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 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 Inference of stress-strength reliability for two-parameter of exponentiated Gumbel distribution based on lower record values

PLoS ONE ◽  
2021 ◽  
Vol 16 (4) ◽  
pp. e0249028
Author(s):  
Ehsan Fayyazishishavan ◽  
Serpil Kılıç Depren
Keyword(s):  
Information Matrix ◽  
Gumbel Distribution ◽  
Sampling Technique ◽  
Real Data ◽  
Record Values ◽  
Unknown Parameters ◽  
Data Set ◽  
Credible Intervals ◽  
Lower Records ◽  
Two Parameter

The two-parameter of exponentiated Gumbel distribution is an important lifetime distribution in survival analysis. This paper investigates the estimation of the parameters of this distribution by using lower records values. The maximum likelihood estimator (MLE) procedure of the parameters is considered, and the Fisher information matrix of the unknown parameters is used to construct asymptotic confidence intervals. Bayes estimator of the parameters and the corresponding credible intervals are obtained by using the Gibbs sampling technique. Two real data set is provided to illustrate the proposed methods.

scholarly journals Bound lengths for type-I progressive hybrid burr type-XII censored data under SS-PALT

2021 ◽  
Vol 10 (1) ◽  
pp. 4-22
Author(s):  
Gyan Prakash
Keyword(s):  
Confidence Intervals ◽  
Asymptotic Variance ◽  
Real Data ◽  
Accelerated Life Test ◽  
Type I ◽  
Unknown Parameters ◽  
Data Set ◽  
Ml Estimation ◽  
Hybrid Censoring ◽  
Burr Type Xii

Our main focus on combining two different approaches, Step-Stress Partially Accelerated Life Test and Type-I Progressive Hybrid censoring criteria in the present article. The fruitfulness of this combination has been investigated by bound lengths for unknown parameters of the Burr Type-XII distribution. Approximate confidence intervals, Bootstrap confidence intervals and One-Sample Bayes prediction bound lengths have been obtained under the above scenario. Particular cases of Type-I Progressive Hybrid censoring (Type-I and Progressive Type-II censoring) has also evaluated under SS-PALT. Optimal stress change time also measured by minimizing the asymptotic variance of ML Estimation. A simulation study based on Metropolis-Hastings algorithm have carried out along with a real data set example.

scholarly journals Bayesian Inference for the Kumaraswamy Distribution under Generalized Progressive Hybrid Censoring

Entropy ◽  
2020 ◽  
Vol 22 (9) ◽  
pp. 1032
Author(s):  
Jiayi Tu ◽  
Wenhao Gui
Keyword(s):  
Real Life ◽  
Unknown Parameters ◽  
Simulation Research ◽  
Kumaraswamy Distribution ◽  
Hybrid Censoring ◽  
Bayesian Estimates ◽  
Squared Error ◽  
Linex Loss ◽  
Lindley Approximation ◽  
Censoring Scheme

Incomplete data are unavoidable for survival analysis as well as life testing, so more and more researchers are beginning to study censoring data. This paper discusses and considers the estimation of unknown parameters featured by the Kumaraswamy distribution on the condition of generalized progressive hybrid censoring scheme. Estimation of reliability is also considered in this paper. To begin with, the maximum likelihood estimators are derived. In addition, Bayesian estimators under not only symmetric but also asymmetric loss functions, like general entropy, squared error as well as linex loss function, are also offered. Since the Bayesian estimates fail to be of explicit computation, Lindley approximation, as well as the Tierney and Kadane method, is employed to obtain the Bayesian estimates. A simulation research is conducted for the comparison of the effectiveness of the proposed estimators. A real-life example is employed for illustration.

scholarly journals Pareto Distribution under Hybrid Censoring: Some Estimation

2021 ◽  
Vol 19 (1) ◽  
pp. 2-17
Author(s):  
Gyan Prakash
Keyword(s):  
Pareto Distribution ◽  
Simulated Data ◽  
Likelihood Estimation ◽  
Real Data ◽  
Loss Functions ◽  
Bayes Estimators ◽  
Unknown Parameters ◽  
Data Set ◽  
Hybrid Censoring ◽  
Pareto Model

In the present study, the Pareto model is considered as the model from which observations are to be estimated using a Bayesian approach. Properties of the Bayes estimators for the unknown parameters have studied by using different asymmetric loss functions on hybrid censoring pattern and their risks have compared. The properties of maximum likelihood estimation and approximate confidence length have also been investigated under hybrid censoring. The performances of the procedures are illustrated based on simulated data obtained under the Metropolis-Hastings algorithm and a real data set.

scholarly journals Bivariate Compound Exponentiated Survival Function of the Lomax Distribution: Estimation and Prediction

2021 ◽  
pp. 163-184
Author(s):  
R. M. Refaey ◽  
G. R. AL-Dayian ◽  
A. A. EL-Helbawy ◽  
A. A. EL-Helbawy
Keyword(s):  
Survival Function ◽  
Real Life ◽  
Likelihood Estimation ◽  
Real Data ◽  
Bivariate Distribution ◽  
Data Set ◽  
Squared Error Loss Function ◽  
Lomax Distribution ◽  
Estimation And Prediction ◽  
Squared Error

In this paper, bivariate compound exponentiated survival function of the Lomax distribution is constructed based on the technique considered by AL-Hussaini (2011). Some properties of the distribution are derived. Maximum likelihood estimation and prediction of the future observations are considered. Also, Bayesian estimation and prediction are studied under squared error loss function. The performance of the proposed bivariate distribution is examined using a simulation study. Finally, a real data set is analyzed under the proposed distribution to illustrate its flexibility for real-life application.

EXPONENTIATED HALF-LOGISTIC LOMAX DISTRIBUTION WITH PROPERTIES AND APPLICATION

2019 ◽  
Vol XVI (2) ◽  
pp. 1-11
Author(s):  
Farrukh Jamal ◽  
Hesham Mohammed Reyad ◽  
Soha Othman Ahmed ◽  
Muhammad Akbar Ali Shah ◽  
Emrah Altun
Keyword(s):  
Real Data ◽  
Continuous Model ◽  
Model Parameters ◽  
Data Set ◽  
Lomax Distribution ◽  
Mathematical Properties ◽  
Proposed Model ◽  
Probability Weighted Moment ◽  
Record Statistics ◽  
Maximum Likelihood Criterion

A new three-parameter continuous model called the exponentiated half-logistic Lomax distribution is introduced in this paper. Basic mathematical properties for the proposed model were investigated which include raw and incomplete moments, skewness, kurtosis, generating functions, Rényi entropy, Lorenz, Bonferroni and Zenga curves, probability weighted moment, stress strength model, order statistics, and record statistics. The model parameters were estimated by using the maximum likelihood criterion and the behaviours of these estimates were examined by conducting a simulation study. The applicability of the new model is illustrated by applying it on a real data set.

scholarly journals On the Estimation of Reliability of Weighted Weibull Distribution: A Comparative Study

2016 ◽  
Vol 5 (4) ◽  
pp. 1
Author(s):  
Bander Al-Zahrani
Keyword(s):  
Maximum Likelihood ◽  
Weibull Distribution ◽  
Real Data ◽  
Reliability Function ◽  
Nonparametric Methods ◽  
Empirical Method ◽  
Density Estimator ◽  
Bayes Estimators ◽  
Unknown Parameters ◽  
Data Set

The paper gives a description of estimation for the reliability function of weighted Weibull distribution. The maximum likelihood estimators for the unknown parameters are obtained. Nonparametric methods such as empirical method, kernel density estimator and a modified shrinkage estimator are provided. The Markov chain Monte Carlo method is used to compute the Bayes estimators assuming gamma and Jeffrey priors. The performance of the maximum likelihood, nonparametric methods and Bayesian estimators is assessed through a real data set.

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 Robust Bayesian Analysis of Lifetime Data from Maxwell Distribution

2018 ◽  
Vol 48 (1) ◽  
pp. 38-55
Author(s):  
M. S. Panwar ◽  
Sanjeev K Tomer
Keyword(s):  
Bayesian Analysis ◽  
Real Data ◽  
Type I ◽  
Lifetime Data ◽  
Maxwell Distribution ◽  
Data Set ◽  
Squared Error ◽  
Robust Bayesian Analysis ◽  
Linex Loss ◽  
Mean Lifetime

In this paper, we consider robust Bayesian analysis of lifetime data from the Maxwell distribution assuming an $\varepsilon$-contamination class of prior distributions for the parameter. We obtain robust Bayes estimates of the parameter and mean lifetime under squared error and LINEX loss functions in presence of uncensored as well as Type-I progressively hybrid censored lifetime data. A real data set is analysed for numerical illustrations.

Sign in / Sign up

Export Citation Format

Share Document