The Fpdf( Command

Command Summary

Evaluates the F-distribution probability density function at a point.

Command Syntax

Fpdf(x, numerator df, denominator df)

Press:

1. 2ND DISTR to access the distribution menu
2. 8 to select Fpdf(, or use arrows.

Press 9 instead of 8 on a TI-84+/SE with OS 2.30 or higher.

TI-83/84/+/SE

2 bytes

Fpdf( is the F-distribution probability density function.

Since the F-distribution is continuous, the value of Fpdf( doesn't represent an actual probability - in fact, one of the only uses for this command is to draw a graph of the distribution. You could also use it for various calculus purposes, such as finding inflection points.

The command takes 3 arguments: x is the point at which to evaluate the function (when graphing, use X for this argument), numerator df and denominator df are the numerator degrees of freedom and denominator degrees of freedom respectively (these specify a single Fpdf( curve out of an infinite family).

The F-distribution is used mainly in significance tests of variance.

# Formulas

The value of the Fpdf( is given by

(1)
\begin{align} \operatorname{Fpdf}(x,d_1,d_2) = \frac{\left( \frac{d_1x}{d_1x+d_2} \right)^{d_1/2} \left(1-\frac{d_1x}{d_1x+d_2}\right)^{d_2/2}}{x \operatorname{B}(d_1/2,d_2/2)} \end{align}

where B(x,y) is the Beta function.

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