有界随机变量随机数的最大值和最小值的分布
Distribution of the Maximum and Minimum of a Random Number of Bounded Random Variables
摘要：
本文研究一类新的随机变量族，每个随机变量都是由i.i.d.~的随机数$N$的最大值或最小值的分布引起的。随机变量$X_1,X_2,\ldots,X_N$，每个变量作为变量$X$分布，支持$[0,1]$。首先概述了一般方案，并详细研究了几种特殊情况。在适当的情况下，我们发现估计的参数$θ$在一个参数的家庭的问题。
英文摘要：
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 $X_1,X_2,\ldots,X_N$, 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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
