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

Published: 2023-11-16

Page: 36-66

Neethu Jacob *

Department of Statistics, Nirmala College, Muvattupuzha, Kerala, India.

Anjana E. J.

Department of Mathematics, Rheinische Friedrich-Wilhelms-Universit ¨ at Bonn, Bonn-53115, Germany.

*Author to whom correspondence should be addressed.

### Abstract

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.

Keywords: Lomax distribution, stress strength reliability, maximum likelihood estimator, quasi likelihood estimator, confidence interval

#### How to Cite

Jacob, Neethu, and Anjana E. J. 2023. “Estimation of Stress Strength Reliability P [Y < X < Z] of Lomax Distribution under Different Sampling Scheme”. Current Journal of Applied Science and Technology 42 (42):36-66. https://doi.org/10.9734/cjast/2023/v42i424271.

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