Relative Frequency of Order Statistics in Independent and Identically Distributed Random Vectors
Relative Frequency of Order Statistics in Independent and Identically Distributed Random Vectors
The relative frequency of order statistics is investigated for independent and identically distributed (i.i.d.) random variables. Specifically, it is shown that the probability <TEX>$Pr\{X_{[s]}=x\}$</TEX> is no less than the probability <TEX>$Pr\{X_{[r]}=x\}$</TEX> at any point <TEX>$x{\geqq}x_0$</TEX> when r<s, where <TEX>$X_{[r]}$</TEX> denotes the r-th order statistic of an i.i.d. discrete random vector …