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

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DOI: 10.4236/ojs.2016.62023    2,271 Downloads   5,614 Views  Citations
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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 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.

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Hao, J. and Godbole, A. (2016) Distribution of the Maximum and Minimum of a Random Number of Bounded Random Variables. Open Journal of Statistics, 6, 274-285. doi: 10.4236/ojs.2016.62023.

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