# Logarithmic normal distribution Calculator

## Calculates the probability density function and lower and upper cumulative distribution functions of the logarithmic normal distribution.

 percentile x x≧0 mean μ standard deviation σ σ＞0 6digit10digit14digit18digit22digit26digit30digit34digit38digit42digit46digit50digit
 $\normal Lognormal\ distribution\ LogN(x,\mu,\sigma)\\[10](1)\ probability\ density\\\hspace{30}f(x,\mu,\sigma)= {\large\frac{1}{\sqrt{2\pi}\sigma x}e^{-\frac{1}{2}\left(\frac{ln(x)-\mu}{\sigma}\right)^2}}\\(2)\ lower\ cumulative\ distribution\\\hspace{30}P(x,\mu,\sigma)={\large\int_{\small 0}^{\hspace{25}\small x}}f(t,\mu,\sigma)dt\\(3)\ upper\ cumulative\ distribution\\\hspace{30}Q(x,\mu,\sigma)={\large\int_{\small x}^{\hspace{25}\small\infty}}f(t,\mu,\sigma)dt\\[10](4)\hspace{20} mean:\ e^{\mu+\frac{\sigma^2}{2}}\\\hspace{25}median:\ e^{\mu}\\\hspace{40}mode:\ e^{\mu-\sigma^2}\\$

Logarithmic normal distribution
 [0-0] / 0 Disp-Num5103050100200
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