Estimation of P(Y X) using record values from the generalized inverted exponential distribution

Abstract

This article deals with the estimation of R = P(Y < X) when X and Y are distributed as two independent generalized inverted exponential with common scale parameter and different shape parameters. The maximum likelihood and Bayesian estimators of R are obtained on the basis of upper record values and upper record ranked set samples. The Bayesian estimator cannot be obtained in explicit form, and therefore it has been achieved using Lindley approximation. Simulation study is performed to compare the reliability estimators in each record sampling scheme with respect to biases and mean square errors.

Estimation of multicomponent stress-strength reliability following Weibull distribution based on upper record values

“…• The AB ofR S,k at n = m increases as the value of λ 1 increases for both (S, k) = (1, 3) and (2,4) [see Tables 1-3 (1, 3) 0.9 (10,10) 0.0630 0.0150 0.3400 (10,15) 0.0007 0.0051 0.2300 (15,10) 0.1310 0.0300 0.3830 (15,15) 0.0530 0.0100 0.2740 (15,20) 0.0120 0.0047 0.2100 (20,15) 0.1030 0.0200 0.3050 (20,20) 0.0530 0.0092 0.2410 (2,4) 0.8 (10,10) 0.0680 0.0220 0.4490 (10,15) 0.0130 0.0120 0.3450 (15,10) 0.1670 0.0460 0.4580 (15,15) 0.0750 0.0190 0.3790 (15,20) 0.0170 0.0110 0.3190 (20,15) 0.1300 0.0320 0.3770 (20,20) 0.0680 0.0160 0.3270…”

“…The length of intervals is the main principle of the performance of the ACI. The numerical study is designed through the following steps: and stress random variables (n, m) are chosen to be (10,10), (10,15), (15,10), (15,15), (15,20), (20,15) and (20,20). • The MLEs of λ 1 and λ 2 are obtained from (9), then the MLE of R S,k is obtained by substitutingλ 1 andλ 2 in (10).…”

“…• Compute the average ABs and average MSEs for reliability estimates over 5000 replications (see Tables 1-7). • Obtain the asymptotic variance of R 1,3 , R 2,4 by using (14) and (15), then compute the asymptotic standard deviation;σ R 1,3 ,σ R 2,4 . • Compute the lower and upper limits of the ACI of R 1,3 , R 2,4 through relation (16).…”

“…The survival probability of stress-strength R = P(Y < X) based on record values is considered in Baklizi [6] for generalized exponential distribution. Subsequent papers extended this work assuming various lifetime distributions for stress-strength random variables, for instance, in Baklizi [7,8,9], for one and two parameter exponential distribution, Essam [10] for type I generalized logistic distribution, Baklizi [11] for two-parameter Weibull distribution, Tarvirdizade and Kazemzadeh Garehchobogh [12] for inverse Rayleigh distribution, Al-Gashgari and Shawky [13] for exponentiated Weibull distribution, Hassan et al [14] for exponentiated inverted Weibull distribution and Hassan et al [15] for generalized inverted exponential distribution.…”

Classical and Bayesian Estimation of Stress-Strength Reliability from Generalized Inverted Exponential Distribution based on Upper Records

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This paper deals with the problem of classical and Bayesian estimation of stress-strength reliability from a generalized inverted exponential distribution (GIED) based on upper record values. Hassan et al (2018) have discussed the maximum likelihood estimator (MLE) and Bayes estimator of R by considering that the scale parameter of defined distribution is known while we have considered the case when all the parameters of GIED are unknown. In classical approach, we have obtained MLE and uniformly minimum variance estimator (UMVUE).

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