HP 48gII - Manual (Page 565)

Page 17-12
0 , 0 ,
)
2
( 2
1
) ( 2
1
2
2
> > ⋅ ⋅
Γ ⋅
=
− −
x e x x f
x
ν
ν
ν
ν
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,
∫ ∫
∞ −
∞
≤ − = − = =
t
t
x X P dx x f dx x f x UTPC
) ( 1 ) ( 1 ) ( ) , (ν
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:
• P(X<a) = 1 - UTPC(ν,a)
• P(a<X<b) = P(X<b) - P(X<a) = 1 - UTPC(ν,b) - (1 - UTPC(ν,a)) =
UTPC( ν,a) - UTPC(ν,b)
• P(X>c) = UTPC(ν,c)
Examples: Given
ν = 6, determine:
P(X<5.32) = 1-UTPC(6,5.32) = 0.4965..
P(1.2<X<10.5) = UTPC(6,1.2)-UTPC(6,10.5) = 0.8717…
P(X> 20) = UTPC(6,20) = 2.769..E-3
The F distribution
The F distribution has two parameters νN = numerator degrees of freedom,
and νD = denominator degrees of freedom. The probability distribution
function (pdf) is given by