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 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 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 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 Estimation of Stress Strength Reliability of Inverse Weibull Distribution under Progressive First Failure Censoring

2018 ◽  
Vol 48 (1) ◽  
pp. 14-37
Author(s):  
Hare Krishna ◽  
Madhulika Dube ◽  
Renu Garg
Keyword(s):  
Monte Carlo ◽  
Real Life ◽  
Credible Interval ◽  
Estimation Methods ◽  
Posterior Density ◽  
Monte Carlo Simulation Study ◽  
Scale Parameters ◽  
Real Life Data ◽  
Inverse Weibull Distribution ◽  
Highest Posterior Density

In this article, estimation of stress-strength reliability $\delta=P\left(Y<X\right)$ based on progressively first failure censored data from two independent inverse Weibull distributions with different shape and scale parameters is studied. Maximum likelihood estimator and asymptotic confidence interval of $\delta$ are obtained. Bayes estimator of $\delta$ under generalized entropy loss function using non-informative and gamma informative priors is derived. Also, highest posterior density credible interval of $\delta$ is constructed. Markov Chain Monte Carlo (MCMC) technique is used for Bayes computation. The performance of various estimation methods are compared by a Monte Carlo simulation study. Finally, a pair of real life data is analyzed to illustrate the proposed methods of estimation.

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 Integration Of Statistical Techniques For Improving Contact Tracing Efforts To Stop The Spread Of Covid-19 Cases In Nigeria

2020 ◽  
Author(s):  
M ◽  
Adekeye. K. S ◽  
Wale-Orojo. O.A ◽  
Ajayi. A. O ◽  
Ogunsola. I. A ◽  
...  
Keyword(s):  
Goodness Of Fit ◽  
R Package ◽  
Predictive Distribution ◽  
Contact Tracing ◽  
Statistical Techniques ◽  
Cluster Sampling ◽  
Mcmc Algorithm ◽  
Posterior Density ◽  
Highest Posterior Density ◽  
Hpd Interval

Abstract COVID-19 is battling with many countries in the world, including Nigeria, and it has affected various sectors. Contact tracing technique without Statisticians in the team as recommended by WHO is being used in Nigeria to curb the spread of COVID-19 virus, yet confirmed cases is on the increase daily. This study proposed the integration of Statistical techniques for improving contact tracing efforts to stop the spread of the virus. A fitted model using the R package, and Adaptive Cluster Sampling mechanism was embedded. Parameters of the model were estimated using Markov Chain Monte-Carlo (MCMC) Algorithm with Winbugs software. Trace plot and correlogram were used for MCMC diagnostics to examine the goodness of fit of the model. The fitted model was used to obtain a predictive distribution for predicting the estimated number of COVID-19 carriers in Nigeria. The model has a good fit since It converged to the representation of the target posterior within the 95% highest posterior density (HPD) interval, its chains mixed well, and autocorrelation is quite similar at each lag. Estimated number of COVID-19 carriers were well estimated and higher in each state than confirmed cases. The present contact tracing process is inefficient to track COVID-19 carriers, hence integrated contact tracing technique with the involvement of Statisticians was recommended. .

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 Phylodynamics of SARS-CoV-2 transmission in Spain

2020 ◽  
Author(s):  
Francisco Díez-Fuertes ◽  
María Iglesias-Caballero ◽  
Sara Monzón ◽  
Pilar Jiménez ◽  
Sarai Varona ◽  
...  
Keyword(s):  
Phylogenetic Analyses ◽  
Geographic Origin ◽  
Recent Common Ancestor ◽  
Whole Genome ◽  
Posterior Density ◽  
Whole Genome Analysis ◽  
Most Recent Common Ancestor ◽  
Highest Posterior Density ◽  
The City ◽  
Hpd Interval

AbstractObjectivesSARS-CoV-2 whole-genome analysis has identified three large clades spreading worldwide, designated G, V and S. This study aims to analyze the diffusion of SARS-CoV-2 in Spain/Europe.MethodsMaximum likelihood phylogenetic and Bayesian phylodynamic analyses have been performed to estimate the most probable temporal and geographic origin of different phylogenetic clusters and the diffusion pathways of SARS-CoV-2.ResultsPhylogenetic analyses of the first 28 SARS-CoV-2 whole genome sequences obtained from patients in Spain revealed that most of them are distributed in G and S clades (13 sequences in each) with the remaining two sequences branching in the V clade. Eleven of the Spanish viruses of the S clade and six of the G clade grouped in two different monophyletic clusters (S-Spain and G-Spain, respectively), with the S-Spain cluster also comprising 8 sequences from 6 other countries from Europe and the Americas. The most recent common ancestor (MRCA) of the SARS-CoV-2 pandemic was estimated in the city of Wuhan, China, around November 24, 2019, with a 95% highest posterior density (HPD) interval from October 30-December 17, 2019. The origin of S-Spain and G-Spain clusters were estimated in Spain around February 14 and 18, 2020, respectively, with a possible ancestry of S-Spain in Shanghai.ConclusionsMultiple SARS-CoV-2 introductions have been detected in Spain and at least two resulted in the emergence of locally transmitted clusters, with further dissemination of one of them to at least 6 other countries. These results highlight the extraordinary potential of SARS-CoV-2 for rapid and widespread geographic dissemination.

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