Abstract
Suppose
be a sequence of independent and identically distributed random variables from Type I extreme value distribution. Let X
L
(1)
, X
L
(2)
, ... be the lower record values of this distribution. We assume the first observation as the first lower record, X
L
(1)
. It is known that X
L
(
m
)
is identically distributed as X
L
(
m
+1)
+ W/m, where W has the exponential distribution with cumulative distribution function F(x) = 1−e
−x
, x>0. In this article we will characterize the Type I extreme value distribution using this distribution property.