HP (Hewlett-Packard) 50g ユーザーズマニュアル

Page 17-13

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,

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:

Θ P(F<a) = 1 - UTPF(

νN, νD,a)

Θ 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)

Θ 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

-1

(p). This value is relatively simple to find for

the cases of the exponential and Weibull distributions since their cdf’s have a
closed form expression:

Θ Exponential, F(x) = 1 - exp(-x/

β)

Θ Weibull, F(x) = 1-exp(-

αx

)

(Before continuing, make sure to purge variables

α and β). To find the inverse

cdf’s for these two distributions we need just solve for x from these expressions,
i.e.,

∫

∞

−

∞

≤

ℑ

−

UTPF

)

(

)

(

)

(

)

(