HP 50G

Page 17-7
,
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
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
While the corresponding cdf is given by
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
(Continuous FUNctions) and define the following functions (change to Approx
mode):
Gamma pdf:
'gpdf(x) = x^(α-1)*EXP(-x/β)/(β^α*GAMMA(α))'
Gamma cdf: 'gcdf(x) = ∫(0,x,gpdf(t),t)'
Beta pdf:
' βpdf(x)= GAMMA(α+β)*x^(α-1)*(1-x)^(β-1)/(GAMMA(α)*GAMMA(β))'
Beta cdf: 'βcdf(x) = ∫(0,x, βpdf(t),t)'
0,0),exp(
1
)( >>−⋅= β
ββ
xfor
x
xf
0,0,10,)1(
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)(
11
>><<−⋅⋅
Γ⋅Γ
+Γ
=
−−
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βα
βα
βα
xforxxxf
0,0,0),exp()(
1
>>>⋅−⋅⋅⋅=
−
βααβα
ββ
xforxxxf
0,0,0),exp(1)( >>>⋅−−= βαα
β
xforxxF