TI-BASIC:Fpdf
Command Summary
Evaluates the F-distribution probability density function at a point.
Command Syntax
Fpdf(x, numerator df, denominator df)
Menu Location
Press:
- 2ND DISTR to access the distribution menu
- 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
<math> \definecolor{darkgreen}{rgb}{0.90,0.91,0.859}\pagecolor{darkgreen} \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)} </math>
Here, B is the [wikipedia:beta_function Beta function].
