scholarly journals Inverted Topp-Leone Distribution: Contribution to a Family of J-Shaped Frequency Functions in Presence of Random Censoring

2021 ◽  
Author(s):  
Hiba Zeyada Muhammed ◽  
Essam Abd Elsalam Muhammed
Keyword(s):  
Monte Carlo ◽  
Real Data ◽  
Posterior Density ◽  
Data Set ◽  
Bayes Estimates ◽  
Squared Error ◽  
Distribution Shape ◽  
Highest Posterior Density Intervals ◽  
Metropolis Hasting Algorithm ◽  
Highest Posterior Density

In this paper, Bayesian and non-Bayesian estimation of the inverted Topp-Leone distribution shape parameter are studied when the sample is complete and random censored. The maximum likelihood estimator (MLE) and Bayes estimator of the unknown parameter are proposed. The Bayes estimates (BEs) have been computed based on the squared error loss (SEL) function and using Markov Chain Monte Carlo (MCMC) techniques. The asymptotic, bootstrap (p,t), and highest posterior density intervals are computed. The Metropolis Hasting algorithm is proposed for Bayes estimates. Monte Carlo simulation is performed to compare the performances of the proposed methods and one real data set has been analyzed for illustrative purposes.

scholarly journals Inferences for Weibull parameters under progressively first-failure censored data with binomial random removals

2020 ◽  
Vol 9 (1) ◽  
pp. 47-60
Author(s):  
Samir K. Ashour ◽  
Ahmed A. El-Sheikh ◽  
Ahmed Elshahhat
Keyword(s):  
Monte Carlo ◽  
Censored Data ◽  
Real Data ◽  
Unknown Parameters ◽  
Data Set ◽  
Monte Carlo Simulation Study ◽  
Squared Error Loss Function ◽  
Bayes Estimates ◽  
Monte Carlo Techniques ◽  
Credible Intervals

In this paper, the Bayesian and non-Bayesian estimation of a two-parameter Weibull lifetime model in presence of progressive first-failure censored data with binomial random removals are considered. Based on the s-normal approximation to the asymptotic distribution of maximum likelihood estimators, two-sided approximate confidence intervals for the unknown parameters are constructed. Using gamma conjugate priors, several Bayes estimates and associated credible intervals are obtained relative to the squared error loss function. Proposed estimators cannot be expressed in closed forms and can be evaluated numerically by some suitable iterative procedure. A Bayesian approach is developed using Markov chain Monte Carlo techniques to generate samples from the posterior distributions and in turn computing the Bayes estimates and associated credible intervals. To analyze the performance of the proposed estimators, a Monte Carlo simulation study is conducted. Finally, a real data set is discussed for illustration purposes.

scholarly journals Parametric inference of Akash distribution for Type-Ⅱ censoring with analyzing of relief times of patients

2021 ◽  
Vol 6 (10) ◽  
pp. 10789-10801
Author(s):  
Tahani A. Abushal ◽  
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Bayesian Inference ◽  
Unknown Parameter ◽  
Maximum Likelihood Estimators ◽  
Real Data ◽  
Posterior Density ◽  
Monte Carlo Simulation Study ◽  
Reliability Characteristics ◽  
Highest Posterior Density

<abstract><p>In this paper, the problem of estimating the parameter of Akash distribution applied when the lifetime of the product follow Type-Ⅱ censoring. The maximum likelihood estimators (MLE) are studied for estimating the unknown parameter and reliability characteristics. Approximate confidence interval for the parameter is derived under the s-normal approach to the asymptotic distribution of MLE. The Bayesian inference procedures have been developed under the usual error loss function through Lindley's technique and Metropolis-Hastings algorithm. The highest posterior density interval is developed by using Metropolis-Hastings algorithm. Finally, the performances of the different methods have been compared through a Monte Carlo simulation study. The application to set of real data is also analyzed using proposed methods.</p></abstract>

scholarly journals Quantifying partial migration with sex-ratio balancing

2019 ◽  
Vol 97 (4) ◽  
pp. 352-361 ◽  
Author(s):  
Haley A. Ohms ◽  
Alix I. Gitelman ◽  
Chris E. Jordan ◽  
Dave A. Lytle
Keyword(s):  
Sex Ratio ◽  
Oncorhynchus Tshawytscha ◽  
Population Based ◽  
Partial Migration ◽  
Ecosystem Dynamics ◽  
Posterior Density ◽  
Data Set ◽  
Animal Populations ◽  
Highest Posterior Density Intervals ◽  
Highest Posterior Density

Partial migration, the phenomenon in which animal populations are composed of both migratory and nonmigratory individuals, is widespread among migrating animals. The proportion of migrants in these populations has direct influences on population genetics and dynamics, ecosystem dynamics, mating systems, evolution, and responses to environmental change, yet there are very few studies that measure the proportion of migrants. This is because existing methods to estimate the proportion of migrants are time-consuming and expensive. In this paper, we demonstrate a new method for estimating the proportion of migrants in a population based on sex ratio measurements. Many partially migratory taxa exhibit sex-biased migration or residency, and in these cases, the sex ratios of migrants and nonmigrants are fundamentally related to the proportion of migrants in the population. We define this relationship quantitatively and show how it can be used to infer the proportion of migrants in a population through a process we term “sex-ratio balancing”. We obtain Bayesian estimates of proportion of migrants and quantify the uncertainty in these estimates with highest posterior density intervals. Lastly, we validate the sex-ratio balancing approach with a Chinook salmon (Oncorhynchus tshawytscha Walbaum in Artedi, 1792) data set. Sex-ratio balancing holds promise as a tool for quantifying partial migration and filling a key data gap about partially migratory taxa.

scholarly journals Statistical Inferences of Type-II Progressively Hybrid Censored Fuzzy Data with Rayleigh Distribution

2018 ◽  
Vol 47 (3) ◽  
pp. 40-62 ◽  
Author(s):  
Ankita Chaturvedi ◽  
Sanjay Kumar Singh ◽  
Umesh Singh
Keyword(s):  
Real Data ◽  
Rayleigh Distribution ◽  
Model Parameters ◽  
Type Ii ◽  
Posterior Density ◽  
Numerical Illustration ◽  
Data Set ◽  
Bayesian Procedures ◽  
Credible Intervals ◽  
Highest Posterior Density

This article presents the procedures for the estimation of the parameter of Rayleighdistribution based on Type-II progressive hybrid censored fuzzy lifetime data. Classicalas well as the Bayesian procedures for the estimation of unknown model parameters has been developed. The estimators obtained here are Maximum likelihood (ML) estimator, Method of moments (MM) estimator, Computational approach (CA) estimator and Bayes estimator. Highest posterior density (HPD) credible intervals of the unknown parameter are obtained by using Markov Chain Monte Carlo (MCMC) technique. For numerical illustration, a real data set has been considered.

scholarly journals Statistical Inference of the Lifetime Performance Index with the Log-Logistic Distribution Based on Progressive First-Failure-Censored Data

Symmetry ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 937 ◽  
Author(s):  
Ying Xie ◽  
Wenhao Gui
Keyword(s):  
Censored Data ◽  
Performance Index ◽  
Manufacturing Industry ◽  
Interval Estimation ◽  
Real Data ◽  
Logistic Distribution ◽  
Posterior Density ◽  
Data Set ◽  
Lifetime Performance ◽  
Highest Posterior Density

Estimating the accurate evaluation of product lifetime performance has always been a hot topic in manufacturing industry. This paper, based on the lifetime performance index, focuses on its evaluation when a lower specification limit is given. The progressive first-failure-censored data we discuss have a common log-logistic distribution. Both Bayesian and non-Bayesian method are studied. Bayes estimator of the parameters of the log-logistic distribution and the lifetime performance index are obtained using both the Lindley approximation and Monte Carlo Markov Chain methods under symmetric and asymmetric loss functions. As for interval estimation, we apply the maximum likelihood estimator to construct the asymptotic confidence intervals and the Metropolis–Hastings algorithm to establish the highest posterior density credible intervals. Moreover, we analyze a real data set for demonstrative purposes. In addition, different criteria for deciding the optimal censoring scheme have been studied.

scholarly journals Statistical Inference on the Shannon Entropy of Inverse Weibull Distribution under the Progressive First-Failure Censoring

Entropy ◽  
2019 ◽  
Vol 21 (12) ◽  
pp. 1209
Author(s):  
Jiao Yu ◽  
Wenhao Gui ◽  
Yuqi Shan
Keyword(s):  
Weibull Distribution ◽  
Importance Sampling ◽  
Complex Form ◽  
Real Data ◽  
Sampling Procedure ◽  
Posterior Density ◽  
Data Set ◽  
Importance Sampling Method ◽  
Inverse Weibull Distribution ◽  
Highest Posterior Density

Entropy is an uncertainty measure of random variables which mathematically represents the prospective quantity of the information. In this paper, we mainly focus on the estimation for the parameters and entropy of an Inverse Weibull distribution under progressive first-failure censoring using classical (Maximum Likelihood) and Bayesian methods. For Bayesian approaches, the Bayesian estimates are obtained based on both asymmetric (General Entropy, Linex) and symmetric (Squared Error) loss functions. Due to the complex form of Bayes estimates, we cannot get an explicit solution. Therefore, the Lindley method as well as Importance Sampling procedure is applied. Furthermore, using Importance Sampling method, the Highest Posterior Density credible intervals of entropy are constructed. As a comparison, the asymptotic intervals of entropy are also gained. Finally, a simulation study is implemented and a real data set analysis is performed to apply the previous methods.

scholarly journals A Bayesian Estimation and Predictionof Gompertz Extension Distribution Using the MCMC Method

2020 ◽  
Vol 19 (1) ◽  
pp. 142-160
Author(s):  
Arun Kumar Chaudhary ◽  
Vijay Kumar
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Real Data ◽  
Simulation Method ◽  
Mcmc Methods ◽  
Mcmc Method ◽  
Data Set ◽  
Bayes Estimates ◽  
Check Method

 In this paper, the Markov chain Monte Carlo (MCMC) method is used to estimate the parameters of the Gompertz extension distribution based on a complete sample. We have developed a procedure to obtain Bayes estimates of the parameters of the Gompertz extension distribution using Markov Chain Monte Carlo (MCMC) simulation method in OpenBUGS, established software for Bayesian analysis using Markov Chain Monte Carlo (MCMC) methods. We have obtained the Bayes estimates of the parameters, hazard and reliability functions, and their probability intervals are also presented. We have applied the predictive check method to discuss the issue of model compatibility. A real data set is considered for illustration under uniform and gamma priors.  

Markov Chain Monte Carlo-Based Estimation of Stress–Strength Reliability Parameter for Generalized Linear Failure Rate Distributions

2021 ◽  
pp. 2150031
Author(s):  
F. Shahsanaei ◽  
A. Daneshkhah
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Failure Rate ◽  
Interval Estimate ◽  
Reliability Parameter ◽  
Bayes Estimates ◽  
Squared Error ◽  
Classical Inference ◽  
Strength Models

This paper provides Bayesian and classical inference of Stress–Strength reliability parameter, [Formula: see text], where both [Formula: see text] and [Formula: see text] are independently distributed as 3-parameter generalized linear failure rate (GLFR) random variables with different parameters. Due to importance of stress–strength models in various fields of engineering, we here address the maximum likelihood estimator (MLE) of [Formula: see text] and the corresponding interval estimate using some efficient numerical methods. The Bayes estimates of [Formula: see text] are derived, considering squared error loss functions. Because the Bayes estimates could not be expressed in closed forms, we employ a Markov Chain Monte Carlo procedure to calculate approximate Bayes estimates. To evaluate the performances of different estimators, extensive simulations are implemented and also real datasets are analyzed.

scholarly journals Estimating the Entropy for Lomax Distribution Based on Generalized Progressively Hybrid Censoring

Symmetry ◽  
2019 ◽  
Vol 11 (10) ◽  
pp. 1219 ◽  
Author(s):  
Shuhan Liu ◽  
Wenhao Gui
Keyword(s):  
Incomplete Data ◽  
Real Data ◽  
Unknown Parameters ◽  
Data Set ◽  
Hybrid Censoring ◽  
Lomax Distribution ◽  
Bayesian Estimates ◽  
Squared Error ◽  
General Entropy Loss Function ◽  
Two Parameter

As it is often unavoidable to obtain incomplete data in life testing and survival analysis, research on censoring data is becoming increasingly popular. In this paper, the problem of estimating the entropy of a two-parameter Lomax distribution based on generalized progressively hybrid censoring is considered. The maximum likelihood estimators of the unknown parameters are derived to estimate the entropy. Further, Bayesian estimates are computed under symmetric and asymmetric loss functions, including squared error, linex, and general entropy loss function. As we cannot obtain analytical Bayesian estimates directly, the Lindley method and the Tierney and Kadane method are applied. A simulation study is conducted and a real data set is analyzed for illustrative purposes.

scholarly journals Estimation of Generalized Gompertz Distribution Parameters under Ranked-Set Sampling

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Mohammed Obeidat ◽  
Amjad Al-Nasser ◽  
Amer I. Al-Omari
Keyword(s):  
Monte Carlo ◽  
Real Data ◽  
Small Samples ◽  
Simple Random Sample ◽  
Unknown Parameters ◽  
Bayesian Approaches ◽  
Bayes Estimates ◽  
Gompertz Distribution ◽  
Distribution Parameters ◽  
Credible Intervals

This paper studies estimation of the parameters of the generalized Gompertz distribution based on ranked-set sample (RSS). Maximum likelihood (ML) and Bayesian approaches are considered. Approximate confidence intervals for the unknown parameters are constructed using both the normal approximation to the asymptotic distribution of the ML estimators and bootstrapping methods. Bayes estimates and credible intervals of the unknown parameters are obtained using differential evolution Markov chain Monte Carlo and Lindley’s methods. The proposed methods are compared via Monte Carlo simulations studies and an example employing real data. The performance of both ML and Bayes estimates is improved under RSS compared with simple random sample (SRS) regardless of the sample size. Bayes estimates outperform the ML estimates for small samples, while it is the other way around for moderate and large samples.

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