is defined over the range 
and has the form
Maximum Value Distribution
The Type-III asymptotic distribution for the maximum
values is useful whenever the parent distribution is defined over the range and has the form
where 
and 
are the parameters of the
distribution. The above distribution denotes a uniform distribution when 
and a triangular
distribution when 
. The
Type-III extreme value distribution for the maximum value, 
, is given by
The corresponding PDF is
where 
is the upper bound of the initial
distribution, 
is the
characteristic maximum value of 
and 
is a shape parameter.
The mean and variance of 
are related to the parameters and as follows:
And
Minimum Value Distribution
The Type-III minimum value distribution can be used
whenever the parent distribution is defined over the range 
and has the form
where and are the parameters of the
distribution. In this case, the Type-III asymptotic distribution for the
minimum value, 
, is given
by
By differentiating the distribution function, the CDF can be obtained as
In this case mean and variance of 
are given by
And
