scholarly journals Classical and Bayesian Estimation of Two-Parameter Power Function Distribution

2021 ◽  
Author(s):  
Xuechen Liu ◽  
Muhammad Arslan ◽  
Majid Khan ◽  
Syed Masroor Anwar ◽  
Zahid Rasheed
Keyword(s):  
Maximum Likelihood ◽  
Power Function ◽  
Real Life ◽  
Maximum Likelihood Estimates ◽  
Time Model ◽  
Data Set ◽  
Bayes Estimates ◽  
Function Distribution ◽  
Power Function Distribution ◽  
Two Parameter

The power function distribution is a flexible waiting time model that may provide better fit for some failure data. This paper presents the comparison of the maximum likelihood estimates and the Bayes estimates of two-parameter power function distribution. The Bayes estimates are obtained, using conjugate priors, under five loss functions consist of square error, precautionary, weighted, LINEX and DeGroot loss function. The Gibbs sampling algorithm is proposed to generate samples from posterior distributions and in result the Bayes estimates are computed. The comparison of the maximum likelihood estimates and the Bayes estimates are done through the root mean squared errors. One real-life data set is analyzed to illustrate the evaluation of proposed methods of estimation. Finally, results from the simulation are discussed to assess the performance behavior of the maximum likelihood estimates and the Bayes estimates.

scholarly journals The Bayesian Estimation for The Shape Parameter of The Power Function Distribution (PFD-I) to Use Hyper Prior Functions

2021 ◽  
Vol 27 (127) ◽  
pp. 229-252
Author(s):  
Jinan Abbas Naser Al-obedy
Keyword(s):  
Maximum Likelihood ◽  
Exponential Distribution ◽  
Power Function ◽  
Loss Function ◽  
Shape Parameter ◽  
Loss Functions ◽  
Erlang Distribution ◽  
Bayes Estimators ◽  
Function Distribution ◽  
Power Function Distribution

The objective of this study is to examine the properties of Bayes estimators of the shape parameter of the Power Function Distribution (PFD-I), by using two different prior distributions for the parameter θ and different loss functions that were compared with the maximum likelihood estimators. In many practical applications, we may have two different prior information about the prior distribution for the shape parameter of the Power Function Distribution, which influences the parameter estimation. So, we used two different kinds of conjugate priors of shape parameter θ of the Power Function Distribution (PFD-I) to estimate it. The conjugate prior function of the shape parameter θ was considered as a combination of two different prior distributions such as gamma distribution with Erlang distribution and Erlang distribution with exponential distribution and Erlang distribution with non-informative distribution and exponential distribution with the non-informative distribution. We derived Bayes estimators for shape parameter θ of the Power Function Distribution (PFD-I) according to different loss functions such as the squared error loss function (SELF), the weighted error loss function (WSELF) and modified linear exponential (MLINEX) loss function (MLF), with two different double priors. In addition to the classical estimation (maximum likelihood estimation). We used simulation to get the results of this study, for different cases of the shape parameter of the Power Function Distribution used to generate data for different samples sizes.

scholarly journals Risk Efficiencies of Empirical Bayes and Generalized Maximum Likelihood Estimates for Rayleigh Model under Censored Data

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Dinesh Barot ◽  
Manhar Patel
Keyword(s):  
Maximum Likelihood ◽  
Loss Function ◽  
Empirical Bayes ◽  
Real Data ◽  
Rayleigh Distribution ◽  
Comparison Method ◽  
Maximum Likelihood Estimates ◽  
Data Set ◽  
Bayes Estimates ◽  
Generalized Maximum Likelihood

The comparison of empirical Bayes and generalized maximum likelihood estimates of reliability performances is made in terms of risk efficiencies when the data are progressively Type II censored from Rayleigh distribution. The empirical Bayes estimates are obtained using an asymmetric loss function. The risk functions of the estimates and risk efficiencies are obtained under this loss function. A real data set is presented to illustrate the proposed comparison method, and the performance of the estimates is examined and compared in terms of risk efficiencies by means of Monte Carlo simulations. The simulation results indicate that the proposed empirical Bayes estimates are more preferable than the generalized maximum likelihood estimates.

scholarly journals Estimation of Information Measures for Power-Function Distribution in Presence of Outliers and Their Applications

2021 ◽  
Vol 21 (No.1) ◽  
pp. 1-25
Author(s):  
Amal Soliman Hassan ◽  
Elsayed Ahmed Elsherpieny ◽  
Rokaya Elmorsy Mohamed
Keyword(s):  
Maximum Likelihood ◽  
Power Function ◽  
Real Data ◽  
The Other ◽  
Loss Functions ◽  
Squared Error Loss Function ◽  
Bayesian Estimates ◽  
Function Distribution ◽  
Power Function Distribution ◽  
Bayesian Estimators

The measure of entropy has an undeniable pivotal role in the field of information theory. This article estimates the Rényi and q-entropies of the power function distribution in the presence of s outliers. The maximum likelihood estimators as well as the Bayesian estimators under uniform and gamma priors are derived. The proposed Bayesian estimators of entropies under symmetric and asymmetric loss functions are obtained. These estimators are computed empirically using Monte Carlo simulation based on Gibbs sampling. Outcomes of the study showed that the precision of the maximum likelihood and Bayesian estimates of both entropies measures improves with sample sizes. The behavior of both entropies estimates increase with number of outliers. Further, Bayesian estimates of the Rényi and q-entropies under squared error loss function are preferable than the other Bayesian estimates under the other loss functions in most of cases. Eventually, real data examples are analyzed to illustrate the theoretical results.

Estimation of Reliability in a Multicomponent Stress–Strength Model Based on Power Transformed Half-Logistic Distribution

2020 ◽  
pp. 2150009 ◽  
Author(s):  
Thomas Xavier ◽  
Joby K. Jose
Keyword(s):  
Maximum Likelihood ◽  
Real Life ◽  
Maximum Likelihood Estimates ◽  
Logistic Distribution ◽  
Strength Model ◽  
Squared Error Loss Function ◽  
Squared Error Loss ◽  
Bayes Estimates ◽  
Squared Error ◽  
Proposed Model

This paper deals with the study of the reliability of multicomponent stress–strength model assuming that the strength components are independently and identically distributed as power transformed half-logistic (PHL) distribution. The strength components which are subject to a common stress are assumed to be independent with either Weibull distribution or PHL distribution. The maximum likelihood estimates of the multicomponent stress–strength reliability and its asymptotic confidence interval under the above said conditions are obtained. The Bayes estimates of the multicomponent stress–strength reliability are also obtained under squared error loss function and using gamma priors for the parameters. To evaluate the performance of the procedure, a simulation study is considered. For illustration purpose of the proposed model, two real life examples are given.

scholarly journals Estimation of power function distribution based on selective order statistic

2018 ◽  
Vol 15 (2) ◽  
Author(s):  
Mohd Alodat ◽  
Mohammad Al-Rawwash ◽  
Sameer Al-Subh
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Power Function ◽  
Method Of Moments ◽  
Order Statistic ◽  
Sampling Scheme ◽  
Likelihood Estimator ◽  
Function Distribution ◽  
Power Function Distribution ◽  
Method Of Moments Estimator

In this article, we present the selective order statistic sampling scheme as a promising approach to estimate the parameter of the univariate power function distribution. We derive the maximum likelihood estimator and the method of moments estimator of the power function distribution parameter as well as the reliability parameter and the ratio of two means. Moreover, we derive the asymptotic properties of the proposed estimators. Finally, we conduct simulation studies to investigate the performance of the selective order statistic scheme and concluded that it suits the power function distribution and we found that the maximum likelihood estimator is better than the method of moments estimator under the selective order statistic sampling scheme.

scholarly journals A Family of Loss Distributions with an Application to the Vehicle Insurance Loss Data

2019 ◽  
pp. 731-744 ◽  
Author(s):  
Zubair Ahmad Ahmad ◽  
Eisa Mahmoudi Mahmoudi ◽  
G. G. Hamedani
Keyword(s):  
Maximum Likelihood ◽  
Financial Risk ◽  
Maximum Likelihood Estimates ◽  
Model Parameters ◽  
Data Set ◽  
Loss Model ◽  
New Class ◽  
Proposed Model ◽  
Loss Distributions ◽  
Loss Data

Actuaries are often in search of nding an adequate loss model in the scenario of actuarial and financial risk management problems. In this work, we propose a new approach to obtain a new class of loss distributions. A special sub-model of the proposed family, called the Weibull-loss model isconsidered in detail. Some mathematical properties are derived and maximum likelihood estimates of the model parameters are obtained. Certain characterizations of the proposed family are also provided. A simulation study is done to evaluate the performance of the maximum likelihood estimators. Finally, an application of the proposed model to the vehicle insurance loss data set is presented.

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