This article deals with the classical and Bayesian estimation of model parameters of Chen distribution under multiple interval type-I censoring. For point estimation, maximum likelihood estimators are derived under the classical framework. Under the Bayesian framework Bayes estimators are constructed under three different loss functions: squared error loss function, linex loss function, and general entropy loss function under both informative and non-informative prior. For interval estimation of parameters three different types of intervals are constructed, asymptotic confidence interval, bootstrap confidence interval, and highest posterior density credible interval. The performance of all the considered estimators is evaluated through an extensive Monte Carlo simulation study. Finally, two real data sets from survival studies that documents graft survival times of 148 renal transplant patients and leukemia free-survival times for the 46 autologous transplant patients are considered and analyzed to illustrate the methodologies established in this paper.

In this paper, we consider the comparative analysis of Bayes and E-Bayes estimates for the newly developed exponential transformed inverse Rayleigh (ETIR) distribution under the symmetric and asymmetric loss function for the progressive Type-II censoring with binomial removals. The comparison between the proposed estimators have been drawn on the basis of the simulated risks. The study also examines the expected experiment time. The suitability of the model and proposed methodology have been through demonstrated using a precipitation data set.

ABSTRACT In this article, the generalized lifetime performance index (GLPI) is taken into consideration where the process distribution follows exponentiated exponential distribution. The different classical estimation procedures, namely, maximum likelihood estimation (MLE), least squares, weighted least squares, and maximum product spacing estimation (MPSE) methods have been discussed using progressively type‐II censored samples. Next, the Bayesian estimation of the considered index with gamma prior distribution has been derived using the symmetric as well as asymmetric loss functions. Further, the different parametric interval estimation techniques, namely, asymptotic confidence interval based on MLE and MPSE, bootstrap confidence intervals, and Bayes credible intervals have been obtained for the considered censoring schemes. Monte Carlo simulation study has been carried out to compare these estimators in terms of their mean squared errors and simulated posterior risks, respectively. Lastly, two real data sets have been re‐analyzed to illustrate applications of the proposed GLPI under progressively type‐II censored scheme.

In this article we propose E-Bayes and hierarchical Bayes (H-Bayes) estimators of the parameters of the exponentiated Rayleigh distribution under adaptive progressive hybrid Type-II censoring with binomial removals (APHT-II CBRs). The prior predictive distribution has been proposed as a method for the selection of hyperparameters value of the priors. The proposed estimators have been derived under scaled squared error loss function (S-SELF). The proposed estimators have been compared within the other obtained estimators (Bayes, E-Bayes and H-Bayes) estimators through their respective simulated risks. The applicability of the proposed estimators are verified via real data set (from medical).

In this paper, we proposed a new class of distributions by introducing a new constant in the existing model. We discuss general properties of the family such as density function, quantile function and hazard rate function. We then discuss a member of the family considering the exponential distribution as baseline distribution. Various properties of the model such as quantile function, moments, moment generating function, order statistics, stress-strength parameter, and mean residual life function are discussed. We also discussed the mean, variance, skewness and kurtosis of the proposed model numerically. The expression for Renyi and Shannon entropies are also derived. The different methods of estimation such as maximum likelihood estimation, maximum product spacing and least squares estimates are used for the estimation of the unknown parameters of the proposed distribution.. The simulation study is performed to study the behaviour of the estimates based on their mean squared errors. Lastly, we apply our proposed model to two real data sets.

This article aims to estimate the parameters and stress-strength reliability R = P(Y < X) based on the generalized progressive hybrid censored data when X and Y follow independent xgamma distributions with different scale parameters. The maximum likelihood estimators and asymptotic confidence intervals for parameters and stress-strength reliability R have been obtained based on both classical and Bayesian setups. The Bayes estimators for the model parameters and stress-strength reliability R are derived under the assumption of independent gamma prior using symmetric and asymmetric loss functions. The Markov chain Monte Carlo technique is employed for Bayesian computations due to the complexity of the posterior, which lacks a closed-form expression for Bayesian estimators. We have also computed the highest probability density credible intervals for the Bayes estimators. Additionally, a simulation study is conducted to study the effectiveness of Bayes and maximum likelihood estimators using mean squared errors. In the end, a real data set has been utilized for illustrative purposes.

The analysis of lifetime data under censoring schemes plays a vital role in reliability studies and survival analysis, where complete information is often difficult to obtain. This work focuses on the estimation of the parameters of the recently proposed generalized Kavya–Manoharan exponential (GKME) distribution under progressive Type-I interval censoring, a censoring scheme that frequently arises in medical and industrial life-testing experiments. Estimation procedures are developed under both classical and Bayesian paradigms, providing a comprehensive framework for inference. In the Bayesian setting, parameter estimation is carried out using Markov Chain Monte Carlo (MCMC) techniques under two distinct loss functions: the squared error loss function (SELF) and the general entropy loss function (GELF). For interval estimation, asymptotic confidence intervals as well as highest posterior density (HPD) credible intervals are constructed. The performance of the proposed estimators is systematically evaluated through a Monte Carlo simulation study in terms of mean squared error (MSE) and the average lengths of the interval estimates. The practical usefulness of the developed methodology is further demonstrated through the analysis of a real dataset on survival times of guinea pigs exposed to virulent tubercle bacilli. The findings indicate that the proposed methods provide flexible and efficient tools for analyzing progressively interval-censored lifetime data.

In this article, we introduce a weighted version of the Xgamma exponential distribution, extending its utility in modeling lifetime data. We derive several important distributional properties of the proposed model, including moments, residual life functions, generating functions, stochastic ordering, aging intensity, and entropy. These properties provide deeper insights into the behavior and structure of the proposed distribution. To estimate the model parameters, we discuss the maximum likelihood estimation approach, focusing on complete sample data. To demonstrate the practical applicability of the proposed distribution, we analyze two real-world lifetime data sets. The performance of the weighted Xgamma exponential distribution is compared with several well-established one- and two-parameter lifetime distributions, along with their weighted versions. Additionally, comparisons are made with length-biased and area-biased lifetime distributions to further assess the robustness of the proposed model. The results of these comparisons indicate that the proposed weighted distribution offers a superior fit, particularly for data sets exhibiting an increasing failure rate. The model’s ability to outperform competing distributions highlights its potential as an effective alternative for analyzing lifetime data in reliability and survival studies.

This article introduces a new method of generating distributions by leveraging the concept of generalization with the hope of achieving more flexibility and greater adaptability. As a baseline distribution, we have considered a one-parameter exponential distribution. Along with studying the behavior of hazard rate, we have explored various statistical characteristics of the proposed distribution. For estimating model parameters we have employed the method of maximum likelihood estimation. To check the empirical validation of estimators obtained, the Monte Carlo simulation technique has been used. To show the model’s flexibility and competency, we have conducted a real data analysis using three real data sets and compared its performance with some widely used existing distributions.

In this article, we propose a Poisson-Lindley distribution as a stochastic abundance model in which the sample is according to the independent Poisson process. Jeffery’s and Bernardo’s reference priors have been obtaining and proposed the Bayes estimators of the number of species for this model. The proposed Bayes estimators have been compared with the corresponding profile and conditional maximum likelihood estimators for their square root of the risks under squared error loss function (SELF). Jeffery’s and Bernardo’s reference priors have been considered and compared with the Bayesian approach based on biological data.

This article carefully defines a multiple interval censoring plan, and its scope of application in the Bayesian setup is demonstrated. The Bayes estimators of shape and scale parameters of the exponentiated exponential distribution are obtained under symmetric and asymmetric loss functions. Additionally, the credible intervals for both parameters are obtained. The performances of Bayes estimators and credible intervals are investigated through the appropriate Monte Carlo method. Furthermore, the authors also considered the prediction of future samples as well as the prediction interval. Lastly, a real-world example is presented in order to illustrate the effectiveness of the proposed methods.

In this article, we propose E-Bayes estimators of the parameter of xgamma distribution under squared error loss function, general entropy loss function, and linear exponential loss function for progressive type II censored data with binomial removals. The proposed estimators, maximum likelihood estimator, and corresponding Bayes estimators are compared in terms of their risks based on simulated samples from xgamma distribution. The proposed methodology is illustrated on two real data sets of bile duct cancer data and the endurance of deep-groove ball bearings data.

In this paper, we propose a new three-parameter lifetime distribution, which has increasing, decreasing and constant failure rate. The new distribution can be use on a latent complementary risk scenario. The properties of the proposed distribution are discussed, including a formal proof of its density function and an explicit algebraic formula for its quantiles, skewness, kurtosis, survival and hazard functions. Also, we have been discussed inference aspects of the model proposed via Bayesian inference by using Markov chain Monte Carlo simulation. A simulation study performed in order to investigate the classical, Bayesian properties of the proposed estimators obtained under the assumptions of non-informative priors. Further, the applicability of proposed distribution is illustrated on a real data set.

In this present work, we are going to show the various useful properties of the existing distribution known as MG(Exp)(epsilon)-distribution which have not quoted by the host authors like moments, mean deviation about mean, mean deviation about median, order statistics, count of uncertainty. Estimation procedures have been adopted under Bayesian estimation for progressive Type-II censored case. Simulation study has also been carried out to judge the behavior of the Bayes estimator at the long-run. Performance of the Bayes estimators and their posterior risks of the considered loss functions have been obtained, reported and compared for the considered values of sample size, effective sample size, parameter and removals. The comparison of Bayes estimators of all 6 chosen loss functions have been done on the ground of lowest posterior risks.

In this paper, we have introduced a new type of censoring scheme named the multiple interval type-I censoring scheme. Further, We have assumed that the test units are drawn from the Weibull population. We have also proposed the maximum product of spacing estimators for unknown parameters under the multiple interval type-I censoring scheme and compare them with the existing maximum likelihood estimators. In addition to this, the Bayes estimators for shape and scale parameters are also obtained under the squared error loss function. Their corresponding asymptotic confidence/credible intervals are also discussed. A real data set containing the breakdown time of insulating fluids are used to demonstrate the appropriateness of the proposed methodology.

In this article, we propose Bayes estimators for the parameters of the Predator-Prey model using non-informative priors. The population dynamics are described by a system of functional response of the Stochastic Predator-Prey model. The Bayes estimators and simulated risk of the parameters are obtained under symmetric loss functions. The efficiency of the proposed estimators is compared through simulated risks (average loss over sample space).

The article addresses the problem of parameter estimation of the inverse Lindley distribution when the observations are fuzzy. The estimation of the unknown model parameter was performed using both classical and Bayesian methods. In the classical approach, the estimation of the population parameter is performed using the maximum likelihood (ML) method and the maximum product of distances (MPS) method. In the Bayesian setup, the estimation is obtained using the squared error loss function (SELF) with the Markov Chain Monte Carlo (MCMC) technique. Asymptotic confidence intervals and highest posterior density (HPD) credible intervals for the unknown parameter are also obtained. The performances of the estimators are compared based on their MSEs. Finally, a real data set is analyzed for numerical illustration of the above estimation methods.

Predicting the dynamics of COVID-19 cases is imperative to enhance the health care system’s capacity, monitor the effects of policy interventions, and control the transmission. With this view, this paper examines the transmission process of the COVID-19 employing three types of confirmed, deceased, and recovered cases in Uttar Pradesh, India. We demonstrated an approach that has the power to sufficiently predict the number of confirmed, deceased, and recovered cases of COVID-19 in the near future, given the past occurrences. We used the logistic and Gompertz non-linear regression model under the Bayesian setup. In this regard, we built the prior distribution of the model using information obtained from some other states of India, which have already reached the advanced stage of COVID-19. This analysis did not consider any changes in government control measures.

This article deals with the estimation problem in step-stress partially accelerated life test of Maxwell Boltzmann distribution in presence of progressive type-II censoring with binomial removals. The maximum likelihood and Bayes estimators of the parameter are obtained under symmetric and asymmetric loss functions. Furthermore, the performances of the obtained estimators are compared in terms of risks. The proposed methodology is illustrated through the time to failure (in days) of Aluminium reduction cells and survival times (in weeks) for male rats that were exposed to a high level of radiation.