Suppose that 
are the measured set from the n
trials of a material strength test. The test results are listed with ascending
order. Then, assume that these measuring are repeated 
times such as , 
,…, 
. From the measured data set, if probable
distribution functions 
and
are made from the minimum
value set 
and the
maximum value set 
, these
PDFs are referred to as Extreme Value Distributions for the
minimum value and the maximum value of 
, respectively.
If the random variables 
are independent and follow a common
distribution 
, the shape of the distribution
function of the extreme value 
and 
becomes increasingly insensitive to
the exact shape of the common distribution function , as 
. These asymptotic distributions often
describe the behavior of the random variable and reasonably well even when the exact
shape of the parent distribution function is not known precisely. These
asymptotic distribution forms are classified into three types based on the
general features of the tail part of the distributions.