The Kumaraswamy GEV distribution - University of Manchester

Double- Bounded probability density function (DB-PDF)
Kumaraswamy (1980)proposed a two parameters distribution with double-bounded
support known as DB-PDF and later so-called The Kumaraswamy distribution.
FKum(z) = 1 −
�
1 −
fKum(z) =
1
a b
(d − c)
� �a�b z − c
;
d − c
� �a−1 � � �a�b−1 z − c
z − c
1 −
.
d − c
d − c
Making the linear transformation X = Z−c
. We can obtain the standard Kumaraswamy
b−c
distribution. The pdf of the latter
FKum(x, a, b) = 1 − (1 − x a ) b ; x ∈ (0, 1)
fKum(x, a, b) = abx a−1 (1 − x a ) b−1 ; x ∈ (0, 1)
Kumaraswamy distribution is very similar to the beta distribution, but this formula has
some advantages over beta distribution. Jones(2009) explored the background of the
Kum distribution and, more importantly, made clear some similarities and differences
between the beta and Kum distributions.
S.Eljabri (University of Manchester) Kum-GEV Distribution MRSc, Sep 28,2012 8 / 39