Bayesian inference from the Kumaraswamy-Weibull distribution with applications to real data

2016 ◽  
Vol 11 ◽  
pp. 119-129
Author(s):  
R. M. Mandouh
Keyword(s):  
Bayesian Inference ◽  
Weibull Distribution ◽  
Real Data

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 Transmuted Weibull distribution and its applications

2018 ◽  
Vol 157 ◽  
pp. 08007 ◽  
Author(s):  
Ivana Pobočíková ◽  
Zuzana Sedliačková ◽  
Mária Michalková
Keyword(s):  
Weibull Distribution ◽  
Real Data ◽  
Data Set ◽  
New Distribution ◽  
Modelling Data

In this paper we study new distribution called transmuted Weibull distribution. Some properties of this distribution are described. The usefulness of the distribution for modelling data is illustrated using real data set.

scholarly journals Bayesian Inference for the Difference of Two Proportion Parameters in Over-Reported Two-Sample Binomial Data Using the Doubly Sample

Stats ◽  
2019 ◽  
Vol 2 (1) ◽  
pp. 111-120 ◽  
Author(s):  
Dewi Rahardja
Keyword(s):  
Bayesian Inference ◽  
Closed Form ◽  
Bayesian Approach ◽  
Interval Estimation ◽  
Real Data ◽  
Simulation Studies ◽  
Posterior Distributions ◽  
Binomial Data ◽  
The Difference ◽  
Data Subject

We construct a point and interval estimation using a Bayesian approach for the difference of two population proportion parameters based on two independent samples of binomial data subject to one type of misclassification. Specifically, we derive an easy-to-implement closed-form algorithm for drawing from the posterior distributions. For illustration, we applied our algorithm to a real data example. Finally, we conduct simulation studies to demonstrate the efficiency of our algorithm for Bayesian inference.

A STATISTICAL FRAMEWORK FOR HAPLOTYPE BLOCK INFERENCE

2005 ◽  
Vol 03 (05) ◽  
pp. 1021-1038
Author(s):  
AO YUAN ◽  
GUANJIE CHEN ◽  
CHARLES ROTIMI ◽  
GEORGE E. BONNEY
Keyword(s):  
Bayesian Inference ◽  
Model Selection ◽  
Haplotype Block ◽  
Block Structure ◽  
Real Data ◽  
Data Sets ◽  
Block Partitioning ◽  
Haplotype Blocks ◽  
Statistical Framework ◽  
Statistical Model Selection

The existence of haplotype blocks transmitted from parents to offspring has been suggested recently. This has created an interest in the inference of the block structure and length. The motivation is that haplotype blocks that are characterized well will make it relatively easier to quickly map all the genes carrying human diseases. To study the inference of haplotype block systematically, we propose a statistical framework. In this framework, the optimal haplotype block partitioning is formulated as the problem of statistical model selection; missing data can be handled in a standard statistical way; population strata can be implemented; block structure inference/hypothesis testing can be performed; prior knowledge, if present, can be incorporated to perform a Bayesian inference. The algorithm is linear in the number of loci, instead of NP-hard for many such algorithms. We illustrate the applications of our method to both simulated and real data sets.

Bayesian Analysis of the Brown–Proschan Model

2015 ◽  
Vol 30 (1) ◽  
Author(s):  
Dinh Tuan Nguyen ◽  
Yann Dijoux ◽  
Mitra Fouladirad
Keyword(s):  
Weibull Distribution ◽  
Bayesian Analysis ◽  
Failure Rate ◽  
Bayesian Approach ◽  
Real Data ◽  
Posterior Distributions ◽  
Imperfect Maintenance ◽  
Maintenance Model ◽  
Informative Prior Distributions

AbstractThe paper presents a Bayesian approach of the Brown–Proschan imperfect maintenance model. The initial failure rate is assumed to follow a Weibull distribution. A discussion of the choice of informative and non-informative prior distributions is provided. The implementation of the posterior distributions requires the Metropolis-within-Gibbs algorithm. A study on the quality of the estimators of the model obtained from Bayesian and frequentist inference is proposed. An application to real data is finally developed.

scholarly journals An Inferential Aptness of a Weibull Generated Distribution and Application

2021 ◽  
Author(s):  
Brijesh P. Singh ◽  
Utpal Dhar Das
Keyword(s):  
Weibull Distribution ◽  
Continuous Distribution ◽  
Selection Criterion ◽  
Real Data ◽  
Rayleigh Distribution ◽  
Single Parameter ◽  
Parameter Distribution ◽  
Data Sets ◽  
Lifetime Distributions ◽  
Limiting Behavior

In this article an attempt has been made to develop a flexible single parameter continuous distribution using Weibull distribution. The Weibull distribution is most widely used lifetime distributions in both medical and engineering sectors. The exponential and Rayleigh distribution is particular case of Weibull distribution. Here in this study we use these two distributions for developing a new distribution. Important statistical properties of the proposed distribution is discussed such as moments, moment generating and characteristic function. Various entropy measures like Rényi, Shannon and cumulative entropy are also derived. The kthkt⁢h order statistics of pdf and cdf also obtained. The properties of hazard function and their limiting behavior is discussed. The maximum likelihood estimate of the parameter is obtained that is not in closed form, thus iteration procedure is used to obtain the estimate. Simulation study has been done for different sample size and MLE, MSE, Bias for the parameter λλ has been observed. Some real data sets are used to check the suitability of model over some other competent distributions for some data sets from medical and engineering science. In the tail area, the proposed model works better. Various model selection criterion such as -2LL, AIC, AICc, BIC, K-S and A-D test suggests that the proposed distribution perform better than other competent distributions and thus considered this as an alternative distribution. The proposed single parameter distribution is found more flexible as compare to some other two parameter complicated distributions for the data sets considered in the present study.

scholarly journals The Modified Kumaraswamy Weibull Distribution: Properties and Applications in Reliability and Engineering Sciences

2020 ◽  
pp. 433-446
Author(s):  
M. E. Mead ◽  
Ahmed Afify ◽  
Nadeem Shafique Butt
Keyword(s):  
Weibull Distribution ◽  
Information Matrix ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Real Data ◽  
Hazard Rates ◽  
Alpha Power ◽  
Mathematical Properties ◽  
Engineering Sciences ◽  
Maximum Likelihood Estimation Method

We introduce the Kumaraswamy alpha power-G (KAP-G) family which extends the alpha power family (Mahdavi and Kundu, 2017) and some other families. We consider the Weibull as baseline for the KAP family and generate Kumaraswamy alpha power Weibull distribution which has right-skewed, left-skewed, symmetrical, and reversed-J shaped densities, and decreasing, increasing, bathtub, upside-down bathtub, increasing-decreasing–increasing, J shaped and reversed-J shaped hazard rates. The proposed distribution can model non-monotone  and monotone failure rates which are quite common in engineering and reliability studies. Some basic mathematical properties of the new model are derived. The maximum likelihood estimation method is used to evaluate the parameters and the observed information matrix is determined. The performance and flexibility of the proposed family is illustrated via two real data applications.

scholarly journals A New Generalized Weighted Weibull Distribution

2019 ◽  
pp. 161-178 ◽  
Author(s):  
Salman Abbas ◽  
Gamze Ozal ◽  
Saman Hanif Shahbaz ◽  
Muhammad Qaiser Shahbaz
Keyword(s):  
Weibull Distribution ◽  
Generating Function ◽  
Probability Generating Function ◽  
Real Data ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Likelihood Method ◽  
Model Parameters ◽  
Data Sets ◽  
Proposed Model

In this article, we present a new generalization of weighted Weibull distribution using Topp Leone family of distributions. We have studied some statistical properties of the proposed distribution including quantile function, moment generating function, probability generating function, raw moments, incomplete moments, probability, weighted moments, Rayeni and q th entropy. The have obtained numerical values of the various measures to see the eect of model parameters. Distribution of of order statistics for the proposed model has also been obtained. The estimation of the model parameters has been done by using maximum likelihood method. The eectiveness of proposed model is analyzed by means of a real data sets. Finally, some concluding remarks are given.

scholarly journals Closed form expressions for moments of the beta Weibull distribution

2011 ◽  
Vol 83 (2) ◽  
pp. 357-373 ◽  
Author(s):  
Gauss M Cordeiro ◽  
Alexandre B Simas ◽  
Borko D Stošic
Keyword(s):  
Weibull Distribution ◽  
Closed Form ◽  
Cumulative Distribution Function ◽  
Information Matrix ◽  
Likelihood Estimation ◽  
Real Data ◽  
Cumulative Distribution ◽  
Data Set ◽  
Expected Information ◽  
Beta Weibull Distribution

The beta Weibull distribution was first introduced by Famoye et al. (2005) and studied by these authors and Lee et al. (2007). However, they do not give explicit expressions for the moments. In this article, we derive explicit closed form expressions for the moments of this distribution, which generalize results available in the literature for some sub-models. We also obtain expansions for the cumulative distribution function and Rényi entropy. Further, we discuss maximum likelihood estimation and provide formulae for the elements of the expected information matrix. We also demonstrate the usefulness of this distribution on a real data set.

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