scholarly journals Bayesian Modeling of 3-Component Mixture of Exponentiated Inverted Weibull Distribution under Noninformative Prior

2020 ◽  
Vol 2020 ◽  
pp. 1-11 ◽  
Author(s):  
Ammara Nawaz Cheema ◽  
Muhammad Aslam ◽  
Ibrahim M. Almanjahie ◽  
Ishfaq Ahmad
Keyword(s):  
Weibull Distribution ◽  
Research Work ◽  
Real Data ◽  
Loss Functions ◽  
Type I ◽  
Bayes Estimators ◽  
Component Mixture ◽  
Type I Censoring ◽  
Censoring Technique ◽  
The Impact

Bayesian study of 3-component mixture modeling of exponentiated inverted Weibull distribution under right type I censoring technique is conducted in this research work. The posterior distribution of the parameters is obtained assuming the noninformative (Jeffreys and uniform) priors. The different loss functions (squared error, quadratic, precautionary, and DeGroot loss function) are used to obtain the Bayes estimators and posterior risks. The performance of the Bayes estimators through posterior risks under the said loss functions is investigated through simulation process. Real data analysis of tensile strength of carbon fiber is also applied for 3 components to conclude the presentation of Bayes estimators. The limiting expressions are also elaborated for Bayes estimators and posterior risks in this study. The impact of some test termination times and sample sizes is reported on Bayes estimators.

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 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 A 3-component mixture of inverse Rayleigh distributions: properties and estimation in Bayesian framework

2016 ◽  
Vol 5 (2) ◽  
pp. 120
Author(s):  
Tabasam Sultana ◽  
Muhammad Aslam
Keyword(s):  
Survival Analysis ◽  
Prior Information ◽  
Bayesian Framework ◽  
Reliability Theory ◽  
Statistical Properties ◽  
Loss Functions ◽  
Bayes Estimators ◽  
Informative Priors ◽  
Component Mixture ◽  
Censored Sampling

<p>This paper is about studying a 3-component mixture of the inverse Rayleigh distributions under Bayesian perspective. The censored sampling scheme is considered due to its popularity in reliability theory and survival analysis. The expressions for the Bayes estimators and their posterior risks are derived under different loss scenarios. In case, no little prior information is available, elicitation of hyper parameters is given. To examine, numerically, the performance of the Bayes estimators using non-informative and informative priors under different loss functions, we have simulated their statistical properties for different sample sizes and test termination times.</p>

scholarly journals Quantile regression for challenging cases of eQTL mapping

2019 ◽  
Vol 21 (5) ◽  
pp. 1756-1765
Author(s):  
Bo Sun ◽  
Liang Chen
Keyword(s):  
Quantile Regression ◽  
Large Scale ◽  
High Throughput Sequencing ◽  
Linear Models ◽  
Real Data ◽  
Type I ◽  
Eqtl Mapping ◽  
Size Estimation ◽  
Rna Seq ◽  
The Impact

Abstract Mapping of expression quantitative trait loci (eQTLs) facilitates interpretation of the regulatory path from genetic variants to their associated disease or traits. High-throughput sequencing of RNA (RNA-seq) has expedited the exploration of these regulatory variants. However, eQTL mapping is usually confronted with the analysis challenges caused by overdispersion and excessive dropouts in RNA-seq. The heavy-tailed distribution of gene expression violates the assumption of Gaussian distributed errors in linear regression for eQTL detection, which results in increased Type I or Type II errors. Applying rank-based inverse normal transformation (INT) can make the expression values more normally distributed. However, INT causes information loss and leads to uninterpretable effect size estimation. After comprehensive examination of the impact from overdispersion and excessive dropouts, we propose to apply a robust model, quantile regression, to map eQTLs for genes with high degree of overdispersion or large number of dropouts. Simulation studies show that quantile regression has the desired robustness to outliers and dropouts, and it significantly improves eQTL mapping. From a real data analysis, the most significant eQTL discoveries differ between quantile regression and the conventional linear model. Such discrepancy becomes more prominent when the dropout effect or the overdispersion effect is large. All the results suggest that quantile regression provides more reliable and accurate eQTL mapping than conventional linear models. It deserves more attention for the large-scale eQTL mapping.

scholarly journals The Half-Logistic Generalized Weibull Distribution

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Masood Anwar ◽  
Amna Bibi
Keyword(s):  
Weibull Distribution ◽  
Information Matrix ◽  
Likelihood Estimation ◽  
Real Data ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Type I ◽  
Failure Rate Function ◽  
New Model ◽  
Compound Distribution

A new three-parameter generalized distribution, namely, half-logistic generalized Weibull (HLGW) distribution, is proposed. The proposed distribution exhibits increasing, decreasing, bathtub-shaped, unimodal, and decreasing-increasing-decreasing hazard rates. The distribution is a compound distribution of type I half-logistic-G and Dimitrakopoulou distribution. The new model includes half-logistic Weibull distribution, half-logistic exponential distribution, and half-logistic Nadarajah-Haghighi distribution as submodels. Some distributional properties of the new model are investigated which include the density function shapes and the failure rate function, raw moments, moment generating function, order statistics, L-moments, and quantile function. The parameters involved in the model are estimated using the method of maximum likelihood estimation. The asymptotic distribution of the estimators is also investigated via Fisher’s information matrix. The likelihood ratio (LR) test is used to compare the HLGW distribution with its submodels. Some applications of the proposed distribution using real data sets are included to examine the usefulness of the distribution.

scholarly journals Bayesian Estimation of the Scale Parameter of Inverse Weibull Distribution under the Asymmetric Loss Functions

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Farhad Yahgmaei ◽  
Manoochehr Babanezhad ◽  
Omid S. Moghadam
Keyword(s):  
Weibull Distribution ◽  
Scale Parameter ◽  
Loss Functions ◽  
Simulation Studies ◽  
Bayes Estimators ◽  
Likelihood Estimator ◽  
Risk Functions ◽  
Inverse Weibull Distribution ◽  
The Mean ◽  
Mean Square Errors

This paper proposes different methods of estimating the scale parameter in the inverse Weibull distribution (IWD). Specifically, the maximum likelihood estimator of the scale parameter in IWD is introduced. We then derived the Bayes estimators for the scale parameter in IWD by considering quasi, gamma, and uniform priors distributions under the square error, entropy, and precautionary loss functions. Finally, the different proposed estimators have been compared by the extensive simulation studies in corresponding the mean square errors and the evolution of risk functions.

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