Page 29 - Contributed Paper Session (CPS) - Volume 5

CPS657 Folorunso Serifat A. et al.
2.3.3 Weibull Distribution
A random variable t is said to follow a Weibull distribution if it satisfies
the density function:

( )

() = −1 − , , > 0

2.3.4 Log-Logistic Model
A random variable () is said to be distributed log-logisticsl if its pdf. is
given as:
−1
( )

(; , ) = 2 , , > 0

[1 + ( ) ]

2.4 Proposed Model: Gamma-generalised gamma mixture cure model
We need a new f(x), so we assume the existing to be G(x), g(x). Thus, link
function of the Gamma - Generated Gamma is given in equation (2.7)
below.
1 −1
() = [−[1 − ()]] () (3)
Γ()

where, a = Shape parameter, G(x) = cdf of baseline distribution, g(x)=
pdf of baseline distribution
If the shape parameter, = 1, then
1
0
() = × [− log[1 − ()]] 1−1 () = [− log[1 − ()]] ()
Γ(1)
∴ () = ()
Gamma-Generalised Gamma Mixture Cure Model
The study employ a new distribution called Gamma-generalised gamma
mixture cure model using both the pdf and cdf defined below
Assume follow a generalised Gamma pdf given as

−1 −( )
() = ( ) (4)
Γ

and its cdf as;

[, ( ) ]

() = (5)
()

But in scale location form, eqn. (4 & 5) becomes

1 − −
() = −( ) − (6)
Γ

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