scholarly journals Bayesian Estimation and Prediction Based on Progressively First Failure Censored Scheme from a Mixture of Weibull and Lomax Distributions

2020 ◽  
pp. 357-372
Author(s):  
Mohamed M. Mahmoud ◽  
Manal Mohamed Nassar ◽  
Marwa Ahmed Aefa
Keyword(s):  
Monte Carlo ◽  
Maximum Likelihood ◽  
Bayesian Estimation ◽  
Likelihood Estimation ◽  
Bayes Estimation ◽  
Maximum Likelihood Estimates ◽  
Monte Carlo Simulation Study ◽  
Estimation And Prediction ◽  
Censored Samples ◽  
Symmetric Square

This paper develops Bayesian estimation and prediction, for a mixture of Weibull and Lomax distributions, in the context of the new life test plan called progressive first failure censored samples. Maximum likelihood  estimation and Bayes estimation, under informative and non-informative priors, are obtained using Markov Chain Monte Carlo methods, based on the symmetric square error Loss function and the asymmetric linear exponential (LINEX) and general entropy loss functions. The maximum likelihood estimates and the different Bayes estimates are compared via a Monte Carlo simulation study. Finally, Bayesian prediction intervals for future observations are obtained using a numerical example

scholarly journals The Beta Log-Logistic Weibull Distribution: Model, Properties and Application

2018 ◽  
Vol 7 (6) ◽  
pp. 49
Author(s):  
Boikanyo Makubate ◽  
Broderick O. Oluyede ◽  
Neo Dingalo ◽  
Adeniyi Francis Fagbamigbe
Keyword(s):  
Maximum Likelihood ◽  
Hazard Function ◽  
Likelihood Estimation ◽  
Quantile Function ◽  
Cumulative Distribution ◽  
Maximum Likelihood Estimates ◽  
Distribution Model ◽  
Monte Carlo Simulation Study ◽  
Special Cases ◽  
Generalized Distribution

We propose and develop the properties of a new generalized distribution called the beta log-logistic Weibull (BLLoGW) distribution. This model contain several new distributions such as beta log-logistic Rayleigh, beta log-logistic exponential, exponentiated log-logistic Weibull, exponentiated log-logistic Rayleigh, exponentiated log-logistic exponential,  log-logistic Weibull, log-logistic Rayleigh and log-logistic distributions as special cases. Structural properties of this generalized distribution including series expansion of the probability density function and cumulative distribution function, hazard function, reverse hazard function, quantile function, moments, conditional moments, mean deviations, Bonferroni and Lorenz curves, R\'enyi entropy and distribution of order statistics are presented. The parameters of the distribution are estimated using maximum likelihood estimation technique. A Monte Carlo simulation study is conducted to examine the bias and mean square error of the maximum likelihood estimates. A real dataset is used to illustrate the applicability and usefulness of the new generalized distribution.

scholarly journals Directional Selection and the Site-Frequency Spectrum

Genetics ◽  
2001 ◽  
Vol 159 (4) ◽  
pp. 1779-1788 ◽  
Author(s):  
Carlos D Bustamante ◽  
John Wakeley ◽  
Stanley Sawyer ◽  
Daniel L Hartl
Keyword(s):  
Maximum Likelihood ◽  
High Power ◽  
Negative Selection ◽  
Likelihood Estimation ◽  
Directional Selection ◽  
Likelihood Ratio Tests ◽  
Maximum Likelihood Estimates ◽  
Likelihood Methods ◽  
Ancestral States ◽  
Asymptotic Variances

Abstract In this article we explore statistical properties of the maximum-likelihood estimates (MLEs) of the selection and mutation parameters in a Poisson random field population genetics model of directional selection at DNA sites. We derive the asymptotic variances and covariance of the MLEs and explore the power of the likelihood ratio tests (LRT) of neutrality for varying levels of mutation and selection as well as the robustness of the LRT to deviations from the assumption of free recombination among sites. We also discuss the coverage of confidence intervals on the basis of two standard-likelihood methods. We find that the LRT has high power to detect deviations from neutrality and that the maximum-likelihood estimation performs very well when the ancestral states of all mutations in the sample are known. When the ancestral states are not known, the test has high power to detect deviations from neutrality for negative selection but not for positive selection. We also find that the LRT is not robust to deviations from the assumption of independence among sites.

A HYBRID GENETIC ALGORITHM FOR THE MAXIMUM LIKELIHOOD ESTIMATION OF MODELS WITH MULTIPLE EQUILIBRIA: A FIRST REPORT

2005 ◽  
Vol 01 (02) ◽  
pp. 295-303 ◽  
Author(s):  
VICTOR AGUIRREGABIRIA ◽  
PEDRO MIRA
Keyword(s):  
Genetic Algorithm ◽  
Maximum Likelihood ◽  
Multiple Equilibria ◽  
Structural Parameters ◽  
Hybrid Genetic Algorithm ◽  
Likelihood Estimation ◽  
Maximum Likelihood Estimates ◽  
Large Space ◽  
Pseudo Maximum Likelihood ◽  
Structural Econometric

This paper presents a hybrid genetic algorithm to obtain maximum likelihood estimates of parameters in structural econometric models with multiple equilibria. The algorithm combines a pseudo maximum likelihood (PML) procedure with a genetic algorithm (GA). The GA searches globally over the large space of possible combinations of multiple equilibria in the data. The PML procedure avoids the computation of all the equilibria associated with every trial value of the structural parameters.

scholarly journals The Weibull Birnbaum-Saunders Distribution And Its Applications

2020 ◽  
Vol 9 (1) ◽  
pp. 61-81
Author(s):  
Lazhar BENKHELIFA
Keyword(s):  
Maximum Likelihood ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Real Data ◽  
Reliability Estimation ◽  
Maximum Likelihood Estimates ◽  
Model Parameters ◽  
Data Sets ◽  
Proposed Model ◽  
Modeling Data

A new lifetime model, with four positive parameters, called the Weibull Birnbaum-Saunders distribution is proposed. The proposed model extends the Birnbaum-Saunders distribution and provides great flexibility in modeling data in practice. Some mathematical properties of the new distribution are obtained including expansions for the cumulative and density functions, moments, generating function, mean deviations, order statistics and reliability. Estimation of the model parameters is carried out by the maximum likelihood estimation method. A simulation study is presented to show the performance of the maximum likelihood estimates of the model parameters. The flexibility of the new model is examined by applying it to two real data sets.

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