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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.
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