7-11-6 Distribution

χ2 Distribution Probability

Command: ChiCD￿

Description: This command calculates the probability of χ2 distribution data falling between a and b.

 

 

 

 

 

 

 

df

b

 

 

 

 

a : lower boundary (Lower)

p =

 

1

 

1

 

2

 

df

–1

x

 

 

 

 

 

 

 

 

x 2

e

 

2 dx

b : upper boundary (Upper)

 

df

2

 

 

 

Γ

 

 

a

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Command Syntax

Lower value, Upper value, df value

Definition of Terms

Lower : lower boundary

Upper : upper boundary

df : degrees of freedom (positive integer)

Input Example:

ChiCD 0.76,3,4

Calculation Result Output

p :

χ2 distribution probability

kF Distribution

F Probability Density

Command: FPD￿

Description: This command calculates the probability density of F distribution from a specified x value.

 

 

Γ n + d

 

 

 

 

 

n

 

n

 

 

n.x

n + d

 

 

 

 

 

 

 

 

 

 

 

 

 

f (x) =

 

 

 

2

 

 

 

 

n 2

x

2

1

1 +

2

 

 

 

 

 

 

 

 

 

 

 

 

n

 

 

d

 

 

d

 

 

 

d

 

 

 

Γ

 

Γ

 

 

 

 

 

 

 

 

 

 

2

 

 

2

 

 

 

 

 

 

 

 

 

 

 

 

 

Command Syntax

x value, n:df value, d:df value

Definition of Terms

x : data value

n:df : degrees of freedom of numerator (positive integer)

d:df : degrees of freedom of denominator (positive integer)

20030421201