scholarly journals Estimation for Entropy and Parameters of Generalized Bilal Distribution under Adaptive Type II Progressive Hybrid Censoring Scheme

Entropy ◽  
2021 ◽  
Vol 23 (2) ◽  
pp. 206
Author(s):  
Xiaolin Shi ◽  
Yimin Shi ◽  
Kuang Zhou
Keyword(s):  
Monte Carlo ◽  
Likelihood Estimation ◽  
Real Data ◽  
Random Variable ◽  
Credible Interval ◽  
Mcmc Methods ◽  
Type Ii ◽  
Data Set ◽  
Lindley’S Approximation ◽  
Bayesian Estimations

Entropy measures the uncertainty associated with a random variable. It has important applications in cybernetics, probability theory, astrophysics, life sciences and other fields. Recently, many authors focused on the estimation of entropy with different life distributions. However, the estimation of entropy for the generalized Bilal (GB) distribution has not yet been involved. In this paper, we consider the estimation of the entropy and the parameters with GB distribution based on adaptive Type-II progressive hybrid censored data. Maximum likelihood estimation of the entropy and the parameters are obtained using the Newton–Raphson iteration method. Bayesian estimations under different loss functions are provided with the help of Lindley’s approximation. The approximate confidence interval and the Bayesian credible interval of the parameters and entropy are obtained by using the delta and Markov chain Monte Carlo (MCMC) methods, respectively. Monte Carlo simulation studies are carried out to observe the performances of the different point and interval estimations. Finally, a real data set has been analyzed for illustrative purposes.

scholarly journals The Weibull Generalized Exponential Distribution with Censored Sample: Estimation and Application on Real Data

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Hisham M. Almongy ◽  
Ehab M. Almetwally ◽  
Randa Alharbi ◽  
Dalia Alnagar ◽  
E. H. Hafez ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Exponential Distribution ◽  
Estimation Method ◽  
Interval Estimation ◽  
Likelihood Estimation ◽  
Real Data ◽  
Mcmc Methods ◽  
Generalized Exponential Distribution ◽  
Censored Sample ◽  
Sample Maximum

This paper is concerned with the estimation of the Weibull generalized exponential distribution (WGED) parameters based on the adaptive Type-II progressive (ATIIP) censored sample. Maximum likelihood estimation (MLE), maximum product spacing (MPS), and Bayesian estimation based on Markov chain Monte Carlo (MCMC) methods have been determined to find the best estimation method. The Monte Carlo simulation is used to compare the three methods of estimation based on the ATIIP-censored sample, and also, we made a bootstrap confidence interval estimation. We will analyze data related to the distribution about single carbon fiber and electrical data as real data cases to show how the schemes work in practice.

scholarly journals A Mixture of Inverse Weibull and Inverse Burr Distributions: Properties, Estimation, and Fitting

2017 ◽  
Vol 2017 ◽  
pp. 1-11
Author(s):  
A. S. Al-Moisheer ◽  
K. S. Sultan ◽  
M. A. Al-Shehri
Keyword(s):  
Mixture Model ◽  
Classical Method ◽  
Likelihood Estimation ◽  
Real Data ◽  
Probability Density Functions ◽  
Density Functions ◽  
Data Set ◽  
Burr Distributions ◽  
Lindley’S Approximation ◽  
Rate Functions

The new mixture model of the two components of the inverse Weibull and inverse Burr distributions (MIWIBD) is proposed. First, the properties of the investigated mixture model are introduced and the behaviors of the probability density functions and hazard rate functions are displayed. Then, the estimates of the five-dimensional vector of parameters by using the classical method such as the maximum likelihood estimation (MLEs) and the approximation method by using Lindley’s approximation are obtained. Finally, a real data set for the proposed mixture model is applied to illustrate the proposed mixture model.

scholarly journals A Study of Perks-II Distribution via Bayesian Paradigm

Pravaha ◽  
2018 ◽  
Vol 24 (1) ◽  
pp. 1-17
Author(s):  
A. K. Chaudhary
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Bayesian Analysis ◽  
Real Data ◽  
Simulation Method ◽  
Mcmc Methods ◽  
Data Set ◽  
Bayesian Paradigm ◽  
Mcmc Simulation

In this paper, the Markov chain Monte Carlo (MCMC) method is used to estimate the parameters of Perks-II distribution based on a complete sample. The procedures are developed to perform full Bayesian analysis of the Perks-II distributions 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 also discussed the issue of model compatibility for the given data set. A real data set is considered for illustration under gamma sets of priors.PravahaVol. 24, No. 1, 2018,page: 1-17 

A bivariate Pareto type I models

2017 ◽  
Vol 5 (1) ◽  
pp. 44
Author(s):  
Mervat Abd Elaal ◽  
Hind Alzahrani
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Maximum Likelihood ◽  
Simulation Study ◽  
Real Data ◽  
Type I ◽  
Data Set ◽  
Monte Carlo Simulation Study ◽  
Bayesian Estimations

In this paper two new bivariate Pareto Type I distributions are introduced. The first distribution is based on copula, and the second distribution is based on mixture of and copula. Maximum likelihood and Bayesian estimations are used to estimate the parameters of the proposed distribution. A Monte Carlo Simulation study is carried out to study the behavior of the proposed distributions. A real data set is analyzed to illustrate the performance and flexibility of the proposed distributions.

scholarly journals Bayesian Analysis of Two Parameter Complementary Exponential Power Distribution

NCC Journal ◽  
2018 ◽  
Vol 3 (1) ◽  
pp. 1-23
Author(s):  
A. K. Chaudhary
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Bayesian Analysis ◽  
Power Distribution ◽  
Real Data ◽  
Mcmc Methods ◽  
Output Analysis ◽  
Data Set ◽  
Exponential Power Distribution

In this paper, the Markov chain Monte Carlo (MCMC) method is used to estimate the parameters of CEP distribution based on a complete sample. A procedure is developed to obtain Bayes estimates of the parameters of the CEP distribution using Markov Chain Monte Carlo (MCMC) simulation method in OpenBUGS, established software for Bayesian analysis using Markov Chain Monte Carlo (MCMC) methods. The MCMC methods have been shown to be easier to implement computationally, the estimates always exist and are statistically consistent, and their probability intervals are convenient to construct. The R functions are developed to study the statistical properties, model validation and comparison tools of the distribution and the output analysis of MCMC samples generated from OpenBUGS. A real data set is considered for illustration under uniform and gamma sets of priors. NCC Journal Vol. 3, No. 1, 2018,   Page: 1-23

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.  

Type II Half Logistic Linear Failure Rate Distribution with Application

2020 ◽  
Vol 17 (7) ◽  
pp. 2912-2917
Author(s):  
Maha A. Aldahlan
Keyword(s):  
Failure Rate ◽  
Probability Distributions ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Real Data ◽  
Model Parameters ◽  
Type Ii ◽  
Data Set ◽  
Rate Distribution ◽  
New Distribution

In recent years, several of new improved probability distributions have been discovered from the current distributions to facilitate their applications in various areas. A new three-parameter model extended from the linear failure rate model, the so called the type II half logistic linear failure rate distribution. Some mathematical properties of the new distribution are proposed. Explicit expressions for the moments, probability weighted moments and order statistics are calculated. Maximum likelihood estimation method is assessed to estimate the model parameters are presented. The superiority of the new distribution is illustrated with an application to one real data set.

scholarly journals Bayesian and E-Bayesian Estimations of Bathtub-Shaped Distribution under Generalized Type-I Hybrid Censoring

Entropy ◽  
2021 ◽  
Vol 23 (8) ◽  
pp. 934
Author(s):  
Yuxuan Zhang ◽  
Kaiwei Liu ◽  
Wenhao Gui
Keyword(s):  
Bayesian Method ◽  
Real Data ◽  
Loss Functions ◽  
Type I ◽  
Statistical Efficiency ◽  
Unknown Parameters ◽  
Data Set ◽  
Hybrid Censoring ◽  
Bayesian Estimations ◽  
Generalized Type

For the purpose of improving the statistical efficiency of estimators in life-testing experiments, generalized Type-I hybrid censoring has lately been implemented by guaranteeing that experiments only terminate after a certain number of failures appear. With the wide applications of bathtub-shaped distribution in engineering areas and the recently introduced generalized Type-I hybrid censoring scheme, considering that there is no work coalescing this certain type of censoring model with a bathtub-shaped distribution, we consider the parameter inference under generalized Type-I hybrid censoring. First, estimations of the unknown scale parameter and the reliability function are obtained under the Bayesian method based on LINEX and squared error loss functions with a conjugate gamma prior. The comparison of estimations under the E-Bayesian method for different prior distributions and loss functions is analyzed. Additionally, Bayesian and E-Bayesian estimations with two unknown parameters are introduced. Furthermore, to verify the robustness of the estimations above, the Monte Carlo method is introduced for the simulation study. Finally, the application of the discussed inference in practice is illustrated by analyzing a real data set.

scholarly journals Transformation of circular random variables based on circular distribution functions

Filomat ◽  
2018 ◽  
Vol 32 (17) ◽  
pp. 5931-5947
Author(s):  
Hatami Mojtaba ◽  
Alamatsaz Hossein
Keyword(s):  
Distribution Function ◽  
Random Variables ◽  
Real Data ◽  
Random Variable ◽  
Distribution Functions ◽  
Likelihood Method ◽  
Circular Distribution ◽  
Data Set ◽  
Trigonometric Moments ◽  
Von Mises

In this paper, we propose a new transformation of circular random variables based on circular distribution functions, which we shall call inverse distribution function (id f ) transformation. We show that M?bius transformation is a special case of our id f transformation. Very general results are provided for the properties of the proposed family of id f transformations, including their trigonometric moments, maximum entropy, random variate generation, finite mixture and modality properties. In particular, we shall focus our attention on a subfamily of the general family when id f transformation is based on the cardioid circular distribution function. Modality and shape properties are investigated for this subfamily. In addition, we obtain further statistical properties for the resulting distribution by applying the id f transformation to a random variable following a von Mises distribution. In fact, we shall introduce the Cardioid-von Mises (CvM) distribution and estimate its parameters by the maximum likelihood method. Finally, an application of CvM family and its inferential methods are illustrated using a real data set containing times of gun crimes in Pittsburgh, Pennsylvania.

scholarly journals Estimation of Multicomponent Reliability Based on Progressively Type II Censored Data from Unit Weibull Distribution

2021 ◽  
Vol 20 ◽  
pp. 288-299
Author(s):  
Refah Mohammed Alotaibi ◽  
Yogesh Mani Tripathi ◽  
Sanku Dey ◽  
Hoda Ragab Rezk
Keyword(s):  
Information Matrix ◽  
Credible Interval ◽  
Estimation Methods ◽  
Type Ii ◽  
Parametric Function ◽  
Data Set ◽  
Common Parameter ◽  
Bayesian Procedures ◽  
Mh Algorithm ◽  
Type Ii Censored Data

In this paper, inference upon stress-strength reliability is considered for unit-Weibull distributions with a common parameter under the assumption that data are observed using progressive type II censoring. We obtain di_erent estimators of system reliability using classical and Bayesian procedures. Asymptotic interval is constructed based on Fisher information matrix. Besides, boot-p and boot-t intervals are also obtained. We evaluate Bayes estimates using Lindley's technique and Metropolis-Hastings (MH) algorithm. The Bayes credible interval is evaluated using MH method. An unbiased estimator of this parametric function is also obtained under know common parameter case. Numerical simulations are performed to compare estimation methods. Finally, a data set is studied for illustration purposes.

Sign in / Sign up

Export Citation Format

Share Document