# Inverse Cumulative Distribution Functions - HP 50g User Manual

Graphing calculator.

The calculator provides for values of the upper-tail (cumulative) distribution
function for the F distribution, function UTPF, given the parameters N and D,
and the value of F. The definition of this function is, therefore,
(
,
UTPF
N
For example, to calculate UTPF(10,5, 2.5) = 0.161834...
Different probability calculations for the F distribution can be defined using the
function UTPF, as follows:
P(F<a) = 1 - UTPF( N D,a)
P(a<F<b) = P(F<b) - P(F<a) = 1 -UTPF( N D,b)- (1 - UTPF( N D,a))
P(F>c) = UTPF( N D,a)
Example: Given N = 10, D = 5, find:
P(F<2) = 1-UTPF(10,5,2) = 0.7700...
P(5<F<10) = UTPF(10,5,5) – UTPF(10,5,10) = 3.4693..E-2
P(F>5) = UTPF(10,5,5) = 4.4808..E-2

## Inverse cumulative distribution functions

For a continuous random variable X with cumulative density function (cdf) F(x) =
P(X<x) = p, to calculate the inverse cumulative distribution function we need to
find the value of x, such that x = F
the cases of the exponential and Weibull distributions since their cdf's have a
closed form expression:
Exponential, F(x) = 1 - exp(-x/ )
Weibull, F(x) = 1-exp(- x )
(Before continuing, make sure to purge variables
cdf's for these two distributions we need just solve for x from these expressions,
i.e.,
,
)
(
D
F
f
F
t
= UTPF( N D,a) - UTPF( N D,b)
t
)
1
dF
-1
(p). This value is relatively simple to find for
(
)
1
f
F
dF
P
and ). To find the inverse
(
)
F
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