Abstract
For the first time and by using an entire sample, we discussed the estimation of the unknown parameters θ1, θ2, and β and the system of stress-strength reliability R=P(Y < X) for exponentiated inverted Weibull (EIW) distributions with an equivalent scale parameter supported eight methods. We will use maximum likelihood method, maximum product of spacing estimation (MPSE), minimum spacing absolute-log distance estimation (MSALDE), least square estimation (LSE), weighted least square estimation (WLSE), method of Cramér-von Mises estimation (CME), and Anderson-Darling estimation (ADE) when X and Y are two independent a scaled exponentiated inverted Weibull (EIW) distribution. Percentile bootstrap and bias-corrected percentile bootstrap confidence intervals are introduced. To pick the better method of estimation, we used the Monte Carlo simulation study for comparing the efficiency of the various estimators suggested using mean square error and interval length criterion. From cases of samples, we discovered that the results of the maximum product of spacing method are more competitive than those of the other methods. A two real‐life data sets are represented demonstrating how the applicability of the methodologies proposed in real phenomena.
Highlights
Since Birnbaum’s [1] pioneering research, statistical inference of a system stress-strength parameter has received increased attention and is widely used in a variety of engineering applications
Introduced the estimation of stress-strength reliability for generalized exponential and Weibull random variables, respectively. um likelihood method, max Raqab et al [4] discussed the estimation of R, where X and Y are distributed as two independent three-parameter generalized exponential random variables
Let x1: n, x2: n, . . . , xn: n be the order statistics of a random sample of size n from exponentiated inverted Weibull (EIW) (θ1, β) and let y1: k, y2: k, . . . , yk: k be the order statistics of a random sample of size k from EIW (θ2, β). e least square estimations (LEs) of the unknown parameters θ1, θ2, and β denoted by θL1SE, θL2SE, and βLSE can be obtained by minimizing the following function with respect to θ1, θ2, and β as follows: 2.4
Summary
Since Birnbaum’s [1] pioneering research, statistical inference of a system stress-strength parameter has received increased attention and is widely used in a variety of engineering applications. Introduced the estimation of stress-strength reliability for generalized exponential and Weibull random variables, respectively. Um likelihood method, max Raqab et al [4] discussed the estimation of R, where X and Y are distributed as two independent three-parameter generalized exponential random variables. E main objective of this study is to estimate unknown parameters θ1, θ2, and β and stress-strength reliability R P(Y < X) when X and Y are independent of a scaled EIW distribution using the eight estimation methods listed above. To compare the efficiency of the various estimates, we conduct an extensive Monte Carlo numerical simulation study, as well as an analysis of two real-life data sets, the applicability of the methodologies proposed in real phenomena.
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