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

In this paper, we investigate the inferential procedures within both classical and Bayesian frameworks for the generalized logistic distribution under a random censoring model. For randomly censored data, our main goals were to develop maximum likelihood estimators and construct confidence intervals using the Fisher information matrix for the unknown parameters. Additionally, we developed Bayes estimators with gamma priors, addressing both squared error and general entropy loss functions. We also calculated Bayesian credible intervals for the parameters. These methods were applied to two real datasets with random censoring to provide valuable insights. Finally, we conducted a simulation analysis to assess the effectiveness of the estimated values. [ABSTRACT FROM AUTHOR]

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]

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]

For operating any new finite capacity (say K) queuing system in which customers arrive according to a Poisson process and are served by a single server under exponential service time (in Kendall's notation M/M/1/K system), the assumption of fixing K and estimating the parameter traffic intensity ρ , is quite practical. But in situation of any pre-existing M/M/1/K queuing system, it is essential to determine an estimator of K to increase system efficiency for fixed value of ρ . This paper therefore considered the problem of estimating the parameter finite buffer (K). A Bayes estimator of K is proposed and compared it with classical estimator based on maximum likelihood principal, under the assumption that ρ is known. A simulation study is carried out to establish the efficacy and effectiveness of the proposed approaches. A real life situation is analyzed to illustrate the applicability of the developed algorithms. [ABSTRACT FROM AUTHOR]

This paper investigates the estimation of the two unknown parameters and the reliability function of the weighted exponential distribution. It explores Bayesian and non-Bayesian (maximum likelihood) estimation methods when the information available is in the form of fuzzy data. The Newton-Raphson algorithm is used to obtain the maximum likelihood estimates. In Bayes estimation, the symmetric squared error loss function is used. This loss function links equal importance to the losses due to overestimating and underestimating equal magnitude. Lindley approximation procedure in Bayesian estimation theory is used to evaluate the ratio of integrals. A comparative analysis using simulation is carried out to evaluate the performance of the obtained parameters estimators using mean squared error criteria and the performance of the obtained reliability estimators using integrated mean squared error criteria. The simulation results demonstrate that, for different sample sizes, the performance of Bayes estimates surpasses the maximum likelihood, and that all estimators perform consistently. [ABSTRACT FROM AUTHOR]

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

In this paper, we propose a lensless three-dimensional (3D) imaging under photon-starved conditions using diffraction grating and computational photon counting method. In conventional 3D imaging with and without the lens, 3D visualization of objects under photon-starved conditions may be difficult due to lack of photons. To solve this problem, our proposed method uses diffraction grating imaging as lensless 3D imaging and computational photon counting method for 3D visualization of objects under these conditions. In addition, to improve the visual quality of 3D images under severely photon-starved conditions, in this paper, multiple observation photon counting method with advanced statistical estimation such as Bayesian estimation is proposed. Multiple observation photon counting method can estimate the more accurate 3D images by remedying the random errors of photon occurrence because it can increase the samples of photons. To prove the ability of our proposed method, we implement the optical experiments and calculate the peak sidelobe ratio as the performance metric. [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]

This paper investigates constant-stress accelerated life tests interrupted by a progressive type-I interval censoring regime. We provide a model based on the Chen distribution with a constant shape parameter and a log-linear connection between the scale parameter and stress loading. Inferential methods, whether classical or Bayesian, are employed to address model parameters and reliability attributes. Classical methods involve the estimation of model parameters through maximum likelihood and midpoint techniques. Bayesian approximations are achieved via the utilization of the Metropolis–Hastings algorithm, Tierney-Kadane procedure, and importance sampling methods. Furthermore, we engage in a discourse on the estimation of confidence intervals, making references to both asymptotic confidence intervals and credible intervals. To conclude, we furnish a simulation study, a corresponding discussion, and supplement these with an analysis of real data. [ABSTRACT FROM AUTHOR]

In this paper, an estimation of the multicomponent stress-strength reliability is introduced subject to the exponentiated generalized inverse Rayleigh distribution. Different methods of estimation are introduced to estimate the multicomponent stress-strength reliability. Simulation method is introduced to illustrate the steps of finding the estimates of the multicomponent stress-strength reliability. Asymptotic and bootstrap confidence intervals are proposed in order to find interval estimations for the multicomponent stress-strength reliability. A Bayesian estimation method is introduced for the multicomponent stress-strength reliability. A simulation study is introduced to obtain the estimates of the multicomponent stress-strength reliability for the different methods of estimation. A real data application is introduced to show how the exponentiated generalized inverse Rayleigh distribution is used to fit the real data sets. [ABSTRACT FROM AUTHOR]

In this paper, the bivariate generalized Rayleigh distribution is introduced based on Clayton copula and denoted as (Clayton-BGR). The likelihood function for progressive Type-II censoring scheme with random removal is derived and applied on the Clayton-BGR distribution. Bayesian and non -Bayesian estimation methods based on progressive Type-II censoring have been discussed. Asymptotic confidence intervals and bootstrap confidence intervals for the unknown parameters are obtained. Also, a simulation study has been conducted to compare the performances between censoring schemes. Also, two real data sets are analyzed to investigate the models and useful results are obtained for illustrative purposes. [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]

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]

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 study the inference of the multicomponent stress–strength reliability (MSSR) based on the Chen distribution using progressively Type-II censored data. Both the stress and strength variables follow the Chen distribution with a common second shape parameter. The maximum likelihood estimates and the asymptotic confidence intervals of the MSSR are developed. The bootstrap confidence interval of the MSSR is also constructed. The Bayesian estimation of the MSSR is obtained under the generalized entropy loss function using the Markov Chain Monte Carlo method. To check the effectiveness of the proposed approach, simulation studies are performed. Finally, a real data set is analyzed. [ABSTRACT FROM AUTHOR]

In this paper, the inference of multicomponent stress-strength reliability has been derived using progressively censored samples from Topp-Leone distribution. Both stress and strength variables are assumed to follow Topp-Leone distributions with different shape parameters. The maximum likelihood estimate along with the asymptotic confidence interval are developed. Boot-p and Boot-t confidence intervals are also constructed. The Bayes estimates under generalized entropy loss function based on gamma priors using Lindley's, Tierney-Kadane's approximation and Markov chain Monte Carlo methods are derived. A simulation study is considered to check the performance of various estimation methods and different censoring schemes. A real data study shows the applicability of the proposed estimation methods. [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]

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 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]

Competing risk analysis of time to failure data is preferred when failure of the unit occurs due to any one of several mutually exclusive causes. Masked data refer to the competing risk data with missing cause of failure. Masking in such data may depend on cause of failure or time to failure of the unit or may be independent of both. In this paper, we discuss competing risk models based on Lindley distribution assuming masking to be symmetric, cause dependent and time dependent. We consider maximum likelihood as well as Bayesian approaches for point and interval estimation of model parameters. We perform extensive simulation study to observe performance of various estimators. Finally, we analyze a real life masked data of cancer patients and select the best masking model for the same. [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]

In this paper, different monetary policy rules are re‐estimated employing real‐time data, known as Greenbook data, through MLE and Bayesian Estimation. The results favour the rule with persistent shocks and show that the inertial movement of the Federal funds rate is an illusion, as mentioned by Rudebusch (2002). Since it would be possible to have an omitted variable bias due to impure serial correlation, however, the rule with persistent shock could imply that the other serially correlated variable is required to explain the inertial movement of Federal funds rates. Based on this idea, serial correlation tests are implemented, showing the possibility of an omitted serial correlated variable. Therefore, it is reasonable to search for other persistent variables. As an illusion implies unpredictability in the movement of the Federal funds rate, this hypothesis could be against the credibility of the central bank. In order to have a reasonable explanation for the inertial movement other than persistent shocks, therefore, modifying the rule with a 3‐month t‐bill rate is re‐estimated. The result shows that the rule with the t‐bill rate outperformed in all aspects and is compatible with one theoretical explanation of minimizing the financial volatility for inertial movement. [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]

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]

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]

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]

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]

This paper deals with the parametric inference for integrated continuous time signals embedded in an additive Gaussian noise and observed at deterministic discrete instants which are not necessarily equidistant. The unknown parameter is multidimensional and compounded of a signal-of-interest parameter and a variance parameter of the noise. We state the consistency and the minimax efficiency of the maximum likelihood estimator and of the Bayesian estimator when the time of observation tends to infinity and the delays between two consecutive observations tend to 0 or are only bounded. The class of signals in consideration contains among others, almost periodic signals and also non-continuous periodic signals. However the problem of frequency estimation is not considered here. Furthermore, in this paper the signal-plus-noise discretely observed in time model is considered as a particular case of a more general model of independent Gaussian observations forming a triangular array. [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]

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]

This paper gives an overview of parameter estimation and system identification for quantum input–output systems by continuous observation of the output field. We present recent results on the quantum Fisher information of the output with respect to unknown dynamical parameters. We discuss the structure of continuous-time measurements as solutions of the quantum Zakai equation, and their relationship to parameter estimation methods. Proceeding beyond parameter estimation, the paper also gives an overview of the emerging topic of quantum system identification for black-box modelling of quantum systems by continuous observation of a travelling wave probe, for the case of ergodic quantum input–output systems and linear quantum systems. Empirical methods for such black-box modelling are also discussed. [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]