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In statistics, the kth order statistic of a statistical sample is equal to its kth-smallest value [1].Together with rank statistics, order statistics are among the most fundamental tools in non-parametric statistics and inference.

Important special cases of the order statistics are the minimum and maximum value of a sample, and (with some qualifications discussed below) the sample median and other sample quantiles.

When using probability theory to analyze order statistics of random samples from a continuous distribution, the cumulative distribution function is used to reduce the analysis to the case of order statistics of the uniform distribution.

Full demonstration can be seen here: https://demonstrations.wolfram.com/DistributionsOfOrderStatistics/