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In this paper, the Bayesian estimators for the Inverse Weibull Distribution (IWD) scale parameter are derived when the shape parameter of distribution is known. The Bayesian estimators for the parameter are obtained by using the Gamma prior under the different types of loss functions such as square error loss function (Self), Entropy loss function (Elf), Precautionary loss function (Plf), Linear exponential loss function (Linexlf) and nonlinear exponential loss function (Nlinexlf). A classical maximum likelihood estimator (mle) for the parameter is also derived. To compare the efficiency of the parameter estimation methods, a simulation study is carried out. The comparison is based on mean square error. [ABSTRACT FROM AUTHOR]

This paper is concerned with applying the Bayesian and E-Bayesian approaches to estimating the unknown parameters of the modified Topp–Leone–Chen distribution under a progressive Type-II censored sample plan. The paper explores the complexities of different estimating methods and investigates the behavior of the estimates through some computations. The Bayes and E-Bayes estimators are obtained under two distinct loss functions, the balanced squared error loss function, as a symmetric loss function, and the balanced linear exponential loss function, as an asymmetric loss function. The estimators are derived using gamma prior and uniform hyperprior distributions. A numerical illustration is given to examine the theoretical results through using the Metropolis–Hastings algorithm of the Markov chain Monte Carlo method of simulation by the R programming language. Finally, real-life data sets are applied to prove the flexibility and applicability of the model. [ABSTRACT FROM AUTHOR]

This paper proposes a semiparametric spatial lag model and develops a Bayesian estimation method for this model. In the estimation of the model, the paper combines Reversible Jump Markov Chain Monte Carlo (RJMCMC) algorithm, random walk Metropolis sampler, and Gibbs sampling techniques to sample all the parameters. The paper conducts numerical simulations to validate the proposed Bayesian estimation theory using a numerical example. The simulation results demonstrate satisfactory estimation performance of the parameter part and the fitting performance of the nonparametric function under different spatial weight matrix settings. Furthermore, the paper applies the constructed model and its estimation method to an empirical study on the relationship between economic growth and carbon emissions in China, illustrating the practical application value of the theoretical results. [ABSTRACT FROM AUTHOR]

In quality engineering, process capability indices play a crucial role in assessing the capability of a given process. Among the widely recognized indices are Cp, Cpk, Cpm, and Cpmk, all of which presuppose the normality of the product lifetime. However, Maiti et al. (2010) proposed a more versatile process capability index, denoted as Cpyk, which does not rely on distributional assumptions. The study is currently investigating statistical inferences for the Cpyk index within the context of progressively type-II censored samples, marking the first exploration of this aspect in the research. This paper investigates maximum likelihood and Bayesian inference for the Cpyk when the underlying distribution follows the inverse Rayleigh distribution. Additionally, the study explores Bayesian credible intervals and the highest posterior density intervals using the Markov Chain Monte Carlo procedure. Various types of bootstrap confidence intervals are also taken into consideration. To assess the performance of these intervals, a Monte Carlo simulation is executed, comparing their coverage probabilities and mean lengths. The paper concludes with an illustrative example utilizing real data, providing a practical application of the discussed methodologies. [ABSTRACT FROM AUTHOR]

This paper explores the likelihood and Bayesian estimation of the stress–strength reliability parameter (R) based on a lower record ranked set sampling scheme from the generalized Rayleigh distribution. Maximum likelihood and Bayesian estimators as well as confidence intervals of R are derived and their properties are studied. Furthermore, two parametric bootstrap confidence intervals are introduced in the paper. A comparative simulation study is conducted to assess the effectiveness of these four confidence interval methodologies in estimating R. The application of the methods is demonstrated using real data on fiber strength to showcase their practicability and relevance in the industry. [ABSTRACT FROM AUTHOR]

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

IRTree models have been receiving increasing attention. However, to date, there are limited sources that provide a systematic introduction to Bayesian modeling techniques using modern probabilistic programming frameworks for the implementation of IRTree models. To facilitate the research and application of IRTree models, this paper introduces how to perform two families of Bayesian IRTree models (i.e., response tree models and latent tree models) in Stan and how to extend them in an explanatory way. Some suggestions on executing Stan codes and checking convergence are also provided. An empirical study based on the Oxford Achieving Resilience during COVID-19 data was conducted as an example to further illustrate how to apply Bayesian IRTree models to address research questions. Finally, strengths and future directions are discussed. [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]

Degradation modeling serves as a valuable tool for assessing the lifetime information of highly reliable products. One frequently employed approach for describing the degradation phenomenon involves the use of a degradation model that relies on stochastic processes. In a stochastic‐process‐based degradation model, it is assumed that the increments follow a distribution with the additivity property. This property makes the further inferences mathematically and statistically tractable. However, it limits the choices of the distributions. This paper aims to use those distributions without the additivity property to model the increments and explores distributions from the log‐location‐scale family. Under the frame of Bayesian analysis, Markov Chain Monte Carlo algorithms are developed for executing the necessary computations. Given that the proposed degradation models do not adhere to the additivity property, this paper tackles the challenges involved in predicting the lifetime of both on‐line and off‐line products. Two illustrative examples are subsequently analyzed to demonstrate the procedural steps outlined. The suitability of the proposed model is finally validated through a simulation study. [ABSTRACT FROM AUTHOR]

In this paper, Bayesian and non-Bayesian estimations of the shape parameter of the Inverted Topp-Leone distribution are studied under a progressive Type I censoring scheme. The maximum likelihood estimator (MLE) and Bayes estimator (BE) of the unknown parameter under the squared error loss (SEL) function are obtained. Three types of confidence intervals are discussed for the unknown parameter. A simulation study is performed to compare the performances of the proposed methods, and two numerical examples have been analyzed for illustrative purposes. [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]

To achieve high-precision geomagnetic matching navigation, a reliable geomagnetic anomaly basemap is essential. However, the accuracy of the geomagnetic anomaly basemap is often compromised by noise data that are inherent in the process of data acquisition and integration of multiple data sources. In order to address this challenge, a denoising approach utilizing an improved multiscale wavelet transform is proposed. The denoising process involves the iterative multiscale wavelet transform, which leverages the structural characteristics of the geomagnetic anomaly basemap to extract statistical information on model residuals. This information serves as the a priori knowledge for determining the Bayes estimation threshold necessary for obtaining an optimal wavelet threshold. Additionally, the entropy method is employed to integrate three commonly used evaluation indexes—the signal-to-noise ratio, root mean square (RMS), and smoothing degree. A fusion model of soft and hard threshold functions is devised to mitigate the inherent drawbacks of a single threshold function. During denoising, the Elastic Net regular term is introduced to enhance the accuracy and stability of the denoising results. To validate the proposed method, denoising experiments are conducted using simulation data from a sphere magnetic anomaly model and measured data from a Pacific Ocean sea area. The denoising performance of the proposed method is compared with Gaussian filter, mean filter, and soft and hard threshold wavelet transform algorithms. The experimental results, both for the simulated and measured data, demonstrate that the proposed method excels in denoising effectiveness; maintaining high accuracy; preserving image details while effectively removing noise; and optimizing the signal-to-noise ratio, structural similarity, root mean square error, and smoothing degree of the denoised image. [ABSTRACT FROM AUTHOR]

Censoring plays an important role in the reliability and life testing trials due to its cost optimality and time reduction properties. The unified hybrid censoring scheme is the combination of the generalized type-I and type-II hybrid censoring schemes. In this paper, our objective is to study the classical and Bayesian estimation methods of the parameter and reliability characteristics from the inverse Pareto lifetime model under the unified hybrid censoring scheme. In the classical estimation methods, the maximum likelihood and associated asymptotic confidence interval estimators are derived. In Bayesian estimation, the Bayes estimators under squared error loss function and the highest posterior density (HPD) credible intervals based on the informative and non-informative priors are developed. For the Bayesian computations, the Markov chain Monte Carlo techniques are used to compute Bayes and HPD credible interval estimates. A quantitative outcome of the objectives has been shown by a Monte Carlo simulation and with the help of a real-life application. [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]

To reduce total test time and increase the efficiency of statistical analysis of a life-testing experiment adaptive progressive Type-II censoring scheme has been proposed. This paper addresses the statistical inference of the unknown parameters, reliability, and hazard rate functions of logistic exponential distribution under adaptive progressive Type-II censored samples. Maximum likelihood estimates (MLEs) and maximum product spacing estimates (MPSEs) for the model parameters, reliability, and hazard rate functions can not be obtained explicitly, hence these are derived numerically using the Newton–Raphson method. Bayes estimates for the unknown parameters and reliability and hazard rate functions are computed under squared error loss function (SELF) and linear exponential loss function (LLF). It has been observed that the Bayes estimates are not in explicit forms, hence an approximation method such as Markov Chain Monte Carlo (MCMC) method is employed. Further, asymptotic confidence intervals (ACIs) and highest posterior density (HPD) credible intervals for the unknown parameters, reliability, and hazard rate functions are constructed. Besides, point and interval Bayesian predictions have been derived for future samples. A Monte Carlo simulation study has been carried out to compare the performance of the proposed estimates. Furthermore, three different optimality criteria have been considered to obtain the optimal censoring plan. Two real-life data sets, one from electronic industry and other one from COVID-19 data set containing the daily death rate from France are re-analyzed to demonstrate the proposed methodology. [ABSTRACT FROM AUTHOR]

Sub-Nyquist synthetic aperture radar (SAR) based on pseudo-random time–space modulation has been proposed to increase the swath width while preserving the azimuthal resolution. Due to the sub-Nyquist sampling, the scene can be recovered by an optimization-based algorithm. However, these methods suffer from some issues, e.g., manually tuning difficulty and the pre-definition of optimization parameters, and a low signal–noise ratio (SNR) resistance. To address these issues, a reweighted optimization algorithm, named pseudo-ℒ0-norm optimization algorithm, is proposed for the sub-Nyquist SAR system in this paper. A modified regularization model is first built by applying the scene prior information to nearly acquire the number of nonzero elements based on Bayesian estimation, and then this model is solved by the Cauchy–Newton method. Additionally, an error correction method combined with our proposed pseudo-ℒ0-norm optimization algorithm is also present to eliminate defocusing in the motion-induced model. Finally, experiments with simulated signals and strip-map TerraSAR-X images are carried out to demonstrate the effectiveness and superiority of our proposed algorithm. [ABSTRACT FROM AUTHOR]

The aim of this study is twofold: on the one hand, to provide evidence of the positive association between the inflation rate and the labor share in the US; on the other, to show that monetary policy slows inflation by depressing the labor share. With the help of Bayesian econometrics, the paper shows evidence of a conflict Phillips curve. Furthermore, a structural vector autoregressive model reveals the detrimental effects of interest rate hikes on the labor share. Together, these results mean the monetary policy of administered interest rates resolves the class conflict in favor of capital to control inflation. Scrutiny of the US monetary policy development and a model of a controlled predator-prey system prepare the way for the empirical sections. Finally, the paper concludes that controlling the distributive conflict matters for impinging on inflation and that the Fed might follow alternative monetary rules to cease being the third party participating in the distributive conflict. [ABSTRACT FROM AUTHOR]

Considering that the choice of loss function plays a significant role in the derivation of Bayesian estimators, we propose a novel asymmetric loss function named the weighted Q-symmetric entropy loss for computing the estimates of the parameter and reliability function of the Burr XII distribution. This paper covers the classical maximum-likelihood, uniformly minimum-variance unbiased, and Bayesian estimation methods under the squared error loss, general entropy loss, Q-symmetric entropy loss, and new loss functions. Through Monte Carlo simulation, the respective performances of the considered estimators for the reliability function are evaluated, indicating that the Bayesian estimator under the new loss function is more efficient than those under other loss functions. Finally, a real data set is used to demonstrate the practicality of the presented estimators. [ABSTRACT FROM AUTHOR]

The issue of modelling observations generated in matrix form over time is key in economics, finance and many domains of application. While it is common to model vectors of observations through standard vector time series analysis, original matrix-valued data often reflect different types of structures of time series observations which can be further exploited to model interdependencies. In this paper, we propose a novel matrix autoregressive model in a bilinear form which, while leading to a substantial dimensionality reduction and enhanced interpretability: (a) allows responses and potential covariates of interest to have different dimensions; (b) provides a suitable estimation procedure for matrix autoregression with lag structure; (c) facilitates the introduction of Bayesian estimators. We propose maximum likelihood and Bayesian estimation with Independent-Normal prior formulation, and study the theoretical properties of the estimators through simulated and real examples. [ABSTRACT FROM AUTHOR]

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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]

Shannon's entropy is a fundamental concept in information theory that quantifies the uncertainty or information in a random variable or data set. This article addresses the estimation of Shannon's entropy for the Maxwell lifetime model based on progressively first-failure-censored data from both classical and Bayesian points of view. In the classical perspective, the entropy is estimated using maximum likelihood estimation and bootstrap methods. For Bayesian estimation, two approximation techniques, including the Tierney-Kadane (T-K) approximation and the Markov Chain Monte Carlo (MCMC) method, are used to compute the Bayes estimate of Shannon's entropy under the linear exponential (LINEX) loss function. We also obtained the highest posterior density (HPD) credible interval of Shannon's entropy using the MCMC technique. A Monte Carlo simulation study is performed to investigate the performance of the estimation procedures and methodologies studied in this manuscript. A numerical example is used to illustrate the methodologies. This paper aims to provide practical values in applied statistics, especially in the areas of reliability and lifetime data analysis. [ABSTRACT FROM AUTHOR]

The shared frailty models are now popular for modelling heterogeneity in survival analysis. It assumes that the same frailty is shared by all individual members within the families. Also, it is believed that all the individuals in the population are susceptible to the event of interest and will eventually experience the event. This may not always be the situation in reality. There may be a certain fraction of the population which is non-susceptible for an event and hence may not experience the event under study. Non-susceptibility is modelled by frailty models with compound frailty distribution. Further, susceptibility may be different for different families. This can be attained by randomizing the parameter of frailty distribution. This paper incorporates both the things, non-susceptibility and different susceptibility for different families by considering compound negative binomial distribution with random probability of susceptibility as frailty distribution. The inferential problem is solved in a Bayesian framework using Markov Chain Monte Carlo methods. The proposed model is then applied to a real-life data set. [ABSTRACT FROM AUTHOR]

In our paper, we introduce a novel extension of the Lomax distribution, aiming to enhance its applicability in various contexts. We emphasize a pragmatic approach in deriving mathematical properties of the new distribution, prioritizing its practical implications. Three distinct methods for characterizing the distribution are thoroughly discussed to provide a comprehensive understanding. The parameters of this newly proposed distribution are estimated through a diverse set of classical methodologies as well as Bayes’ method. Additionally, we develop the censored case maximum likelihood method to address scenarios where data may be incomplete. We meticulously compare the efficacy of likelihood estimation and Bayesian estimation using Pitman’s proximity criterion, thereby offering insights into their relative performance. For Bayesian estimation, we employ three distinct loss functions: the generalized quadratic, the Linex, and the entropy functions, each offering unique perspectives on the estimation process. Through extensive simulation experiments, we meticulously evaluate the performance of all estimation methods under various conditions, providing valuable insights into their practical utility. Furthermore, we conduct a comparative analysis between the Bayesian technique and the censored maximum likelihood method using the BB algorithm, facilitating a nuanced understanding of their respective strengths and weaknesses. In addition to estimation methodologies, we delve into the construction of the Nikulin-Rao-Robson statistic for the new model under both uncensored and censored cases. Detailed simulation studies and the presentation of two real-world applications elucidate the practical significance of our proposed statistics in diverse scenarios. Overall, our paper not only introduces a novel extension of the Lomax distribution but also provides a comprehensive exploration of various estimation techniques and statistical measures, underpinning its practical relevance across different domains. [ABSTRACT FROM AUTHOR]

In this paper, based on the mixed Gibbs sampling algorithm, a Bayesian estimation procedure is proposed for a new Pareto-type distribution in the case of complete and type II censored samples. Simulation studies show that the proposed method is consistently superior to the maximize likelihood estimation in the context of small samples. Also, an analysis of some real data is provided to test the Bayesian estimation. [ABSTRACT FROM AUTHOR]

The discrete Weibull model can be adapted to capture different levels of dispersion in the count data. This paper takes into account the direct relationship between explanatory variables and the median of discrete Weibull response variable. Additionally, it provides the Bayesian estimate of the discrete Weibull regression model using the random walk Metropolis algorithm. The prior distributions of the coeficient predictors were carried out based on the uniform non-informative, normal and Laplace distributions. The performance of the Bayes estimators was also compared with the maximum likelihood estimator in terms of the mean square error and the coverage probability through the Monte Carlo simulation study. Meanwhile, a real data set was analyzed to show how the proposed model and the methods work in practice. [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]

This tutorial presents the factor graph, a recently introduced estimation framework that is a generalization of the Kalman filter. An approach for constructing a factor graph, with its associated optimization problem and efficient sparse linear algebra formulation, is described. A comparison with Kalman filters is presented, together with examples of the generality of factor graphs. A brief survey of previous applications of factor graphs to navigation problems is also presented. Source code for the extended Kalman filter comparison and for generating the graphs in this paper is available at https://github.com/cntaylor/ factorGraph2DsatelliteExample. [ABSTRACT FROM AUTHOR]

Due to the scarcity of subnational interregional input–output (IRIO), various approaches to their estimation are actively under investigation in the literature. This paper focuses on the application of spatial econometric method. It determines intra- and interregional coefficients through a joint procedure which successfully avoids the direct recycling of estimates for other geographies and granularities. Instead, the use of Bayesian methods is proposed, which formally integrate limited evidence from existing regional tables (Finland) with a set of sectoral data on value added for 73 NUTS-3 regions in Poland, the latter being dominant. An empirical test of replicating the Korean survey-based IRIO table demonstrates that the accuracy of this approach slightly outperforms an alternative IRIOLQ procedure. The incorporation of time-based distance measurement has only modest effects on empirical fit, and the use of big geolocation dataset to account for commuting relocates 18.9% of the induced effect from a city to its periphery. [ABSTRACT FROM AUTHOR]

The joint progressive Type‐II censoring scheme is an advantageous cost‐saving strategy. In this paper, investigated classical and Bayesian methodologies for estimating the combined parameters of two distinct Lomax distributions employing the joint progressive Type‐II censoring scheme. Maximum likelihood estimators have been derived, and asymptotic confidence intervals are presented. Bayesian estimates and their corresponding credible intervals are calculated, incorporating both symmetry and asymmetry loss functions through the utilization of the Markov Chain Monte Carlo (MCMC) method. The simulation aspect has employed the MCMC approximation method. Furthermore, discussed the practical application of these methods, providing illustration through the analysis of a real dataset. [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, 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]

It is a great pleasure to have the opportunity to write a discussion on "Specifying Prior Distributions in Reliability Applications" by Tian et al. Appl Stochast Models Bus Ind, (2023). One coauthor of the paper, Dr Meeker, has conducted Bayesian methodology research on reliability data analysis for many years, and I have followed his work on the subject for quite some time. The work by Dr Meeker helped us develop Bayesian estimation products which are both powerful and easy to use. This time, I learned something new as usual. In this discussion, I will focus on the great value of the paper for developing user friendly Bayesian estimation software. [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 provides pioneering estimates of the impact of loan-to-value (LTV) ratios, also known as leverage, on Bolivia's GDP. The empirical evidence reveals the pro-cyclicality between the economic and financial cycles, which affects the intertemporal resource allocation processes between the financial and real sectors. The findings from the RBC model demonstrate that shocks in the loan-to-value (LTV) ratios trigger a rise in housing prices and greater consumption by entrepreneurs, leading to an increase in investment, employment, and output. Additionally, the study confirms that LTV ratios can be a double-edged instrument, as excessive use can potentially destabilize the economy. [ABSTRACT FROM AUTHOR]

Shared frailty models are used despite their limitations. To overcome their disadvantages correlated frailty models may be used. In this paper, we introduce the correlated compound Poisson frailty models with two different baseline distributions namely, the generalized log logistic and the generalized Weibull. We introduce the Bayesian estimation procedure using Markov Chain Monte Carlo (MCMC) technique to estimate the parameters involved in these models. We present a simulation study to compare the true values of the parameters with the estimated values. Also we apply these models to a real life bivariate survival data set of McGilchrist and Aisbett (1991) related to the kidney infection data and a better model is suggested for the data. [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]