Abstract
In this paper we use the maximum likelihood (ML) and the modified maximum likelihood (MML) methods to estimate the unknown parameters of the inverse Weibull (IW) distribution as well as the corresponding approximate confidence intervals. The estimates of the unknown parameters are obtained based on two sampling schemes, namely, simple random sampling (SRS) and ranked set sampling (RSS). Comparison between the different proposed estimators is made through simulation via their mean square errors (MSE), Pitman nearness probability (PN) and confidence length.
Highlights
Ranked set sampling is recognized as a useful sampling technique for improving the precision and increasing the efficiency of estimation when the variable under consideration is expensive to measure or difficult to obtain but cheap and easy to rank
We have considered the estimation problem of the unknown parameters of the inverse Weibull (IW) distribution based on simple random sampling (SRS) and ranked set sampling (RSS)
It is noted that the maximum likelihood (ML) estimators cannot be obtained in closed forms, so, the MML estimates (MMLEs) have been presented
Summary
Ranked set sampling is recognized as a useful sampling technique for improving the precision and increasing the efficiency of estimation when the variable under consideration is expensive to measure or difficult to obtain but cheap and easy to rank. Many authors have studied the RSS and its modifications; for example, Al-Saleh and Al-Hadrami (2003a) studied the ML and MML estimation of location parameters of symmetric distribution using moving extremes ranked set sampling and SRS. Al-Saleh et al (2003b) studied ML and MML estimation of the mean of exponential distribution based on moving extremes ranked set sampling under both perfect and imperfect ranking. Balci et al (2013) used RSS, ranked set sampling by choosing both diagonal elements and ranked set sampling by choosing extremes of the samples to derive the MML estimates (MMLEs) for the population mean and variance of normal distribution. The main objective of this study is to obtain the MLEs and MMLEs as well as the approximate confidence intervals for the scale and the shape parameters of the IW distribution based on SRS and RSS.
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