Estimation of the Weibull Distribution Parameters and Reliability Using Kernel and Bayes Approaches

A new estimation technique based on the non-parametric kernel density estimation is introduced as an alternative and reliable technique for estimation in life testing models. This technique estimates the density functions of the parameters and reliability directly from the data without any prior assumptions about the underlying distribution parameters. The efficiency of this technique has been studied comparing to the Bayesian estimation of the parameters and reliability of the Weibull distribution based on the non-informative, informative and the informative conjugate priors, via Monte Carlo simulations, which indicated the robustness of the proposed method than the Bayesian approach. Finally, a numerical example is given to illustrate the densities and the inferential methods developed in this paper

Statistical Inference for the Modified Weibull Model Based on the Generalized Order Statistics

In recent years, a new class of models has been proposed to exhibit bathtub-shaped failure rate functions. The modified Weibull is one of these models, which is a generalization for the Weibull distribution and is capable of modeling bathtub-shaped and increasing failure rate lifetime data. In this paper, conditional inference has been applied to constructing the confidence intervals for its parameters based on the generalized order statistics. For measuring the performance of this approach compared to the Asymptotic Maximum Likelihood estimates (AMLEs), simulations studies have been carried out for different values of sample sizes and shape parameters. The simulation results indicated that the conditional intervals possess good statistical properties and they can perform quite well even when the sample size is extremely small compared to the AMLE intervals. Finally, a numerical example is given to illustrate the confidence intervals developed in this paper

Characterization of the Generalized Life Model Based on the Generalized Order Statistics

In this paper, a characterization of the generalized life model based on some recurrence relations for single and product moments based on the generalized order statistics are obtained. The results presented here are a generalization of the recurrence relations for single and product moments of many lifetime distributions in the literature, which are special cases such as the generalized Pareto model and the generalized Weibull model based on the ordinary order statistics

Recurrence Relations for Moment Generating Functions of the Generalized Compound Rayleigh Distribution

In this paper, we consider the three-parameter generalized compound Rayleigh distribution. The recurrence relations for moment generating functions based on the generalized order statistics are obtained. The results presented here are a generalization of the recurrence relations for Single and product moment generating functions, based on the ordinary order statistics and the upper record statistics for some lifetime distributions in the literature such as Beta-Prime, Lomax, Burr XII, and Compound Rayleigh distributions which are special cases from the generalized compound Rayleigh distribution

An Optimal Estimation Method on the Analysis of the Generalized Gamma Distribution Parameters Using Runge-Kutta Method

Abstract Recently, in the literature many modifications introduced to improve the maximum likelihood estimation method, however most of them are less efficient than the Bayesian method especially for small samples. Therefore, in this study an improvement method based on the Runge-Kutta technique has been introduced for estimating the generalized gamma distribution parameters and compare them with the Bayesian estimates based on the informative gamma and kernel priors. A comparison between these estimators is provided by using an extensive Monte Carlo simulation based on two criteria, namely, the absolute bias and mean squared error. The simulation results indicated that the Runge-Kutta method is highly favorable, which provides better estimates and outperforms the Bayesian estimates using different loss functions based on the generalized progressive hybrid censoring scheme. Finally, two real datasets analyses for COVID-19 epidemic in Egypt are presented to illustrate the efficiency of the proposed methods.</jats:p

Conditional Inference on the Generalized Shape-Scale Family

In parameter estimation techniques, there are many methods for estimating the distribution parameters in life data analyses. However, most of them are less efficient than the Bayesian method, despite its subjectivity. Thus, the main objective of this study is to present the conditional inference method as an alternative and efficient method for estimating the generalized shape-scale family parameters and comparing them with the Bayesian estimates. A comparison between these estimators is provided by using an extensive Monte Carlo simulation study based on two criteria, namely, the absolute average bias and mean squared error based on the generalized progressive hybrid censoring scheme. The simulation results indicated that the conditional inference is highly efficient, which provides better estimates and outperforms the Bayesian inference. Finally, two real dataset analyses are presented to illustrate the efficiency of the proposed methods.</jats:p