# 3.5.3.3.11 Logninv

## Definition:

$xp = logninv(p, mu, sigma)$ computes the deviate,$x_p$, associated with the given lower tail probability, $p$, of the Lognormal distribution with parameters mu and sigma.

$x_p$ is calculated for the give $p$ such that:

$p=\int_{0}^{x_p}\frac{1}{t\sqrt{2\pi}\sigma}e^{-\frac{\left(ln(t)-\mu\right)^2}{2\sigma^2}}dt$

where $0 < x_p$

## Parameters:

p (input, double)
The probability,$p$, from the Lognormal distribution.$0
mu (input, double)
The mean of the associated Lognormal distribution .
sigma (input, double)
The standard deviation of the associated Lognormal distribution, $sigma > 0$
xp (output, double)
The deviate,$x_p$.