scholarly journals Does the Type of Records Affect the Estimates of the Parameters?

2022 ◽  
Vol 19 (1) ◽  
Author(s):  
Mohd. Arshad ◽  
Qazi J. Azhad
Keyword(s):  
Bayesian Approach ◽  
Maximum Likelihood Estimators ◽  
Reliability Function ◽  
Record Values ◽  
Loss Functions ◽  
Bayes Estimators ◽  
Unknown Parameters ◽  
Numerical Examples ◽  
Record Data ◽  
Family Of Distributions

A general family of distributions, namely Kumaraswamy generalized family of (Kw-G) distribution, is considered for estimation of the unknown parameters and reliability function based on record data from Kw-G distribution. The maximum likelihood estimators (MLEs) are derived for unknown parameters and reliability function, along with its confidence intervals. A Bayesian study is carried out under symmetric and asymmetric loss functions in order to find the Bayes estimators for unknown parameters and reliability function. Future record values are predicted using Bayesian approach and non Bayesian approach, based on numerical examples and a monte carlo simulation.

Inference on P(Y

2020 ◽  
Vol 72 (2) ◽  
pp. 89-110
Author(s):  
Manoj Chacko ◽  
Shiny Mathew
Keyword(s):  
Maximum Likelihood ◽  
Pareto Distribution ◽  
Generalized Pareto Distribution ◽  
Maximum Likelihood Estimators ◽  
Record Values ◽  
Asymptotic Distributions ◽  
Bayes Estimators ◽  
Generalized Pareto ◽  
Pareto Distributions ◽  
Generalized Pareto Distributions

In this article, the estimation of [Formula: see text] is considered when [Formula: see text] and [Formula: see text] are two independent generalized Pareto distributions. The maximum likelihood estimators and Bayes estimators of [Formula: see text] are obtained based on record values. The Asymptotic distributions are also obtained together with the corresponding confidence interval of [Formula: see text]. AMS 2000 subject classification: 90B25

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 The Comparison Between the MLE and Standard Bayes Estimators of the Reliability Function of Exponential Distribution

2019 ◽  
Vol 32 (1) ◽  
pp. 103
Author(s):  
Mohammed Jamel Ali ◽  
Hazim Mansoor Gorgees
Keyword(s):  
Loss Function ◽  
Reliability Function ◽  
Loss Functions ◽  
Mean Square ◽  
Bayes Estimators ◽  
Squared Error Loss Function ◽  
Monte Carlo Simulation Technique ◽  
Error Loss ◽  
Squared Error ◽  
The One

     In this paper, a Monte Carlo Simulation technique is used to compare the performance of MLE and the standard Bayes estimators of the reliability function of the one parameter exponential distribution.Two types of loss functions are adopted, namely, squared error  loss function (SELF) and modified square error loss function (MSELF) with informative and non- informative prior. The criterion integrated mean square error (IMSE) is employed to assess the performance of such estimators .

scholarly journals Bayes Estimation of the Reliability Function of Pareto Distribution Under Three Different Loss Functions

2020 ◽  
Author(s):  
Gaurav Shukla ◽  
Umesh Chandra ◽  
Vinod Kumar
Keyword(s):  
Shape Parameter ◽  
Pareto Distribution ◽  
Risk Function ◽  
Simulated Data ◽  
Reliability Function ◽  
Minimum Variance ◽  
Bayes Estimation ◽  
Loss Functions ◽  
Bayes Estimators ◽  
Data Set

In this paper, we have proposed Bayes estimators of shape parameter of Pareto distribution as well as reliability function under SELF, QLF and APLF loss functions. For better understanding of Bayesian approach, we consider Jeffrey’s prior as non-informative prior, exponential and gamma priors as informative priors. The proposed estimators have been compared with Maximum likelihood estimator (MLE) and the uniformly minimum variance unbiased estimator (UMVUE). Moreover, the current study also derives the expressions for risk function under these three loss functions. The results obtained have been illustrated with the real as well as simulated data set.

scholarly journals Pareto Distribution under Hybrid Censoring: Some Estimation

2021 ◽  
Vol 19 (1) ◽  
pp. 2-17
Author(s):  
Gyan Prakash
Keyword(s):  
Pareto Distribution ◽  
Simulated Data ◽  
Likelihood Estimation ◽  
Real Data ◽  
Loss Functions ◽  
Bayes Estimators ◽  
Unknown Parameters ◽  
Data Set ◽  
Hybrid Censoring ◽  
Pareto Model

In the present study, the Pareto model is considered as the model from which observations are to be estimated using a Bayesian approach. Properties of the Bayes estimators for the unknown parameters have studied by using different asymmetric loss functions on hybrid censoring pattern and their risks have compared. The properties of maximum likelihood estimation and approximate confidence length have also been investigated under hybrid censoring. The performances of the procedures are illustrated based on simulated data obtained under the Metropolis-Hastings algorithm and a real data set.

scholarly journals Approximate Bayes Estimators of the Parameters of the Inverse Gaussian Distribution Under Different Loss Functions

2020 ◽  
Author(s):  
Ilhan Usta ◽  
Merve Akdede
Keyword(s):  
Gaussian Distribution ◽  
Inverse Gaussian Distribution ◽  
Loss Functions ◽  
Approximation Methods ◽  
Inverse Gaussian ◽  
Bayes Estimators ◽  
Unknown Parameters ◽  
Data Set ◽  
Bayes Estimates ◽  
Two Parameters

Inverse Gaussian is a popular distribution especially in the reliability and life time modelling, and thus the estimation of its unknown parameters has received considerable interest. This paper aims to obtain the Bayes estimators for the two parameters of the inverse Gaussian distribution under varied loss functions (squared error, general entropy and linear exponential). In Bayesian procedure, we consider commonly used non-informative priors such as the vague and Jeffrey’s priors, and also propose using the extension of Jeffrey’s prior. In the case where the two parameters are unknown, the Bayes estimators cannot be obtained in the closed-form. Hence, we employ two approximation methods, namely Lindley and Tierney Kadane (TK) approximations, to attain the Bayes estimates of the parameters. In this paper. the effects of considered loss functions, priors and approximation methods on Bayesian parameter estimation are also presented. The performance of Bayes estimates is compared with the corresponding classical estimates in terms of the bias and the relative efficiency throughout an extensive simulation study. The results of the comparison show that Bayes estimators obtained by TK method under linear exponential loss function using the proposed prior outperform the other estimators for estimating the parameters of inverse Gaussian distribution most of the time. Finally, a real data set is provided to illustrate the results.

scholarly journals The Comparison Between Standard Bayes Estimators of the Reliability Function of Exponential Distribution

2018 ◽  
Vol 31 (3) ◽  
pp. 135 ◽  
Author(s):  
Mohammed Jamel Ali ◽  
Hazim Mansoor Gorgees ◽  
Adel Abdul Kadhim Hussein
Keyword(s):  
Exponential Distribution ◽  
Loss Function ◽  
Reliability Function ◽  
Loss Functions ◽  
Bayes Estimators ◽  
Squared Error Loss Function ◽  
Monte Carlo Simulation Technique ◽  
Error Loss ◽  
Squared Error ◽  
The One

   In this paper, a Monte Carlo Simulation technique is used to compare the performance of the standard Bayes estimators of the reliability function of the one parameter exponential distribution .Three types of loss functions are adopted, namely, squared error  loss function (SELF) ,Precautionary error loss function (PELF) andlinear exponential error  loss function(LINEX) with informative and non- informative prior .The criterion integrated mean square error (IMSE) is employed to assess the performance of such estimators

Estimations and Prediction for the Compound Rayleigh Distribution Based on Upper Record Values

2018 ◽  
Vol 15 (2) ◽  
pp. 711-718 ◽  
Author(s):  
M. M. Badr
Keyword(s):  
Prediction Interval ◽  
Record Values ◽  
Rayleigh Distribution ◽  
Bayes Estimators ◽  
Unknown Parameters ◽  
Hazard Functions ◽  
Upper Record Values ◽  
Upper Record ◽  
Two Parameters ◽  
Compound Rayleigh Distribution

This article considers estimation of the unknown parameters for the compound Rayleigh distribution (CRD) based on upper record values. We have derived the maximum likelihood (ML) and Bayesian estimators for the unknown two parameters, as well as the reliability and hazard functions. We obtained Bayes estimators on the basis of the symmetric (squared error) and asymmetric (linear exponential (LINEX) and general entropy (GE)) loss functions. It has been seen that the symmetric and asymmetric Bayes estimators are obtained in closed forms. Furthermore, Bayesian prediction interval of the future upper record values are discussed and obtained. Finally, estimation of the parameters, practical examples of real record values and simulated record values are given to illustrate the theoretical results of prediction interval.

scholarly journals Estimation of Scale Parameter of Weibull-Lomax distribution via Bayesian Approach

2021 ◽  
Vol 09 (05) ◽  
Author(s):  
Arun Kumar Rao, ◽  
Keyword(s):  
Bayesian Analysis ◽  
Bayesian Approach ◽  
Scale Parameter ◽  
Loss Functions ◽  
Bayes Estimators ◽  
Lomax Distribution ◽  
Squared Error

In this paper, the Weibull-Lomax distribution is considered for Bayesian analysis. The expressions for Bayes estimators of the parameter have been derived under squared error, precautionary, entropy, K-loss, and Al-Bayyati’s loss functions by using quasi and gamma priors.

Sign in / Sign up

Export Citation Format

Share Document