Abstract: A natural generalization of the normal distribution with two
parameters m
and s is defined by replacing the
power 2 in the exponent of the normal distribution with a power of any order. In this article, we
consider one class of this generalization when for any positive
integer z, i.e., when is a positive
integer. An explicit form for the moments of order statistics of a random sample
taken from any incidence of this class is derived. For the cases when and where and 5, short
tables are given for the first two moments of all order statistics in random
samples of size to 10.
Keywords and phrases: generalized normal distribution, multinomial theorem, moments of order statistics.
