HP 48gII - Manual (Page 560)

Page 17-7
The corresponding (cumulative) distribution function (cdf) would be given by
an integral that has no closed-form solution.
The exponential distribution
The exponential distribution is the gamma distribution with a = 1. Its pdf is
given by
0 , 0 ), exp(
1
) ( > > − ⋅ = β
β β
x for
x
x f
,
while its cdf is given by F(x) = 1 - exp(-x/
β), for x>0, β >0.
The beta distribution
The pdf for the gamma distribution is given by
0 , 0 , 1 0 , ) 1 (
) ( ) (
) (
) ( 1 1 > > < < − ⋅ ⋅
Γ ⋅ Γ
+ Γ
= − − β α
β α
β α
β α x for x x x f
As in the case of the gamma distribution, the corresponding cdf for the beta
distribution is also given by an integral with no closed-form solution.
The Weibull distribution
The pdf for the Weibull distribution is given by
0 , 0 , 0 ), exp( ) ( 1 > > > ⋅ − ⋅ ⋅ ⋅ = − β α α β α β β x for x x x f
While the corresponding cdf is given by
0 , 0 , 0 ), exp( 1 ) ( > > > ⋅ − − = β α α β x for x x F
Functions for continuous distributions
To define a collection of functions corresponding to the gamma, exponential,
beta, and Weibull distributions, first create a sub-directory called CFUN