# Inverse Cumulative Distribution Functions - HP 48gII User Manual

Graphing calculator.

f
(
x
)
The calculator provides for values of the upper-tail (cumulative) distribution
function for the F distribution, function UTPF, given the parameters νN and νD,
and the value of F. The definition of this function is, therefore,
(
ν
,
ν
,
)
UTPF
N
D
F
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(νN, νD,a)
P(a<F<b) = P(F<b) - P(F<a) = 1 -UTPF(νN, νD,b)- (1 - UTPF(νN, νD,a))
= UTPF(νN, νD,a) - UTPF(νN, νD,b)
P(F>c) = UTPF(νN, νD,a)
Example: Given νN = 10, νD = 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
find for the cases of the exponential and Weibull distributions since their cdf's
have a closed form expression:
ν
N
ν
N
ν
D
ν
N
(
)
(
)
2
2
ν
D
ν
N
ν
D
ν
N
(
)
(
)
1 (
2
2
ν
t
(
)
1
f
F
dF
f
t
-1
(p). This value is relatively simple to
ν
N
1
F
2
ν
N
+
ν
D
F
(
)
)
2
D
(
)
1
(
F
dF
P
F
Page 17-13
)