Rayleigh Distribution CDF and Quantile Calculator

An implementation of the Rayleigh Distribtuion CDF and Quantile function Calculator occurs below. The Rayleigh distribution function (for real parameter $\sigma>0$) is:-

$\large \frac{x}{\sigma^2}e^{-\frac{x^2}{2\sigma^2}}$  

where $x>0$ is a real number. The $\sigma$ parameter 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 a number greater than or equal to 0. The upper limit field needs to contain either a number greater than or equal to 0 or the string inf (for plus infinity). The probability field must contain a number only.

$\sigma$:

Lower limit:

Upper limit:

Probablility:

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