Visual Statistics Studio

 

 

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