CRUISE SCIENTIFIC           Visual Statistics Studio           STATISTICAL DISTRIBUTIONS

 

 

The F Distribution

Among the higher transcendental functions, a frequently used function within the area of statistical inference is the inverted beta distribution, also called, as coined by Snedecor, the F distribution. As other probability distributions, the F distribution belongs to the family of gamma functions. The density function for the F-distribution, associated with certain number of degrees of freedoms signified by the Greek letter n, is

 

                                

 

To understand the role ratios of factorials within the Pascal’s Triangle help us with simplification of the above expression, consider that the y for (10, 10) degrees of freedom can be written as

 

                                                    

where the constant 630 was computed as the ratio of .

 

The F Distribution within the Microsoft Excel Framework

For its both degrees of freedom equal to 10, the above equation was written for Microsoft Excel as

 

Microsoft Excel

630 * a1^4 * (1 + a1) ^ -10

F Distribution

 

The constant 630 within the above expression was computed as (9! / 4! 4!). This F(10,10) distribution is shown in the figure below.

The F Distribution within the Cruise Scientific Visual Statistics Studio Framework

Select (Arguments, .01 F 10 F)

mark the preferred argument's length, and click on the Generate and on the Display the Sequence commands. Select (Distributions, Ordinates of F Distributions)

 mark the Argument, select the Degrees of Freedom, and click the Accept command.

Select (Stereoimages, Image Data on Vector Display)

mark the F Ordinate, and click on the Accept command.


You can also select (Stereographs, Display Stereograph) and rotate the Stereograph as, e.g.,

To view this stereograph in color, select (Stereographs, Define Stereograph)

fill-in the required definitions, and view the stereograph in color