Simulating percentile points: stopping rules, precision, and scale

Abstract

Two stopping rules are defined for the purpose of minimizing the number of iterations needed to provide simulated percentile points with a certain precision: one stopping rule is a result of defining precision relative to the scale of the random variable while the other is a result of defining precision relative to the tail area of the distribution. A simulation experiment is conducted to investigate the effects of the stopping rules as well as the effects of changes in scale. The effects of interest are the precision of the simulated percentile point and the number of iterations needed to achieve that precision. It is shown that the stopping rules are effective in reducing the number of iterations while providing an acceptable precision in the percentile points. Also, increases in scale produce increases in the number of iterations and/or decreases in certain measures of precision

Keywords:

• critical values
• order statistics
• sample size