney-Kadane(TK) approximation and Markov chain Monte Carlo(MCMC) method are employed to obtain Bayesian estimates. Then, combining the MCMC algorithm mentioned in the article, the one- and two- samples Bayesian prediction are obtained. Finally, the simulation results are provided and a real-life data set is used for illustration purpose. [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]

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]

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]

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]

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, the likelihood function under progressive Type II censoring is generalized for Marshal-Olkin bivariate class of distributions and applied it on the bivariate Dagum distribution. Maximum likelihood estimation is considered for the model unknown parameters. Asymptotic and bootstrap confidence intervals for the unknown parameters are evaluated under progressive Type II censoring. Bayesian estimation is also considered in both complete and progressive Type II censored samples; moreover, the Bayes estimators are obtained explicitly with respect to square error loss function in both cases. [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]

Modeling the failure times of processors and memories in computers is crucial for ensuring the reliability and robustness of data science workflows. By understanding the failure characteristics of the hardware components, data scientists can develop strategies to mitigate the impact of failures on their computations, and design systems that are more fault-tolerant and resilient. In particular, failure time modeling allows data scientists to predict the likelihood and frequency of hardware failures, which can help inform decisions about system design and resource allocation. In this paper, we aimed to model the failure times of processors and memories of computers; this was performed by formulating a new type of bivariate model using the copula function. The modified extended exponential distribution is the suggested lifetime of the experimental units. It was shown that the new bivariate model has many important properties, which are presented in this work. The inferential statistics for the distribution parameters were obtained under the assumption of a Type-II censored sampling scheme. Therefore, point and interval estimation were observed using the maximum likelihood and the Bayesian estimation methods. Additionally, bootstrap confidence intervals were calculated. Numerical analysis via the Markov Chain Monte Carlo method was performed. Finally, a real data example of processors and memories failure time was examined and the efficiency of the new bivariate distribution of fitting the data sample was observed by comparing it with other bivariate models. [ABSTRACT FROM AUTHOR]

The ranked set sampling (RSS) is an efficient and flexible sampling method. Based on a modified RSS named minimum ranked set sampling samples (MinRSSU), inference of a dependent competing risks model is proposed in this paper. Then, Marshall–Olkin bivariate distribution model is used to describe the dependence of competing risks. When the competing risks data follow the proportional hazard rate distribution, a dependent competing risks model based on MinRSSU sampling is constructed. In addition, the model parameters and reliability indices were estimated by the classical and Bayesian method. Maximum likelihood estimators and corresponding asymptotic confidence intervals are constructed by using asymptotic theory. In addition, the Bayesian estimator and highest posterior density credible intervals are established under the general prior. Furthermore, according to E-Bayesian theory, the point and interval estimators of model parameters and reliability indices are obtained by a sampling algorithm. Finally, extensive simulation studies and a real-life example are presented for illustrations. [ABSTRACT FROM AUTHOR]

The aim of the present paper is to deal with the analysis of the classical and Bayesian estimation of various measures of system effectiveness in a two non-identical unit parallel system. Each unit has two possible modes Normal (N) and total failure (F). A single repairman is always available with the system and after working for a random period he goes for rest for a random period. After taking complete rest he again starts the repair of the failed unit on a pre-emptive repeat basis. The system failure occurs when both the units are in (F-mode). The distributions of failure time as well as working and rest time of repairman are assumed to be exponential whereas repair time and rest time distribution of repairman are taken as general. A simulation study is also conducted for analysing the considered system model both in Classical and Bayesian setups. Bayesian estimates of various measure of system effectiveness are also obtained by taking different priors. The comparative study is made to judge the performance of Maximum likelihood estimation and Bayesian estimation methods. A simulation study at the end exhibits the behaviour of such a system. The Monte-Carlo technique is employed to draw observations for this simulation study. To obtain various interesting measure of system effectiveness technique have used the Regenerative point technique, MCMC technique and Gibbs sampler technique. From the graphs and tables we have drawn various important conclusions such that a smaller value of failure rate 1 introduces a larger value of Maximum likelihood estimate and Bayes estimates for fixed value of the parameter of the repairman rest time distribution. Moreso, when the value of the failure rate 1 increases the mean time to system failure and net expected profit are also decreases. To compare the performance of asymptotic confidence interval and highest posterior density interval with the maximum likelihood estimates technique, it has been observed that width of the highest posterior density interval is less than the width of an asymptotic confidence interval. [ABSTRACT FROM AUTHOR]

The aim of the paper is to estimate the unknown parameters of weighted exponential distribution based on the competing risks model under progressively Type-II censoring. It is supposed that the latent causes of failures have weighted exponential distributions with different parameters. The maximum likelihood estimations of four unknown parameters are derived and the uniqueness and existence of them are theoretically proved. Moreover, approximate intervals are proposed and constructed with the delta method and Fisher information matrix. Bootstrap methods are also applied to calculate the confidence intervals. Furthermore, Bayes estimates and the corresponding credible intervals under three various loss functions are computed by using the Monte Carlo Markov Chain method. A simulation study is conducted to assess the statistical performance of all the estimators. Ultimately, real data analysis is provided to illustrate all the statistical inferential procedures developed in the paper. [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]

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]

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]

In this paper, by including a trigonometric function, we propose a family of heavy-tailed distribution called the arcsine Kumaraswamy generalized-X family of distributions. Based on the proposed approach, a four-parameter extension of the Lomax distribution called the arcsine Kumaraswamy generalized Lomax (ASKUG-LOMAX) distribution is discussed in detail. Maximum likelihood, bootstrap, and Bayesian estimation are used to estimate the model parameters. A simulation study is used to evaluate ASKUG-LOMAX performance. The flexibility and usefulness of the proposed ASKUG-LOMAX distribution to predict unique symmetric and asymmetric patterns is demonstrated by analyzing real data. The results show that the ASKUG-LOMAX model is a good candidate for analyzing claims based on heavy-tailed data. [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]

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]

In this paper, classical and Bayesian estimation for the parameters and the reliability function for the generalized logarithmic transformation exponential (GLTE) distribution has been proposed when the life-times are progressively censored. The maximum likelihood estimator of unknown parameters and their corresponding reliability function are obtained under the classical setup. The Bayes estimators are obtained for symmetric (squared error) and asymmetric (LINEX and general entropy) loss functions. This was achieved by considering discrete prior for the scale parameter and conditional gamma prior for the shape parameter. Interval estimation of the unknown parameters and reliability function for classical and Bayesian schemes is also considered. The performances of various derived estimators are recorded using simulation study for different sample sizes and progressive censoring schemes. Finally, the COVID-19 mortality data sets are provided to illustrate the computation of various estimators. [ABSTRACT FROM AUTHOR]

In this paper, based on combined Type-II censored samples, an exponential form for the underlaying distributions is considered for estimating the unknown parameters using the maximum likelihood and Bayesian methods. Three loss functions are used to derive the Bayesian estimators. Also, the Bayesian prediction for the order statistics from a future sample is calculated. Moreover, the results of the exponential and Pareto distributions are presented as illustrative examples. Finally, for illustrating all the inferential methods discussed in this paper, Monte Carlo simulation and data analysis for the exponential distribution are presented. [ABSTRACT FROM AUTHOR]

In this paper, we consider inference problems including estimation for a Rayleigh Pareto distribution under progressively type-II right censored data. We use two approaches, the classical maximum likelihood approach and the Bayesian approach for estimating the distribution parameters and the reliability characteristics. Bayes estimators and corresponding posterior risks (PR) have been derived using different loss functions (symmetric and asymmetric). The estimators cannot be obtained explicitly, so we use the method of Monte Carlo. Also we use the integrated mean square error (IMSE) and the Pitman closeness criterion to compare the results of the two methods. Finally, a real data set has been analyzed to investigate the applicability and the usefulness of the proposed model. [ABSTRACT FROM AUTHOR]

In this paper, we consider Marshall-Olkin extended exponential (MOEE) distribution which is capable of modelling various shapes of failure rates and aging criteria. The purpose of this paper is three fold. First, we derive the maximum likelihood estimators of the unknown parameters and the observed the Fisher information matrix from progressively type-II censored data. Next, the Bayes estimates are evaluated by applying Lindley’s approximation method and Markov Chain Monte Carlo method under the squared error loss function. We have performed a simulation study in order to compare the proposed Bayes estimators with the maximum likelihood estimators. We also compute 95% asymptotic confidence interval and symmetric credible interval along with the coverage probability. Third, we consider one-sample and two-sample prediction problems based on the observed sample and provide appropriate predictive intervals under classical as well as Bayesian framework. Finally, we analyse a real data set to illustrate the results derived. [ABSTRACT FROM AUTHOR]

In this paper, based on hybrid censored sample from a two parameter exponentiated half logistic distribution, we consider the problem of estimating the unknown parameters using frequentist and Bayesian approaches. Expectation-Maximization, Lindley's approximation and Metropolis-Hastings algorithms are used for obtaining point estimators and corresponding confidence intervals for the shape and scale parameters involved in the underlying model. Data analyses involving the survival times of patients suffering from cancer diseases and treated radiotherapy and/or chemotherapy have been performed. Finally, numerical simulation study was conducted to assess the performances of the so developed methods and conclusions on our findings are reported. [ABSTRACT FROM AUTHOR]

There are many situations in reliability or medical studies, where items may fail due to one of several causes. Further, censoring is unavoidable in any life testing. In this paper attempts to estimate problem for the competing risks model where the data are adaptive type-II progressive hybrid censored scheme and follow the inverse Weibull distribution. In this regards, we obtain the maximum likelihood estimation of the parameters and the asymptotic confidence intervals for the unknown parameters. Further, Bayes estimates of the parameters which obtained based on squared error and LINEX loss functions under the assumptions of independent gamma priors. For Bayesian estimation, we take advantage of Markov Chain Monte Carlo techniques by applying the Metropolis-Hasting algorithm under the square error and LINEX loss function to derive Bayesian estimators. Finally, two data sets with a Monte Carlo simulation study and a real data set of the electronic applications are analyzed for illustrative purposes. [ABSTRACT FROM AUTHOR]

In this paper, we have considered estimation of unknown parameters based on lower record values for Inverted Kumaraswamy distribution. Maximum likelihood and approximate Bayes estimators based on lower record values for unknown parameters of this distribution are obtained. Lindley's approximation (L-approximation) is used to obtain approximate Bayes estimators under DeGroot loss function based on lower record values. A Simulation study and a real data analysis are presented to illustrate the results. [ABSTRACT FROM AUTHOR]

In a different area of life testing, designing experiments needs higher stress level than normal stress one. Also, the time to failure of experimental units is resulted by one of a fetal risk factors, only. In this paper, we adopted partially step-stress accelerates life-tests (ALTs) model on the Lomax lifetime unites under the two different risk factors with type-I censoring scheme. Under this assumption, we will estimate the Lomax parameters as well as accelerated factor by maximum likelihood method, point and asymptotic confidence intervals. Also, the Bayesian MCMC approach is used in obtaining point and credible interval estimations. Theoretical results are discussed and assessed through data analysis and Monte Carlo simulation study. comments. [ABSTRACT FROM AUTHOR]

The paper illustrates the application of at-site frequency analysis using relatively nontraditional probability distributions adopting four methods of parameter estimation using annual maximum rainfall series (AMRS) (from 1980 to 2015) of three sites; Muzaffarabad, Garhi Dupatta and Kotli of Azad Jammu and Kashmir, Pakistan. Critical assumptions related to AMRS for frequency analysis have been validated through run test (to check the randomness of AMRS at each site) and Mann Whitney test (to check the distribution of AMRS at given sites as identical or not). Two probability distributions; Frechet and Log-logistic have been used as candidate distributions to model AMRS at given sites. The parameters of these distributions have been estimated using four methods; Probability Weighted Moments Estimation (PWME), Maximum Likelihood Estimation (MLE), Bayesian Estimation (BE) and Moments Estimation (ME) methods. The Kolmogorov Smirnov test has been used as goodnessof- fit criteria. The results show suitability of the selected probability distributions for the observed AMRS series at given sites with BE and MLE methods as adequate for estimation. Moreover, the results indicate that ME method is not a preferred choice for the estimation of parameters and quantiles for various return periods. [ABSTRACT FROM AUTHOR]

In this paper, based on progressively Type-II censored samples, the problem of estimation of multicomponent stress–strength reliability under generalized half-normal (GHN) distribution is considered. The reliability of a k-component stress-strength system is estimated when both stress and strength variates are assumed to have a GHN distribution with various cases of same and different shape and scale parameters. Different methods such as the maximum likelihood estimates (MLEs) and Bayes estimation are discussed. The expectation maximization algorithm and approximate maximum likelihood methods are proposed to compute the MLE of reliability. The Lindley's approximation method, as well as Metropolis–Hastings algorithm, are applied to compute Bayes estimates. The performance of the proposed procedures is also demonstrated via a Monte Carlo simulation study and an illustrative example. [ABSTRACT FROM AUTHOR]

Inverse Weibull (IW) distribution is widely used due to its non-monotonic hazard function. For the IW distribution, existing research on statistical inference has mostly focused on censored data, but there has been no study on multiply Type-I censoring until now as far as we know. The multiple Type-I censoring, acted as an extended form of Type-I censoring, is frequently encountered in industry and medicine research, which also needs to be paid attention. Thus, this study conducts detailed analyses on the reliability of IW distribution with multiply Type-I censored data, including point estimation and confidence interval (CI) construction. Four methods, including the maximum likelihood estimation (MLE), least square estimation (LSE), and two Bayesian estimations, namely MCMC and Lindley, are adopted in point estimation. Results show that the Lindley method performs best with small mission times, while MLE is optimal for large mission times. Specifically, for the CIs construction, we proposed a pivotal quantity based on LSE to construct the CIs of reliability and compare it with two popular methods, Fisher information matrix (FIM) derivation and MCMC algorithm. Our proposed method shows competitive performance as the MCMC and outperforms FIM. Finally, those estimation methods are applied to an example for illustration. [ABSTRACT FROM AUTHOR]

Copula models are increasingly recognized for their ability to capture complex dependencies among random variables. In this study, we introduce three innovative bivariate models utilizing copula functions: the XLindley (XL) distribution with Frank, Gumbel, and Clayton copulas. The results highlight the fundamental characteristics and effectiveness of these newly introduced bivariate models. Statistical inference for the distribution parameters is conducted using a Type II censored sampling design. This employs maximum likelihood and Bayesian estimation techniques. Asymptotic and credible confidence intervals are calculated, and numerical analysis is performed using the Markov Chain Monte Carlo method. The proposed methodology's applicability is illustrated by analyzing several real-world datasets. The initial dataset examines burr formation occurrences and consists of two observation sets. Additionally, the second and third datasets contain medical information. The second dataset focuses on diabetic nephropathy, while the third dataset explores infection and recurrence time among kidney patients. [ABSTRACT FROM AUTHOR]

This paper discusses maximum likelihood and Bayes estimation of the two unknown parameters of Nadarajah and Haghighi distribution based on record values. Different Bayes estimates are derived under squared error, balanced squared error and general entropy loss functions by using Jeffreys' prior information and extension of Jeffreys' prior information. It is observed that the associated posterior distribution appears in an intractable form. So, we have used Tierney and Kadane approximation method to compute these estimates. Finally, numerical computations are presented based on generated record values using R software. [ABSTRACT FROM AUTHOR]

In this paper, a new censoring test plan called progressively double Type-II hybrid censoring scheme is introduced for the first time. Based on this type of censored data, the maximum likelihood estimates of the unknown parameters and reliability for the two-parameter Pareto distribution are obtained. Using the Bayesian method, the Bayesian estimates of the unknown parameters and reliability are obtained under the symmetric and asymmetric loss functions. The failure times of all withdrawn units are predicted using the classical and Bayesian methods, including the predictive values and the prediction intervals. The mean values and mean square errors of the estimators are calculated by Monte-Carlo simulation, and the mean square errors between them are compared, and the results show that all Bayesian estimates are better than the corresponding maximum likelihood estimates. Using a real data set, we compute the Bayesian estimates of the unknown parameters and reliability, and predict the observations of the censored units. [ABSTRACT FROM AUTHOR]

In this paper, we first introduce the exponentiated generalized alpha power family of distributions to extend several other distributions. We use the new family and develop a new distribution, called the exponentiated generalized alpha power exponential (EGAPEx) distribution. The proposed EGAPEx distribution provides greater flexibility in modeling data from a practical point of view. The new model includes the exponential; alpha power exponential; alpha power generalized exponential, generalized exponential, standardized generalized exponential and exponentiated generalized exponential distributions as a special cases. This distribution exhibits four hazard rate shapes such as L shaped, increasing, decreasing, and upside-down bathtub. Some statistical properties of the EGAPEx distribution are obtained. The model parameters are obtained by maximum likelihood, maximum product spacing, and Bayesian estimation methods. In addition, we have obtained approximate confidence intervals, two bootstrap confidence intervals, and Bayes credible intervals. A Monte Carlo Simulation is performed to compare the different methods of estimation. We illustrate the performance of the proposed distribution through two real data sets; one is related to economic data and another is failure time data and the data sets show the proposed distribution is superior in its ability to model the data sets as compared to the exponentiated generalized exponential, alpha power generalized exponential, alpha power exponential, generalized exponential and exponential distributions. [ABSTRACT FROM AUTHOR]

In this paper, a study of the stress-strength reliability model is introduced subject to the exponentiated power generalized Weibull distribution. The maximum likelihood estimator for the stress-strength reliability function is deduced. The asymptotic confidence interval for the stressstrength reliability function is derived. The fuzzy stressstrength reliability function is discussed using the triangular membership function. A Bayesian estimator for the stressstrength reliability function is deduced. A real data application is introduced to show the results for the stress-strength model based on real data and compare the use of exponentiated power generalized Weibull distribution with existing distributions. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of estimating unknown parameters of the Burr XII distribution under classical and Bayesian approaches when samples are observed under progressive type-I interval censoring. Under classical approach we employ the stochastic expectation maximization algorithm to obtain maximum likelihood estimators for the unknown parameters and also compute associated interval estimates. Further under Bayesian approach we obtain Bayes estimators with respect to different symmetric, asymmetric and balanced loss functions. In this regard we use Tierney–Kadane and Metropolis–Hastings (MH) algorithm. For illustration purpose we analyse a real data set and conduct a Monte Carlo simulation study to observe the performance of the proposed estimators. Finally we present a discussion on inspection times and optimal censoring. [ABSTRACT FROM PUBLISHER]

Copyright of Journal of Guangxi Normal University - Natural Science Edition is the property of Gai Kan Bian Wei Hui and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this article, the problem of estimation of reliability of a ℓ-component system when both the stress and strength components are assumed to have a power Lindley distribution is discussed. The multicomponent stress–strength reliability parameter is obtained using both the Bayesian and the classical approaches when component-wise each unit follows a power Lindley distribution. To estimate the multicomponent stress–strength reliability parameter under the classical approach, the method of maximum likelihood and the asymptotic confidence interval estimation method are used as point and interval estimation methods, respectively. Under the Bayesian paradigm, the reliability parameter is estimated under the linear exponential loss function using the Lindley approximation, the Tierney–Kadane approximation and the Markov chain Monte Carlo (MCMC) techniques and subsequently highest posterior density credible intervals are obtained. To validate the efficacy of the proposed estimation strategies, a simulation study is carried out. Finally, two real-life data sets are re-analysed for illustrative purposes. [ABSTRACT FROM AUTHOR]

In this paper, based on an adaptive Type-II progressive censoring scheme, estimation of flexible Weibull extension-Burr XII distribution is discussed. Maximum likelihood estimation and asymptotic confidence intervals of the unknown parameters are obtained. The adaptive Metropolis (AM) method is applied to carry out a Bayesian estimation procedure under symmetric and asymmetric loss functions and calculate the credible intervals. A simulation study is carried out to assess the performance of the estimators. Finally, a real life data set is used for illustration purpose. [ABSTRACT FROM AUTHOR]

In this paper, based on an adaptive Type-II progressively censored sample from the generalized exponential distribution, the maximum likelihood and Bayesian estimators are derived for the unknown parameters as well as the reliability and hazard functions. Also, the approximate confidence intervals of the unknown parameters, and the reliability and hazard functions are calculated. Markov chain Monte Carlo method is applied to carry out a Bayesian estimation procedure and in turn calculate the credible intervals. Moreover, results from simulation studies assessing the performance of our proposed method are included. Finally, an illustrative example using real data set is presented for illustrating all the inferential procedures developed here. [ABSTRACT FROM AUTHOR]

Products come from different lines with the same facility are tested under comparative life tests which known with the jointly censoring scheme. In this paper, two sets of products under the same facility have Weibull lifetime distributions are selected to test under Type- I generalized hybrid censoring scheme (GHCS). The observed censoring data are used to build the maximum likelihood (ML) estimators as well as approximate confidence intervals for the model parameters. Also, Bayes estimators with the help of MCMC methods are discussed. The analysis of simulated data set with Monte Carlo simulation study is used to illustrate and compare the theoretical results. Finally, a brief comment is summarized in concluding section. [ABSTRACT FROM AUTHOR]

In this paper, the shape parameters, reliability and hazard rate functions of the inverted Kumaraswamy distribution are estimated using maximum likelihood and Bayesian methods based on dual generalized order statistics. The Bayes estimators are derived under the squared error loss function as a symmetric loss function and the linear-exponential loss function as an asymmetric loss function based on dual generalized order statistics. Confidence and credible intervals for the parameters, reliability and hazard rate functions are obtained. All results are specialized to lower record values, also a numerical study is presented to illustrate the theoretical procedures. [ABSTRACT FROM AUTHOR]

In this paper, based on a jointly type-II censored sample from two exponential populations, the Bayesian inference for the two unknown parameters are developed with the use of squared-error, linear-exponential and general entropy loss functions. The problem of predicting the future failure times, both point and interval prediction, based on the observed joint type-II censored data, is also addressed from a Bayesian viewpoint. A Monte Carlo simulation study is conducted to compare the Bayesian estimators with the maximum likelihood estimator developed by Balakrishnan and Rasouli [Exact likelihood inference for two exponential populations under joint type-II censoring. Comput Stat Data Anal. 2008;52:2725–2738]. Finally, a numerical example is utilized for the purpose of illustration. [ABSTRACT FROM AUTHOR]

The competing risks problem is ubiquitous in different areas of life science, in engineering and science where failure of one component causes to fail all the system. Studying life testing experiment of a product or material, usual requires long period of time to monitoring. For the purpose of reducing the testing period, test units may be presented under conditions more severe than normal circumstances, which is called accelerated life tests (ALTs). More precisely, this procedure makes the lives shorter than would be spotted or monitored under normal conditions. Burr XII model has increasingly important in engineering statistics than other model. So, within this paper, maximum likelihood and Bayesian estimations will be discussed under the type-II censored Burr XII life time data. The Burr XII parameters as well as accelerated factor under competing risks model will be estimated. Also, the asymptotic confidence intervals under normality theory and credible intervals are obtained from MCMC sampling method will be drawn. Finally, the maximum likelihood and Bayesian estimations will be considered and a simulation investigation is described and reported by comparing the two approaches. [ABSTRACT FROM AUTHOR]

In this paper, Burr-X distribution with unified hybrid censored data is considered. The maximum likelihood method, the Bayesian and the E-Bayesian (the expectation of the Bayesian estimate) approaches are studied for the distribution parameter and the associated reliability function. The Bayesian and the E-Bayesian estimates are derived under LINEX and squared error loss (SEL) functions. We apply Markov chain Monte Carlo (MCMC) techniques to derive the Bayesian and the E-Bayesian estimates. Also, confidence intervals (CIs) of the maximum likelihood estimates, as well as credible intervals (CRIs) of the Bayesian and the E-Bayesian estimates, are computed. On the other hand, an example of a real data set is provided for the purpose of illustration. Finally, a numerical comparison among the proposed methods is performed. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a new model based on Burr X and Fréchet distributions for extreme values and derive some of its properties. Maximum likelihood estimation along with asymptotic confidence intervals is considered for estimating the parameters of the distribution. We demonstrate empirically the flexibility of the distribution in modeling various types of real data. Furthermore, we also provide Bayes estimators and highest posterior density (HPD) intervals of the parameters of the distribution using Markov Chain Monte Carlo (MCMC) methods. [ABSTRACT FROM AUTHOR]

In life testing and reliability studies, most researchers have used the maximum likelihood estimation method to estimate unknown parameters, even though it has been proven that the maximum product of spacing method has properties as good as the maximum likelihood estimation method and sometimes even better. In this study, we aim to estimate the unknown parameters of the modified Kies exponential distribution along with the reliability and hazard rate functions under progressive type-II censoring scheme. The maximum likelihood and maximum product of spacing methods are considered in order to find the point estimates and approximate confidence intervals of the various parameters. Moreover, Bayesian estimations based on the likelihood function and the product of the spacing function of the unknown parameters are obtained using the squared error loss function with independent gamma priors. It is observed that the joint posterior distributions have complicated forms. Because of this, Lindley's approximation and the Markov chain Monte Carlo technique are used to obtain the Bayesian estimates and highest posterior credible intervals. Monte Carlo simulations are performed in order to evaluate the performance of the proposed estimation methods. Two real datasets are studied to demonstrate the efficacy of the offered methodologies and highlight how simple and applicable it might be to apply them in practical fields. [ABSTRACT FROM AUTHOR]

In this research, random censoring is employed as a methodology for parameter estimation within the context of an exponential distribution. These parameter estimations are conducted using both the Bayesian and maximum likelihood approaches. In the Bayesian framework, Lindley's approximation method is applied to derive estimates, which are subsequently assessed under three distinct balanced loss functions. To gauge the efficacy of different estimation techniques, simulation-based investigations are conducted. Additionally, a real-world data analysis is executed to illustrate the practical applicability of these methodologies. The findings consistently underscore the superiority of Bayesian parameter estimates in comparison with their maximum likelihood counterparts across all analyzed methodologies. [ABSTRACT FROM AUTHOR]

In this paper, maximum likelihood and Bayesian methods of estimation are used to estimate the unknown parameters of two Weibull populations with the same shape parameter under joint progressive Type-I (JPT-I) censoring scheme. Bayes estimates of the parameters are obtained based on squared error and LINEX loss functions under the assumption of independent gamma priors. We propose to apply Markov Chain Monte Carlo (MCMC) technique to carry out a Bayesian estimation procedure. The approximate confidence intervals and the credible intervals for the unknown parameters are also obtained. Finally, we analyze a one real data set for illustration purpose. [ABSTRACT FROM AUTHOR]