Distribution |
F(x) |
g(x) |
a |
b |
c |
d |
Weibull |
![](../../../../contents/figures/TOSPJ/TOSPJ-7-36_sh1eq1.jpg) |
xp |
1 |
-1 |
θ |
1 |
Pareto of the first kind |
![](../../../../contents/figures/TOSPJ/TOSPJ-7-36_sh1eq2.jpg) |
lnx |
1 |
-λp
|
p |
1 |
Burr XII |
![](../../../../contents/figures/TOSPJ/TOSPJ-7-36_sh1eq3.jpg) |
ln (1+θxp) |
1 |
-1 |
λ |
1 |
Rayleigh |
![](../../../../contents/figures/TOSPJ/TOSPJ-7-36_sh1eq4.jpg) |
x2 |
1 |
-1 |
θ |
1 |
Lomax |
![](../../../../contents/figures/TOSPJ/TOSPJ-7-36_sh1eq5.jpg) |
ln (1+θx) |
1 |
-1 |
λ |
1 |
Inverse Weibull |
![](../../../../contents/figures/TOSPJ/TOSPJ-7-36_sh1eq6.jpg) |
x-p |
0 |
1 |
θ |
1 |
Power function |
![](../../../../contents/figures/TOSPJ/TOSPJ-7-36_sh1eq7.jpg) |
![](../../../../contents/figures/TOSPJ/TOSPJ-7-36_sh2eq25.jpg) |
0 |
1 |
-p |
1 |
Rectangular |
![](../../../../contents/figures/TOSPJ/TOSPJ-7-36_sh1eq8.jpg) |
ln(x-β) |
0 |
![](../../../../contents/figures/TOSPJ/TOSPJ-7-36_sh2eq27.jpg) |
-1 |
1 |
Pareto of the second kind |
![](../../../../contents/figures/TOSPJ/TOSPJ-7-36_sh1eq9.jpg) |
ln (1+x) |
1 |
-1 |
λ |
1 |
Exponential |
![](../../../../contents/figures/TOSPJ/TOSPJ-7-36_sh1eq10.jpg) |
x |
1 |
-1 |
λ |
1 |
Inverse Exponential |
![](../../../../contents/figures/TOSPJ/TOSPJ-7-36_sh1eq11.jpg) |
![](../../../../contents/figures/TOSPJ/TOSPJ-7-36_sh2eq16.jpg) |
0 |
1 |
λ |
1 |
Kumaraswamy |
![](../../../../contents/figures/TOSPJ/TOSPJ-7-36_sh1eq12.jpg) |
ln (1-xp) |
1 |
-1 |
-λ |
1 |
Exponentiated Frechet |
![](../../../../contents/figures/TOSPJ/TOSPJ-7-36_sh1eq13.jpg) |
![](../../../../contents/figures/TOSPJ/TOSPJ-7-36_sh2eq26.jpg) |
1 |
-1 |
-θ |
1 |
Exponentiated exponential |
![](../../../../contents/figures/TOSPJ/TOSPJ-7-36_sh1eq14.jpg) |
ln (1-e -λx) |
0 |
1 |
-θ |
1 |
Burr X (Exponentiated Rayleigh) |
![](../../../../contents/figures/TOSPJ/TOSPJ-7-36_sh1eq15.jpg) |
x2
|
1 |
-1 |
β |
α |
Exponentiated Weibull |
![](../../../../contents/figures/TOSPJ/TOSPJ-7-36_sh1eq16.jpg) |
xp
|
1 |
-1 |
β |
α |