TITLE:
Distribution of the Maximum and Minimum of a Random Number of Bounded Random Variables
AUTHORS:
Jie Hao, Anant Godbole
KEYWORDS:
Maximum and Minimum, Random Number of i.i.d. Variables, Statistical Inference
JOURNAL NAME:
Open Journal of Statistics,
Vol.6 No.2,
April
26,
2016
ABSTRACT: We study a new family of random variables that each arise as the
distribution of the maximum or minimum of a random number N of i.i.d. random
variables X1, X2,…, XN, each distributed as a variable X with support on [0,
1]. The general scheme is first outlined, and several special cases are studied
in detail. Wherever appropriate, we find estimates of the parameter θ in the
one-parameter family in question.