# Distributions of Discrete Order Statistics

Distributions of Discrete Order Statistics

Let , …, be a random sample from a discrete 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. This Demonstration shows the distributions of the order statistics (the red curves) when the sample is from a uniform, binomial, geometric, or Poisson distribution or when the sample is made without replacement from a finite set (the underlying distribution is shown in blue).

X

1

X

n

Y

1

Y

n

Y

1

X

Y

2

Y

n

Y

i

th

i