Ranked set sampling on estimation of $P[Y<X]$ for inverse Weibull distribution and its applications

Abstract

Purpose

Distribution. The purpose of this study is to obtain the modified maximum likelihood estimator of stress–strength model using the ranked set sampling, to obtain the asymptotic and bootstrap confidence interval of P[Y < X], to compare the performance of author’s estimates with the estimates under simple random sampling and to apply author’s estimates on head and neck cancer.

Design/methodology/approach

The maximum likelihood estimator of R = P[Y < X], where X and Y are two independent inverse Weibull random variables common shape parameter that affect the shape of the distribution, and different scale parameters that have an effect on the distribution dispersion are given under ranked set sampling. Together with the asymptotic and bootstrap confidence interval, Monte Carlo simulation shows that this estimator performs better than the estimator under simple random sampling. Also, the asymptotic and bootstrap confidence interval under ranked set sampling is better than these interval estimators under simple random sampling. The application to head and neck cancer disease data shows that the estimator of R = P[Y < X] that shows the treatment with radiotherapy is more efficient than the treatment with a combined radiotherapy and chemotherapy under ranked set sampling that is better than these estimators under simple random sampling.

Findings

The ranked set sampling is more effective than the simple random sampling for the inference of stress-strength model based on inverse Weibull distribution.

Originality/value

This study sheds light on the author’s estimates on head and neck cancer.

Citation

Hassan, M.K. (2022), "Ranked set sampling on estimation of $P[Y<X]$ for inverse Weibull distribution and its applications", International Journal of Quality & Reliability Management, Vol. 39 No. 7, pp. 1535-1550. https://doi.org/10.1108/IJQRM-06-2021-0166