scholarly journals Estimation and Prediction for Gompertz Distribution under General Progressive Censoring

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 858
Author(s):  
Yuxuan Wang ◽  
Wenhao Gui
Keyword(s):  
Information Matrix ◽  
Expectation Maximization Algorithm ◽  
Maximum Likelihood Estimates ◽  
Posterior Density ◽  
Gompertz Distribution ◽  
Bayesian Estimates ◽  
Asymptotic Confidence Intervals ◽  
Mh Algorithm ◽  
Highest Posterior Density Intervals ◽  
Highest Posterior Density

In this article, we discuss the estimation of the parameters for Gompertz distribution and prediction using general progressive Type-II censoring. Based on the Expectation–Maximization algorithm, we calculate the maximum likelihood estimates. Bayesian estimates are considered under different loss functions, which are symmetrical, asymmetrical and balanced, respectively. An approximate method—Tierney and Kadane—is used to derive the estimates. Besides, the Metropolis-Hasting (MH) algorithm is applied to get the Bayesian estimates as well. According to Fisher information matrix, we acquire asymptotic confidence intervals. Bootstrap intervals are also established. Furthermore, we build the highest posterior density intervals through the sample generated by the MH algorithm. Then, Bayesian predictive intervals and estimates for future samples are provided. Finally, for evaluating the quality of the approaches, a numerical simulation study is implemented. In addition, we analyze two real datasets.

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 The Exponentiated Lindley Geometric Distribution with Applications

Entropy ◽  
2019 ◽  
Vol 21 (5) ◽  
pp. 510
Author(s):  
Bo Peng ◽  
Zhengqiu Xu ◽  
Min Wang
Keyword(s):  
Maximum Likelihood ◽  
Geometric Distribution ◽  
Residual Life ◽  
Information Matrix ◽  
Expectation Maximization Algorithm ◽  
Likelihood Estimation ◽  
Real Data ◽  
Quantile Function ◽  
Maximum Likelihood Estimates ◽  
Unknown Parameters

We introduce a new three-parameter lifetime distribution, the exponentiated Lindley geometric distribution, which exhibits increasing, decreasing, unimodal, and bathtub shaped hazard rates. We provide statistical properties of the new distribution, including shape of the probability density function, hazard rate function, quantile function, order statistics, moments, residual life function, mean deviations, Bonferroni and Lorenz curves, and entropies. We use maximum likelihood estimation of the unknown parameters, and an Expectation-Maximization algorithm is also developed to find the maximum likelihood estimates. The Fisher information matrix is provided to construct the asymptotic confidence intervals. Finally, two real-data examples are analyzed for illustrative purposes.

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 Inference of Left Truncated and Right Censored Data from Marshall–Olkin Bivariate Rayleigh Distribution

Mathematics ◽  
2021 ◽  
Vol 9 (21) ◽  
pp. 2703
Author(s):  
Ke Wu ◽  
Liang Wang ◽  
Li Yan ◽  
Yuhlong Lio
Keyword(s):  
Statistical Inference ◽  
Information Matrix ◽  
Real Life ◽  
High Posterior Density ◽  
Rayleigh Distribution ◽  
Maximum Likelihood Estimates ◽  
Approximate Theory ◽  
Posterior Density ◽  
Unknown Parameters ◽  
Right Censored Data

In this paper, statistical inference and prediction issue of left truncated and right censored dependent competing risk data are studied. When the latent lifetime is distributed by Marshall–Olkin bivariate Rayleigh distribution, the maximum likelihood estimates of unknown parameters are established, and corresponding approximate confidence intervals are also constructed by using a Fisher information matrix and asymptotic approximate theory. Furthermore, Bayesian estimates and associated high posterior density credible intervals of unknown parameters are provided based on general flexible priors. In addition, when there is an order restriction between unknown parameters, the point and interval estimates based on classical and Bayesian frameworks are discussed too. Besides, the prediction issue of a censored sample is addressed based on both likelihood and Bayesian methods. Finally, extensive simulation studies are conducted to investigate the performance of the proposed methods, and two real-life examples are presented for illustration purposes.

BAYESIAN STUDY OF A TWO-COMPONENT SYSTEM WITH COMMON-CAUSE SHOCK FAILURES

2005 ◽  
Vol 22 (01) ◽  
pp. 105-119 ◽  
Author(s):  
V. S. S. YADAVALLI ◽  
A. BEKKER ◽  
J. PAUW
Keyword(s):  
Steady State ◽  
Posterior Density ◽  
Two Component System ◽  
Unknown Parameters ◽  
Component System ◽  
Common Cause ◽  
Two Component ◽  
Highest Posterior Density Intervals ◽  
In Series ◽  
Highest Posterior Density

The steady-state availability of a two-component system in series and parallel subject to individual failures (I-failures) and common-cause shock (CCS) failures is studied from a Bayesian viewpoint with different types of priors assumed for the unknown parameters in the system. Monte Carlo simulation is used to derive the posterior distribution for the steady-state availability and subsequently the highest posterior density intervals. A numerical example illustrates the results.

Revisit to progressively Type-II censored competing risks data from Lomax distributions

2021 ◽  
pp. 1748006X2098397
Author(s):  
Rui Hua ◽  
Wenhao Gui
Keyword(s):  
Confidence Intervals ◽  
Competing Risks ◽  
Maximum Likelihood Estimates ◽  
Type Ii ◽  
Posterior Density ◽  
Unknown Parameters ◽  
Linex Loss ◽  
Credible Intervals ◽  
Competing Risks Data ◽  
Highest Posterior Density

In survival analysis, more than one factor typically contributes to individual failure. In addition, censoring is inevitable in lifespan tests or reliability studies due to external causes or experimental purposes. In this article, the competing risks model is considered and investigated under progressively Type-II censoring where data is from Lomax distributions. Assumptions are further made that these competitive factors are independently distributed, and the latent lifetimes of these factors follow Lomax distributions where both scale parameters and shape parameters are different. For all unknown parameters, maximum likelihood estimates have been attained by Newton-Raphson (NR) method as well as expectation maximization (EM) method, and then the approximate confidence intervals are acquired, in addition to bootstrap confidence intervals. Furthermore, under square error and LINEX loss functions, Bayes estimates and corresponding highest posterior density credible intervals are successively constructed. Finally, simulation experiments are implemented to access performance of several proposed methods in this article, and laboratory dataset is presented and analyzed for illustrative purposes.

scholarly journals Classical and Bayesian Inference of an Exponentiated Half-Logistic Distribution under Adaptive Type II Progressive Censoring

Entropy ◽  
2021 ◽  
Vol 23 (12) ◽  
pp. 1558
Author(s):  
Ziyu Xiong ◽  
Wenhao Gui
Keyword(s):  
Confidence Intervals ◽  
Bootstrap Method ◽  
Information Matrix ◽  
Logistic Distribution ◽  
Type Ii ◽  
Progressive Censoring ◽  
Posterior Density ◽  
Unknown Parameters ◽  
Data Set ◽  
Highest Posterior Density

The point and interval estimations for the unknown parameters of an exponentiated half-logistic distribution based on adaptive type II progressive censoring are obtained in this article. At the beginning, the maximum likelihood estimators are derived. Afterward, the observed and expected Fisher’s information matrix are obtained to construct the asymptotic confidence intervals. Meanwhile, the percentile bootstrap method and the bootstrap-t method are put forward for the establishment of confidence intervals. With respect to Bayesian estimation, the Lindley method is used under three different loss functions. The importance sampling method is also applied to calculate Bayesian estimates and construct corresponding highest posterior density (HPD) credible intervals. Finally, numerous simulation studies are conducted on the basis of Markov Chain Monte Carlo (MCMC) samples to contrast the performance of the estimations, and an authentic data set is analyzed for exemplifying intention.

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