The Beta Distribution; The Weibull Distribution; Functions For Continuous Distributions - HP 50g User Manual

Graphing calculator.

while its cdf is given by F(x) = 1 - exp(-x/ ), for x>0,

The beta distribution

The pdf for the gamma distribution is given by
(
f
(
x
)
(
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
f
(
x
)
While the corresponding cdf is given by
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
(Continuous FUNctions) and define the following functions (change to Approx
mode):
Gamma pdf:
Gamma cdf:
Beta pdf:
' pdf(x)= GAMMA( + )*x^( -1)*(1-x)^( -1)/(GAMMA( )*GAMMA( ))'
Beta cdf:
1
f
(
x
)
exp(
)
1
x
)
(
)
1
x
exp(
x
)
1
exp(
'gpdf(x) = x^( -1)*EXP(-x/ )/( ^ *GAMMA( ))'
'gcdf(x) = ∫(0,x,gpdf(t),t)'
' c
df(x)
x
),
for
1
1 (
x
)
,
for
x
),
for
x
),
for
x
∫(0,x, pdf(t),t)'
=
x
, 0
0
,
>0.
0
x
, 1
x
, 0
, 0
, 0
, 0
, 0
0
0
0
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