Using the Jackknife method and the Bayesian method to estimator the reliability function of the beta distribution

A Thesis Submitted to

Council of  The Administration and Economics/ Karbala University as Partial fulfillment of the Requirements for the Degree of Master of Science in

 Statistics  

Presented by

Alaa Adnan Aoda

Supervised ByAss. Prof. Dr. Enas Abdel- Hafez Mohamed

Abstract

The beta distribution is one of the continuous probability distributions with two parameters of the form (β, α) and defined by the time period [0,1]. The reliability function of the beta distribution, given the parameter (1=β) using two methods, the first is the Jackknife method, which is based on the maximum potential estimator (Jac1) and the Jackknife method is based on the moment estimator (Jac2), and the second is the Bayes method with a loss function Quadratic (bayes1) and pes with a modified quadratic loss function (bayes2) The simulation method was employed by the Monte-Carlo method and the (Mathematica 12.2) program was used to design a number of simulation experiments using different default values ​​for parameters and sample sizes         ( 10,20,25,75,100) and the experiment was repeated (1000) times to obtain high homogeneity in order to compare the estimation methods to show which estimators are the most accurate in use in estimating the shape parameter (α) and the reliability function for this distribution among the methods used in this thesis. Depending on my score To determine the best of them, they are the mean squared error (MSE) and the mean squared integral error (IMSE). The results showed the convergence of the bayes1 method) and the (jac2) method in terms of preference in estimating a function Reliability compared with the rest of the estimation methods, and a practical application of data on the pulmonary resuscitation system (CPAP) was carried out using the best methods that were reached on the experimental side in estimating the reliability function of the beta distribution, where it was shown the preference of the Jack Knife method (Jac2) over the Bayes1 in estimating the reliability function of the beta distribution of real data by using comparison criteria.                                                             

Using the Jackknife method and the Bayesian method to estimator the reliability function of the beta distribution

A Thesis Submitted to

Council of  The Administration and Economics/ Karbala University as Partial fulfillment of the Requirements for the Degree of Master of Science in

 Statistics  

Presented by

Alaa Adnan Aoda

Supervised ByAss. Prof. Dr. Enas Abdel- Hafez Mohamed

Abstract

The beta distribution is one of the continuous probability distributions with two parameters of the form (β, α) and defined by the time period [0,1]. The reliability function of the beta distribution, given the parameter (1=β) using two methods, the first is the Jackknife method, which is based on the maximum potential estimator (Jac1) and the Jackknife method is based on the moment estimator (Jac2), and the second is the Bayes method with a loss function Quadratic (bayes1) and pes with a modified quadratic loss function (bayes2) The simulation method was employed by the Monte-Carlo method and the (Mathematica 12.2) program was used to design a number of simulation experiments using different default values ​​for parameters and sample sizes         ( 10,20,25,75,100) and the experiment was repeated (1000) times to obtain high homogeneity in order to compare the estimation methods to show which estimators are the most accurate in use in estimating the shape parameter (α) and the reliability function for this distribution among the methods used in this thesis. Depending on my score To determine the best of them, they are the mean squared error (MSE) and the mean squared integral error (IMSE). The results showed the convergence of the bayes1 method) and the (jac2) method in terms of preference in estimating a function Reliability compared with the rest of the estimation methods, and a practical application of data on the pulmonary resuscitation system (CPAP) was carried out using the best methods that were reached on the experimental side in estimating the reliability function of the beta distribution, where it was shown the preference of the Jack Knife method (Jac2) over the Bayes1 in estimating the reliability function of the beta distribution of real data by using comparison criteria.