Sunday, 27 October 2013

Log-normal CDF and Quantile Calculator

An implementation of the Log-normal CDF and Quantile function Calculator occurs below. The Log-normal distribution function (for mean $\mu$ and standard deviation $\sigma$) is:-

$\large N(t)=\frac{1}{t\sigma\sqrt{2\pi}}exp(\frac{-(log(t)-\mu)^2}{2\sigma^2})$  

Note that the Log-normal describes the distribution of random variable $exp(x)$ where $x$ has Normal distribution with mean $\mu$ and standard deviation $\sigma$. The mean and std (standard deviation) 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 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.



mean:
std:


Lower limit:
Upper limit:
Probablility:



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