The Characteristic Property of Five Parameter Type II Generalized Logistic Distribution

Abstract

Order statistics are among the most fundamental tools in non-parametric statistics and inference. Special important cases of the order statistics are the minimum and maximum value of a sample, sample median and other sample quantiles. On this note, we obtained the rth minimum and maximum order statistic for the five parameter type II generalized logistic distribution using the probability distribution function and cumulative density function to obtain another five parameter type II generalized logistic distribution which shares the same properties by replacing p with np. We also obtain the quantile function by inverting the cumulative density function of the distribution which can be used to generate random samples arising from the distribution. The survival and hazard functions of the distribution are also obtained.