# Logarithmic normal distribution (percentile) Calculator

## Calculates the percentile from the lower or upper cumulative distribution function of the logarithmic normal distribution.

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

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