%0 Journal Article
%T Distribution of the Maximum and Minimum of a Random Number of Bounded Random Variables
%A Jie Hao
%A Anant Godbole
%J Open Journal of Statistics
%P 274-285
%@ 2161-7198
%D 2016
%I Scientific Research Publishing
%R 10.4236/ojs.2016.62023
%X 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 X<sub>1</sub>, X<sub>2</sub>,<span style=\"white-space:nowrap;\">¡­</span>, X<sub>N</sub>, 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 ¦È in the
one-parameter family in question.
%K Maximum and Minimum
%K Random Number of i.i.d. Variables
%K Statistical Inference
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=65869