Binomial Distributions
Normal Distribution
t-Distributions
F Distributions
Chi Square Distributions
Microsoft Excel
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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 .
For its both degrees of freedom equal to 10, the above equation was written for Microsoft Excel as
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Microsoft Excel |
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630 * a1^4 * (1 + a1) ^ -10 |
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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.
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Select (Arguments, .01 F 10 F)
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mark the preferred argument's length, and click on the Generate and on the Display the Sequence commands. Select (Distributions, Ordinates of F Distributions)
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mark the Argument, select the Degrees of Freedom, and click the Accept command.
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Select (Stereoimages, Image Data on Vector Display)
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mark the F Ordinate, and click on the Accept command.
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You can also select (Stereographs, Display Stereograph) and rotate the
Stereograph as, e.g.,
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To view this stereograph in color, select (Stereographs, Define Stereograph)
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fill-in the required definitions, and view the stereograph in color
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