## Thursday, 17 October 2013

### Student's t-Distribution CDF and Quantile Calculator

An implementation of the Student's t CDF and Quantile function Calculator occurs below. The Student's t distribution function (for degree of freedom $v$) is:-

$\Large\frac{\Gamma(\frac{v+1}{2})}{\sqrt{v\pi}\Gamma(\frac{v}{2})}(1+\frac{x^2}{v})^{-\frac{v+1}{2}}$

In the unlikely event that you have downloaded my free App SciStatCalc on your iPhone, please note that the displayed equation for the Student-t distribution (panel 19 of the blue landscape display) is missing the minus sign before the raised power, but it works functionally, which is the main thing. As a matter of fact, I have converted the Objective-C routines to Javascript to implement this calculator!

The degree of freedom field has to be filled in, as well as two out of the three fields which are labelled Lower Limit, Upper Limit and Probability. The lower limit field needs to contain either a number or the string -inf (for minus infinity). The upper limit field needs to contain either a number or the string inf (for plus infinity). The probability field must contain a number only.

 Degrees of freedom (df):

 Lower limit: Upper limit: Probablility:

Extra probability results pending...

 Plot of distribution ($f(x)$) values against $x$ values $f(x)$ $x$