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Distribution of the Maximum and Minimum of a Random Number of Bounded Random Variables
Department of Statistics and Analytical Sciences, Kennesaw State University, Kennesaw, USA
Department of Mathematics and Statistics, East Tennessee State University, Johnson City, USA
- 1 Department of Statistics and Analytical Sciences, Kennesaw State University, Kennesaw, USA
- 2 Department of Mathematics and Statistics, East Tennessee State University, Johnson City, USA
Open Journal of Statistics·Volume 06 (2016)·Pages 274–285·Published 12 April 2016·DOI10.4236/ojs.2016.62023
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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 , … , 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.
KeywordsMaximum and MinimumRandom Number of i.i.d. VariablesStatistical Inference
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