Hp 49g+ User Manual download pdf (Page 562)

100

101

Page 17-13

)

(

)1()

()

(

)()

(

)(

FNDN

NDN

νν

ννν

−

⋅

−⋅Γ⋅Γ

⋅⋅

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,

∫∫

∞−

∞

≤ℑ−=−==

FPdFFfdFFfFDNUTPF )(1)(1)(),,( νν

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

-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:

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Hp 49g+ User Manual Page 562

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