Product Spacing of Stress–Strength under Progressive Hybrid Censored for Exponentiated-Gumbel Distribution

Maximum product spacing for stress–strength model based on progressive Type-II hybrid censored samples with different cases has been obtained.This paper deals with estimation of the stress strength reliability model R=P(Y<X)when the stress and strength are two independent exponentiated Gumbel distribution random variables with different shape parameters but having the same scale parameter.The stress–strength reliability model is estimated under progressive Type-II hybrid censoring samples.Two progressive Type-II hybrid censoring schemes were used,Case I:A sample size of stress is the equal sample size of strength,and same time of hybrid censoring,the product of spacing function under progressive Type-II hybrid censoring schemes.Case II:The sample size of stress is a different sample size of strength,in which the life-testing experiment with a progressive censoring scheme is terminated at a random time T 2 e0;1T.The maximum likelihood estimation and maximum product spacing estimation methods under progressive Type-II hybrid censored samples for the stress strength model have been discussed.A comparison study with classical methods as the maximum likelihood estimation method is discussed.Furthermore,to compare the performance of various cases,Markov chain Monte Carlo simulation is conducted by using iterative procedures as Newton Raphson or conjugate-gradient procedures.Finally,two real datasets are analyzed for illustrative purposes,first data for the breaking strengths of jute fiber,and the second data for the waiting times before the service of the customers of two banks.

Kumaraswamy Inverted Topp–Leone Distribution with Applications to COVID-19 Data

In this paper, an attempt is made to discover the distributionof COVID-19 spread in different countries such as;Saudi Arabia, Italy,Argentina and Angola by specifying an optimal statistical distribution for analyzing the mortality rate of COVID-19. A new generalization of the recentlyinverted Topp Leone distribution, called Kumaraswamy inverted Topp–Leonedistribution, is proposed by combining the Kumaraswamy-G family and theinverted Topp–Leone distribution. We initially provide a linear representationof its density function. We give some of its structure properties, such as quantile function, median, moments, incomplete moments, Lorenz and Bonferronicurves, entropies measures and stress-strength reliability. Then, Bayesian andmaximum likelihood estimators for parameters of the Kumaraswamy invertedTopp–Leone distribution under Type-II censored sample are considered.Bayesian estimator is regarded using symmetric and asymmetric loss functions. As analytical solution is too hard, behaviours of estimates have beendone viz Monte Carlo simulation study and some reasonable comparisonshave been presented. The outcomes of the simulation study confirmed theefficiencies of obtained estimates as well as yielded the superiority of Bayesianestimate under adequate priors compared to the maximum likelihood estimate.Application to COVID-19 in some countries showed that the new distributionis more appropriate than some other competitive models.

Assessing the Performance of Some Ranked Set Sampling Designs Using Hybrid Approach

In this paper,a joint analysis consisting of goodness-of-fit tests and Markov chain Monte Carlo simulations are used to assess the performance of some ranked set sampling designs.The Markov chain Monte Carlo simulations are conducted when Bayesian methods with Jeffery’s priors of the unknown parameters of Weibull distribution are used,while the goodness of fit analysis is conducted when the likelihood estimators are used and the corresponding empirical distributions are obtained.The ranked set sampling designs considered in this research are the usual ranked set sampling,extreme ranked set sampling,median ranked set sampling,and neoteric ranked set sampling designs.An intensive Monte Carlo simulation study is conducted using Lindley’s approximation algorithm to compute the different designs’-based estimators.The study showed that the dependent design“neoteric ranked set sampling design”is superior to other ranked set designs and the total relative efficiency is higher than the other designs’total relative efficiency.

Bayesian and Non-Bayesian Analysis for the Sine Generalized Linear Exponential Model under Progressively Censored Data

This article introduces a novel variant of the generalized linear exponential(GLE)distribution,known as the sine generalized linear exponential(SGLE)distribution.The SGLE distribution utilizes the sine transformation to enhance its capabilities.The updated distribution is very adaptable and may be efficiently used in the modeling of survival data and dependability issues.The suggested model incorporates a hazard rate function(HRF)that may display a rising,J-shaped,or bathtub form,depending on its unique characteristics.This model includes many well-known lifespan distributions as separate sub-models.The suggested model is accompanied with a range of statistical features.The model parameters are examined using the techniques of maximum likelihood and Bayesian estimation using progressively censored data.In order to evaluate the effectiveness of these techniques,we provide a set of simulated data for testing purposes.The relevance of the newly presented model is shown via two real-world dataset applications,highlighting its superiority over other respected similar models.

Exponentiated Generalized Inverse Flexible Weibull Distribution:Bayesian and Non-Bayesian Estimation Under Complete and TypeⅡCensored Samples with Applications

In this paper,a new 4-parameter exponentiated generalized inverse flexible Weibull distribution is proposed.Some of its statistical properties are studied.The aim of this paper is to estimate the model parameters via several approaches,namely,maximum likelihood,maximum product spacing and Bayesian.According to Bayesian approach,several techniques are used to get the Bayesian estimators,namely,standard error function,Linex loss function and entropy loss function.The estimation herein is based on complete and censored samples.Markov Chain Monte Carlo simulation is used to discuss the behavior of the estimators for each approach.Finally,two real data sets are analyzed to obtain the flexibility of the proposed model.