Different estimation methods for the generalized unit half-logistic geometric distribution: Using ranked set sampling

Abstract

The generalized unit half-logistic geometric distribution (GUHLGD) is a modern two-parameter unit distribution with attractive shape flexibility for the corresponding probability density and hazard rate functions. Due to its versatility, it may be used to model a variety of current bounded real-world datasets. On the other hand, an effective sampling strategy for both parametric and non-parametric inferences is the ranked set sampling (RSS) method. This article focuses on estimating the parameters of the GUHLGD based on the RSS method as well as the simple random sampling (SRS) method. Eleven traditional estimation methods are taken into consideration, including the percentile, Cramér–von Mises, maximum likelihood, Anderson–Darling, right-tailed Anderson–Darling, left-tailed Anderson–Darling, least squares, weighted least squares, minimum spacing absolute-log distance, maximum product of spacing, and minimum spacing absolute distance methods. A Monte Carlo simulation is employed to compare the performance of the resultant estimates based on some accuracy measures. We draw the conclusion that, for both sampling procedures, the maximum likelihood estimation methodology is the best option among the rest based on the partial and total ranking measures. The estimates based on the RSS method are more efficient than the others based on the SRS method. Results from actual data further support the advantage of the RSS design over the SRS design.