scholarly journals Estimation of the Reliability of a Stress–Strength System from Poisson Half Logistic Distribution

Entropy ◽  
2020 ◽  
Vol 22 (11) ◽  
pp. 1307
Author(s):  
Isyaku Muhammad ◽  
Xingang Wang ◽  
Changyou Li ◽  
Mingming Yan ◽  
Miaoxin Chang
Keyword(s):  
Confidence Interval ◽  
Loss Function ◽  
Credible Interval ◽  
Absolute Error ◽  
Asymptotic Distributions ◽  
Logistic Distribution ◽  
Bayes Estimators ◽  
Posterior Density ◽  
Error Loss ◽  
Highest Posterior Density

This paper discussed the estimation of stress-strength reliability parameter R=P(Y<X) based on complete samples when the stress-strength are two independent Poisson half logistic random variables (PHLD). We have addressed the estimation of R in the general case and when the scale parameter is common. The classical and Bayesian estimation (BE) techniques of R are studied. The maximum likelihood estimator (MLE) and its asymptotic distributions are obtained; an approximate asymptotic confidence interval of R is computed using the asymptotic distribution. The non-parametric percentile bootstrap and student’s bootstrap confidence interval of R are discussed. The Bayes estimators of R are computed using a gamma prior and discussed under various loss functions such as the square error loss function (SEL), absolute error loss function (AEL), linear exponential error loss function (LINEX), generalized entropy error loss function (GEL) and maximum a posteriori (MAP). The Metropolis–Hastings algorithm is used to estimate the posterior distributions of the estimators of R. The highest posterior density (HPD) credible interval is constructed based on the SEL. Monte Carlo simulations are used to numerically analyze the performance of the MLE and Bayes estimators, the results were quite satisfactory based on their mean square error (MSE) and confidence interval. Finally, we used two real data studies to demonstrate the performance of the proposed estimation techniques in practice and to illustrate how PHLD is a good candidate in reliability studies.

scholarly journals Bayesian Estimation for the Coefficients of Variation of Birnbaum–Saunders Distributions

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2130
Author(s):  
Wisunee Puggard ◽  
Sa-Aat Niwitpong ◽  
Suparat Niwitpong
Keyword(s):  
Confidence Interval ◽  
Simulation Study ◽  
Average Length ◽  
Credible Interval ◽  
Posterior Density ◽  
Concentration Data ◽  
Monte Carlo Simulation Study ◽  
The Difference ◽  
Highest Posterior Density ◽  
Hpd Interval

The Birnbaum–Saunders (BS) distribution, which is asymmetric with non-negative support, can be transformed to a normal distribution, which is symmetric. Therefore, the BS distribution is useful for describing data comprising values greater than zero. The coefficient of variation (CV), which is an important descriptive statistic for explaining variation within a dataset, has not previously been used for statistical inference on a BS distribution. The aim of this study is to present four methods for constructing confidence intervals for the CV, and the difference between the CVs of BS distributions. The proposed methods are based on the generalized confidence interval (GCI), a bootstrapped confidence interval (BCI), a Bayesian credible interval (BayCI), and the highest posterior density (HPD) interval. A Monte Carlo simulation study was conducted to evaluate their performances in terms of coverage probability and average length. The results indicate that the HPD interval was the best-performing method overall. PM 2.5 concentration data for Chiang Mai, Thailand, collected in March and April 2019, were used to illustrate the efficacies of the proposed methods, the results of which were in good agreement with the simulation study findings.

scholarly journals Bayesian Estimation of the Exponential Parameter under a Multiply Type-II Censoring Scheme

2016 ◽  
Vol 36 (3) ◽  
Author(s):  
Umesh Singh ◽  
Anil Kumar
Keyword(s):  
Monte Carlo ◽  
Loss Function ◽  
Scale Parameter ◽  
Type Ii ◽  
Bayes Estimators ◽  
Conjugate Prior ◽  
Exponential Parameter ◽  
Type Ii Censoring ◽  
Error Loss ◽  
Censoring Scheme

This paper provides the estimation of the scale parameter of the exponential distribution under multiply type-II censoring. Using generalized non-informative prior and natural conjugate prior, Bayes estimator and approximate Bayes estimators of the scale parameter have been obtained under square error loss function. The proposed Bayes estimators and approximate Bayes estimators are compared with the estimators proposed by Singh et al. (2005) and Balasubramanian and Balakrishnan (1992) on the basis of theirsimulated risks under square error loss function of 1000 randomly generated Monte Carlo samples.

scholarly journals The Bayesian Confidence Interval for Coefficient of Variation of Zero-inflated Poisson Distribution with Application to Daily COVID-19 Deaths in Thailand

2021 ◽  
Vol 5 ◽  
pp. 62-76
Author(s):  
Sunisa Junnumtuam ◽  
Sa-Aat Niwitpong ◽  
Suparat Niwitpong
Keyword(s):  
Confidence Interval ◽  
Coefficient Of Variation ◽  
Average Length ◽  
Simulated Data ◽  
Posterior Density ◽  
The World ◽  
Bayesian Confidence Interval ◽  
Percentile Bootstrap ◽  
Highest Posterior Density ◽  
Better Than

Coronavirus disease 2019 (COVID-19) has spread rapidly throughout the world and has caused millions of deaths. However, the number of daily COVID-19 deaths in Thailand has been low with most daily records showing zero deaths, thereby making them fit a Zero-Inflated Poisson (ZIP) distribution. Herein, confidence intervals for the Coefficient Of Variation (CV) of a ZIP distribution are derived using four methods: the standard bootstrap (SB), percentile bootstrap (PB), Markov Chain Monte Carlo (MCMC), and the Bayesian-based highest posterior density (HPD), for which using the variance of the CV is unnecessary. We applied the methods to both simulated data and data on the number of daily COVID-19 deaths in Thailand. Both sets of results show that the SB, MCMC, and HPD methods performed better than PB for most cases in terms of coverage probability and average length. Overall, the HPD method is recommended for constructing the confidence interval for the CV of a ZIP distribution. Doi: 10.28991/esj-2021-SPER-05 Full Text: PDF

scholarly journals The Bayesian confidence intervals for measuring the difference between dispersions of rainfall in Thailand

PeerJ ◽  
2020 ◽  
Vol 8 ◽  
pp. e9662
Author(s):  
Noppadon Yosboonruang ◽  
Sa-Aat Niwitpong ◽  
Suparat Niwitpong
Keyword(s):  
Confidence Interval ◽  
Confidence Intervals ◽  
Rainfall Data ◽  
Posterior Density ◽  
Lognormal Distributions ◽  
Coefficients Of Variation ◽  
Coverage Probabilities ◽  
The Difference ◽  
Fiducial Generalized Confidence Interval ◽  
Highest Posterior Density

The coefficient of variation is often used to illustrate the variability of precipitation. Moreover, the difference of two independent coefficients of variation can describe the dissimilarity of rainfall from two areas or times. Several researches reported that the rainfall data has a delta-lognormal distribution. To estimate the dynamics of precipitation, confidence interval construction is another method of effectively statistical inference for the rainfall data. In this study, we propose confidence intervals for the difference of two independent coefficients of variation for two delta-lognormal distributions using the concept that include the fiducial generalized confidence interval, the Bayesian methods, and the standard bootstrap. The performance of the proposed methods was gauged in terms of the coverage probabilities and the expected lengths via Monte Carlo simulations. Simulation studies shown that the highest posterior density Bayesian using the Jeffreys’ Rule prior outperformed other methods in virtually cases except for the cases of large variance, for which the standard bootstrap was the best. The rainfall series from Songkhla, Thailand are used to illustrate the proposed confidence intervals.

scholarly journals On Reliability in a Multicomponent Stress-Strength Model with Power Lindley Distribution

2018 ◽  
Vol 41 (2) ◽  
pp. 251-267 ◽  
Author(s):  
Abbas Pak ◽  
Arjun Kumar Gupta ◽  
Nayereh Bagheri Khoolenjani
Keyword(s):  
Interval Estimation ◽  
Parametric Bootstrap ◽  
Real Data ◽  
Credible Interval ◽  
Data Sets ◽  
Strength Model ◽  
Reliability Parameter ◽  
Posterior Density ◽  
Bayes Estimate ◽  
Highest Posterior Density

In this paper  we study the reliability of a multicomponent stress-strength model assuming that the components follow power Lindley model.  The maximum likelihood estimate of the reliability parameter and its asymptotic confidence interval are obtained. Applying the parametric Bootstrap technique, interval estimation of the reliability is presented.  Also, the Bayes estimate and highest posterior density credible interval of the reliability parameter are derived using suitable priors on the parameters. Because there is no closed form for the Bayes estimate, we use the Markov Chain Monte Carlo method to obtain approximate Bayes  estimate of the reliability. To evaluate the performances of different procedures,  simulation studies are conducted and an example of real data sets is provided.

scholarly journals Bayesian Inference on the Shape Parameter and Future Observation of Exponentiated Family of Distributions

2011 ◽  
Vol 2011 ◽  
pp. 1-17
Author(s):  
Sanku Dey ◽  
Sudhansu S. Maiti
Keyword(s):  
Loss Function ◽  
Shape Parameter ◽  
Quadratic Loss ◽  
Posterior Density ◽  
Scale Invariant ◽  
Data Set ◽  
Future Observation ◽  
Hpd Intervals ◽  
Highest Posterior Density ◽  
Family Of Distributions

The Bayes estimators of the shape parameter of exponentiated family of distributions have been derived by considering extension of Jeffreys' noninformative as well as conjugate priors under different scale-invariant loss functions, namely, weighted quadratic loss function, squared-log error loss function and general entropy loss function. The risk functions of these estimators have been studied. We have also considered the highest posterior density (HPD) intervals for the parameter and the equal-tail and HPD prediction intervals for future observation. Finally, we analyze one data set for illustration.

scholarly journals Influence of Institution-Based Factors on Preoperative Blood Testing Prior to Low-Risk Surgery: A Bayesian Generalized Linear Mixed Approach

2017 ◽  
Vol 2017 ◽  
pp. 1-6 ◽  
Author(s):  
Kazuki Ide ◽  
Hiroshi Yonekura ◽  
Yohei Kawasaki ◽  
Koji Kawakami
Keyword(s):  
Health Care Services ◽  
Credible Interval ◽  
Low Risk ◽  
Institutional Factors ◽  
Posterior Density ◽  
Blood Testing ◽  
Blood Tests ◽  
The Difference ◽  
Mixed Approach ◽  
Highest Posterior Density

To optimize delivery of health care services in clinical practice, the use of unnecessary interventions should be reduced. Although recommendations for this reduction have been accepted worldwide, recent studies have revealed that the use of such procedures continues to increase. We conducted a retrospective cohort study using a nationwide claim-based database to evaluate factors influencing preoperative blood testing prior to low-risk surgery, via a Bayesian generalized linear mixed approach. The study period was set from April 1, 2012, to March 31, 2016, and 69,252 surgeries performed at 9,922 institutions were included in the analysis. Mean patient age was 44.3 ± 11.3 years (57% female). Preoperative blood tests were performed for 59.0% of procedures. Among institutional factors, the number of beds was strongly associated with preoperative blood testing (odds ratio [95% highest posterior density interval (HPD interval)], 2.64 [2.53 to 2.75]). The difference (95% credible interval) in the rate of preoperative blood testing between institutions with <100 beds and ≥100 beds was 0.315 [0.309 to 0.322], and the Bayesian indexθwas 1.00. This indicated that preoperative blood tests are strongly influenced by institutional factors, suggesting that specific guidelines should be developed to avoid excessive preoperative testing for low-risk surgery.

scholarly journals The Comparison Between the MLE and Standard Bayes Estimators of the Reliability Function of Exponential Distribution

2019 ◽  
Vol 32 (1) ◽  
pp. 103
Author(s):  
Mohammed Jamel Ali ◽  
Hazim Mansoor Gorgees
Keyword(s):  
Loss Function ◽  
Reliability Function ◽  
Loss Functions ◽  
Mean Square ◽  
Bayes Estimators ◽  
Squared Error Loss Function ◽  
Monte Carlo Simulation Technique ◽  
Error Loss ◽  
Squared Error ◽  
The One

     In this paper, a Monte Carlo Simulation technique is used to compare the performance of MLE and the standard Bayes estimators of the reliability function of the one parameter exponential distribution.Two types of loss functions are adopted, namely, squared error  loss function (SELF) and modified square error loss function (MSELF) with informative and non- informative prior. The criterion integrated mean square error (IMSE) is employed to assess the performance of such estimators .

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