Distribution of the Sample Range of Continuous Random Variables

distribution

uniform

beta

exponential

gamma

Pareto

normal

logistic

extreme value

number of variables

2

Let

X

1

, …,

X

n

be a random sample from a continuous distribution. Let

Y

1

and

Y

n

be the smallest and the largest value in the sample. The sample range

W

is

W=

Y

n

-

Y

1

, that is, the difference between the largest and the smallest value. The sample range is a crude measure of the variation in the sample. This Demonstration shows the distribution of the sample range when the sample is drawn from some well-known continuous distributions.