Likelihood and Bayesian Inference in the Lomax Distribution under Progressive Censoring

Baklizi, A.; Nik, A. Saadati; Asgharzadeh, A.

doi:10.13189/ms.2022.100318

Cited by 1 publication

(1 citation statement)

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“…[11] studied the Power of Lomax Distribution with an application to bladder cancer data. The recent developments in stress strength reliability was discussed by [12], [13], [14], [15], [16], [17], [18], [19] and [20]. In this paper estimates the stress strength reliability for a component with a strength independent of opposite lower and upper bound stresses when the stresses and strength have Lomax distribution under different sampling schemes.…”

Section: Introductionmentioning

confidence: 99%

Estimation of Stress Strength Reliability P [Y < X < Z] of Lomax Distribution under Different Sampling Scheme

Jacob,

Anjana E. J.

2023

CJAST

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Lomax distribution can be considered as the mixture of exponential and gamma distribution. This distribution is an advantageous lifetime distribution in reliability analysis. The applicability of Lomax distribution is not restricted only to the reliability field, but it has broad applications in Economics, actuarial modelling, queuing problems,biological sciences, etc. Initially, Lomax distribution was proposed by Lomax in 1954, and it is also known as Pareto Type II distribution. Many statistical methods have been developed for this distribution; for a review of Lomax Distribution, see [1] and the references. The stress strength model plays an important role in reliability analysis. The term stress strength was first introduced by [2]. In the context of reliability, R is defined as the probability that the unit strength is greater than stress, that is, R = P (X > Y ), where X is the random strength of the unit, and Y is the instant stress applied to it. Thus, estimation of R is very important in Reliability Analysis.The estimates of R discussed in the context of Lomax distribution are limited to the study of a single stress strength model with upper stress. But in real life, there are situations where we have to consider not only the upper stress Neethu and Anjana; Curr. J. Appl. Sci. Technol., vol. 42, no. 42, pp. 36-66, 2023; Article no.CJAST.107238 but also the lower stress. Accordingly, in the present paper, the estimation of stress strength model R = P (Y < X < Z) represents the situation where the strength X should be greater than stress Y and smaller than stress Z for Lomax distribution, Shrinkage maximum likelihood estimate and Quasi likelihood estimate are obtained both under complete and right censored data. We have considered the asymptotic confidence interval (CI) based on MLE and bootstrap CI for R. Monte Carlo simulation experiments were performed to compare the performance of estimates obtained.

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