TI-BASIC:Tpdf
Command Summary
Evaluates the Student's t probability density function with degrees of freedom ν.
Command Syntax
tpdf(t, ν)
Menu Location
Press:
- 2ND DISTR to access the distribution menu
- 4 to select tpdf(, or use arrows.
Press 5 instead of 4 on a TI-84+/SE with OS 2.30 or higher.
TI-83/84/+/SE
2 bytes
tpdf( is the Student's t probability density function.
Since the t distribution is continuous, the value of tpdf( doesn't represent an actual probability -- in fact, one of the few uses for this command is to draw a graph of the bell curve. You could also use it for various calculus purposes, such as finding inflection points.
The command takes two arguments: the first is the value where the PDF is to be evaluated, and the second is the number of degrees of freedom (so the calculator knows which t distribution to use). As the degrees of freedom increases without bound, tpdf( approaches Normalpdf(; i.e.
<math> \definecolor{darkgreen}{rgb}{0.90,0.91,0.859}\pagecolor{darkgreen} \lim_{\nu\rightarrow\infty}\operatorname{tpdf}(x,\nu)=\operatorname{normalpdf}(x) </math>
Formulas
The value of tpdf( is given by
(where Γ is the [wikipedia:Gamma_function gamma function]), or alternatively
(where B is the [wikipedia:Beta_function beta function])
