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Distribution of the Maximum and Minimum of a Random Number of Bounded Random Variables

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Type
Preprint
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Submission Date
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arXiv ID: 1403.1302
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arXiv
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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 $X_1,X_2,\ldots,X_N$, 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 $\theta$ in the one-parameter family in question.

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