Monte Carlo Generation of Order Statistics from General Distributions

Abstract

Several methods are considered for the generation of a complete set of order statistics from a specified distribution. In the case of the uniform distribution, several methods in the literature are collected and reviewed. Three methods appropriate for general distributions are then described, with the normal and beta distributions considered as examples. The recommended method, which appears to be new, consists of dividing the range of the distribution into a large number of intervals and applying rejection sampling on each interval.

Economical sampling plans with warranty based on truncated data from Burr type XII distribution

“…Step 1: Generate a pseudo (n, r) II sample by using the analogous algorithm proposed by Gerontidis and Smith (1982).…”

Uniform Sampling on the Standard Simplex

“…Devroye attributes the last two methods to Lurle and Hartley [4], Schucany [8], and Lurle and Mason [5]. Devroye also cites the experimental comparison studies by Rabinowitz and Berenson [7], Gerontides and Smith [3], and Bentley and Saxe [1].…”

Random Number Generation and Monte Carlo Methods

“…Reeder (1972), Lurie and Mason (1973), and Rabinowitz and Berenson (1974) compare the performance of these methods for generating order statistics from a uniform distribution, and Gerontidis and Smith (1982) compare the performance for some nonuniform distributions. Reeder (1972), Lurie and Mason (1973), and Rabinowitz and Berenson (1974) compare the performance of these methods for generating order statistics from a uniform distribution, and Gerontidis and Smith (1982) compare the performance for some nonuniform distributions.…”