Abstract
A flexible ranked set sampling scheme including some various existing sampling methods is proposed. This scheme may be used to minimize the error of ranking and the cost of sampling. Based on the data obtained from this scheme, the maximum likelihood estimation as well as the Fisher information are studied for the scale family of distributions. The existence and uniqueness of the maximum likelihood estimator of the scale parameter of the exponential and normal distributions are investigated. Moreover, the optimal scheme is derived via simulation and numerical computations.
Highlights
Ranked set sampling (RSS) was introduced by [14] as a method for unbiased selective sampling
The maximum likelihood estimator (MLE) was considered in scale family of distributions based on the flexible RSS (FRSS)
The amount of Fisher information (FI) about the parameter of interest was studied and some results were presented in detail for the case of exponential distribution
Summary
Ranked set sampling (RSS) was introduced by [14] as a method for unbiased selective sampling In this scheme, k independent sets each contains k units are randomly selected from the population of interest. When judgment ranking is accurate, we say the ranking is perfect and the selected units are a sample of k independent order statistics This scheme may be repeated at some cycles to attain a reasonable data set. We consider three existing types of ranking sampling schemes which are briefly explained as follows: Extreme ranked set sampling (ERSS): This procedure was introduced by [19] in estimating problem of the population mean which is similar to RSS but only minimum or maximum of each set is measured and it is assumed that they can be detected visually. The minimum of the first [k/2] sets and the maximum of the last [k/2] sets are selected, where [a] is the integer part of a, the median of the ((k + 1)/2)th set is measured
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