Distributions of Continuous Order Statistics
Distributions of Continuous Order Statistics
Let , ..., be a random sample from a continuous distribution. Reorder the sample in increasing order; denote the corresponding variables by , ..., . Thus, for example, is the smallest of the variables, the second smallest, and the largest. The variable is called the order statistic. The Demonstration shows the probabilities of the order statistics (the red curves) when the sample is from a uniform, beta, exponential, gamma, normal, or extreme value distribution (the probability density function of is shown in blue).
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