Sunday, 27 October 2013

Cauchy Distribution CDF and Quantile Calculator

An implementation of the Cauchy Distribution CDF and Quantile function Calculator occurs below. The Cauchy distribution is also known as the Cauchy-Lorentz distribution, and for real parameters $-\infty < x_0 <\infty$ location and scale $\gamma>0$ it is:-

$\Large \frac{1}{\pi\gamma[1+(\frac{(x-x_0)}{\gamma})^2]}$  

where variable $-\infty < x <\infty$ is a real number. The $x_0$ and the $\gamma$ parameter fields have 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 real number or string -inf for minus infinity. The upper limit field needs to contain either a real number or the string inf (for plus infinity). The probability field must contain a number only.



$x_0$:
$\gamma$:


Lower limit:
Upper limit:
Probablility:



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