Different Estimation Methods of the Stress-Strength Reliability Restricted Exponentiated Lomax Distribution

Abstract

Lomax distribution, a large-scale probabilistic distribution used in industry, economics, actuarial science, queue theory, and Internet traffic modeling, is the most important distribution in reliability theory. In this paper estimating the reliability of Restricted exponentiated Lomax distribution in two cases, when one component X strength and Y stress R=P(Y<X), and when system content two component series strength, Y stress by using different estimation method. such as maximum likelihood, least square and shrinkage methods. A comparison between the outcomes results of the applied methods has been carried out based on mean square error (MSE) to investigate the best method and the obtained results have been displayed via MATLAB software package.

Properties and Application of the Suggested Exponentiated Lomax Distribution Family

“…Assuming that (θ =2) and (θ =1), then we get two proposed new distributions; the Modified Exponentiated Lomax Distribution and the Restricted Exponentiated Lomax Distribution. This is will be a new family for the (ELD) [8], [9]. In Figure 1, it is possible to describe the proposed exponentiated Lomax distribution family.…”

“…Real data app is analysis and will be tested their flexibility for the suggested distributions. In comparison with Modified Exponentiated Lomax (MELD) and the Restricted Exponentiated Lomax distributions (RELD) with family distributions "Exponentiated Lomax (ELD), Lomax (LD), power Lomax (Polo) [9], Exponentiated (ED)". The MATLAB environment package was implemented to find the analytical measures according to statistic criteria (Akaike Information Criteria, Bayesian Information Criteria, Consistent Akaike Information Criteria, in addition to Hanan and Quinn Criteria [11], [12], [13].…”

“…The maximum likelihood estimator of the both two distributions introduced in section 5 as well as the numerical illustrations. [8], [9].…”

Reliability Estimation in Stress Strength for Generalized Rayleigh Distribution Using a Lower Record Ranked Set Sampling Scheme

“…Bi et al [2] studied the R estimation problem of the inverse Weibull distribution of the stress intensity. Hamad et al [3] utilized maximum likelihood estimation and the least squares method to estimate R in Lomax distributed models. Beyond single-component models, multi-component stress-strength frameworks have increasingly attracted scholarly interest.…”