BAYESIAN ESTIMATION IN RANDOM CENSORSHIP MODEL FOR WEIBULL DISTRIBUTION UNDER DIFFERENT LOSS FUNCTIONS

2012 ◽  
Vol 04 (03) ◽  
pp. 1250021 ◽  
Author(s):  
MUHAMMAD YAMEEN DANISH ◽  
MUHAMMAD ASLAM
Keyword(s):  
Weibull Distribution ◽  
Bayesian Estimation ◽  
Proportional Hazards ◽  
Proportional Hazards Model ◽  
Real Data ◽  
Loss Functions ◽  
Maximum Likelihood Estimates ◽  
Model Parameters ◽  
Estimation Of Parameters ◽  
Random Censorship

This paper deals with Bayesian estimation of parameters in the proportional hazards model of random censorship for the Weibull distribution under different loss functions. We consider both the informative and noninformative priors on the model parameters to obtain the Bayes estimates using Gibbs sampling scheme. Maximum likelihood estimates are also obtained for comparison purposes. A simulation study is carried out to observe the behavior of the proposed estimators for different sample sizes and for different censoring parameters. One real data analysis is performed for illustration.

scholarly journals Generalized Weighted Rama Distribution: Properties and Application to Model Lifetime Data

2021 ◽  
pp. 9-37
Author(s):  
Samuel U. Enogwe ◽  
Chisimkwuo John ◽  
Happiness O. Obiora-Ilouno ◽  
Chrisogonus K. Onyekwere
Keyword(s):  
Maximum Likelihood ◽  
Likelihood Estimation ◽  
Real Data ◽  
Maximum Likelihood Estimates ◽  
Model Parameters ◽  
Data Sets ◽  
Estimation Of Parameters ◽  
Data Set ◽  
Bathtub Shape ◽  
Asymptotic Confidence Intervals

In this paper, we propose a new lifetime distribution called the generalized weighted Rama (GWR) distribution, which extends the two-parameter Rama distribution and has the Rama distribution as a special case. The GWR distribution has the ability to model data sets that have positive skewness and upside-down bathtub shape hazard rate. Expressions for mathematical and reliability properties of the GWR distribution have been derived. Estimation of parameters was achieved using the method of maximum likelihood estimation and a simulation was performed to verify the stability of the maximum likelihood estimates of the model parameters. The asymptotic confidence intervals of the parameters of the proposed distribution are obtained. The applicability of the GWR distribution was illustrated with a real data set and the results obtained show that the GWR distribution is a better candidate for the data than the other competing distributions being investigated.

PARAMETER ESTIMATE WITH ONLY ONE COMPLETE FAILURE OBSERVATION USING MONTE CARLO EM ALGORITHM

2001 ◽  
Vol 08 (02) ◽  
pp. 109-122 ◽  
Author(s):  
WAN-KAI PANG ◽  
PING-KEI LEUNG ◽  
XIAO-LONG PU ◽  
SHI-SONG MAO
Keyword(s):  
Monte Carlo ◽  
Weibull Distribution ◽  
Real Data ◽  
Model Parameters ◽  
Reliability Model ◽  
Estimation Of Parameters ◽  
Data Set ◽  
Failure Data ◽  
Mcem Algorithm ◽  
Monte Carlo Em

In reliability studies, often we only have one failure data recorded in a life testing experiment. If there are two parameters in the reliability model, such as the model using Weibull distribution, then maximum likelihood estimation of parameters becomes a difficult problem. Mao and Chen published a real data set of the lifetime of a certain type of bearings which only contains one failure data. They used a Bayesian method to analyze the data and obtained some results for model parameter estimation. However, in their method the choice of prior distribution will affect heavily the final results. In this paper, we propose a Monte Carlo EM (MCEM) algorithm to estimate reliability model parameters using the Weibull distribution. Based on the same data set of Mao and Chen, we obtain some results using the MCEM algorithm. Our results do not depend on the choice of arbitrary prior distributions.

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.

scholarly journals Robust Mixture Modeling Based on Two-Piece Scale Mixtures of Normal Family

Axioms ◽  
2019 ◽  
Vol 8 (2) ◽  
pp. 38 ◽  
Author(s):  
Mohsen Maleki ◽  
Javier Contreras-Reyes ◽  
Mohammad Mahmoudi
Keyword(s):  
Real Data ◽  
Finite Mixture ◽  
Maximum Likelihood Estimates ◽  
Model Parameters ◽  
Normal Distributions ◽  
Scale Mixtures ◽  
Robust Model ◽  
Heavy Tailed Distributions ◽  
The Family ◽  
Heavy Tailed

In this paper, we examine the finite mixture (FM) model with a flexible class of two-piece distributions based on the scale mixtures of normal (TP-SMN) family components. This family allows the development of a robust estimation of FM models. The TP-SMN is a rich class of distributions that covers symmetric/asymmetric and light/heavy tailed distributions. It represents an alternative family to the well-known scale mixtures of the skew normal (SMSN) family studied by Branco and Dey (2001). Also, the TP-SMN covers the SMN (normal, t, slash, and contaminated normal distributions) as the symmetric members and two-piece versions of them as asymmetric members. A key feature of this study is using a suitable hierarchical representation of the family to obtain maximum likelihood estimates of model parameters via an EM-type algorithm. The performances of the proposed robust model are demonstrated using simulated and real data, and then compared to other finite mixture of SMSN models.

scholarly journals Statistical Inference for the Weibull Distribution Based on δ-Record Data

Symmetry ◽  
2019 ◽  
Vol 12 (1) ◽  
pp. 20 ◽  
Author(s):  
Raúl Gouet ◽  
F. Javier López ◽  
Lina Maldonado ◽  
Gerardo Sanz
Keyword(s):  
Maximum Likelihood ◽  
Experimental Design ◽  
Weibull Distribution ◽  
Bayesian Estimation ◽  
Statistical Inference ◽  
Numerical Computation ◽  
Weibull Model ◽  
Rainfall Series ◽  
Estimation Of Parameters ◽  
Record Data

We consider the maximum likelihood and Bayesian estimation of parameters and prediction of future records of the Weibull distribution from δ -record data, which consists of records and near-records. We discuss existence, consistency and numerical computation of estimators and predictors. The performance of the proposed methodology is assessed by Montecarlo simulations and the analysis of monthly rainfall series. Our conclusion is that inferences for the Weibull model, based on δ -record data, clearly improve inferences based solely on records. This methodology can be recommended, more so as near-records can be collected along with records, keeping essentially the same experimental design.

scholarly journals Accelerated Life Tests under Pareto-IV Lifetime Distribution: Real Data Application and Simulation Study

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1786 ◽  
Author(s):  
A. M. Abd El-Raheem ◽  
M. H. Abu-Moussa ◽  
Marwa M. Mohie El-Din ◽  
E. H. Hafez
Keyword(s):  
Simulation Study ◽  
Stress Test ◽  
Real Data ◽  
Accelerated Life Test ◽  
Maximum Likelihood Estimates ◽  
Cumulative Exposure ◽  
Exposure Model ◽  
Model Parameters ◽  
Data Set ◽  
Accelerated Life

In this article, a progressive-stress accelerated life test (ALT) that is based on progressive type-II censoring is studied. The cumulative exposure model is used when the lifetime of test units follows Pareto-IV distribution. Different estimates as the maximum likelihood estimates (MLEs) and Bayes estimates (BEs) for the model parameters are discussed. Bayesian estimates are derived while using the Tierney and Kadane (TK) approximation method and the importance sampling method. The asymptotic and bootstrap confidence intervals (CIs) of the parameters are constructed. A real data set is analyzed in order to clarify the methods proposed through this paper. Two types of the progressive-stress tests, the simple ramp-stress test and multiple ramp-stress test, are compared through the simulation study. Finally, some interesting conclusions are drawn.

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