The f distribution, The f distribution ,17-12 – HP 50g Graphing Calculator User Manual
Page 561
Page 17-12
The calculator provides for values of the upper-tail (cumulative) distribution
function for the
χ
2
-distribution using [UTPC] given the value of x and the
parameter
ν. The definition of this function is, therefore,
To use this function, we need the degrees of freedom,
ν, and the value of the
chi-square variable, x, i.e., UTPC(
ν,x). For example, UTPC(5, 2.5) =
0.776495…
Different probability calculations for the Chi-squared distribution can be defined
using the function UTPC, as follows:
Θ P(X ν,a) Θ P(a ν,b) - (1 - UTPC(ν,a)) = UTPC( ν,a) - UTPC(ν,b) Θ P(X>c) = UTPC( ν,c) Examples: Given ν = 6, determine: P(X<5.32) = 1-UTPC(6,5.32) = 0.4965.. The F distribution The F distribution has two parameters νN = numerator degrees of freedom, and νD = denominator degrees of freedom. The probability distribution ∫ ∫ ∞ − ∞ ≤ − = − = = t t x X P dx x f dx x f x UTPC ) ( 1 ) ( 1 ) ( ) , ( ν ) 2 ( 1 2 2 ) 1 ( ) 2 ( ) 2 ( ) ( ) 2 ( ) ( D N N N D F N D N F D N D N x f ν ν ν ν ν ν ν ν ν ν ν ν + − ⋅ − ⋅ Γ ⋅ Γ ⋅ ⋅ + Γ =
P(1.2
function (pdf) is given by