# Log-normal distribution

It calculates the probability density function (PDF) and cumulative distribution function (CDF) of long-normal distribution by a given mean and variance.

Lognormal distribution is a continuous probability distribution of a random variable whose logarithm is normally distributed.
Probability density function (PDF) of the log-normal distribution formula:
${\frac {1}{x\sigma {\sqrt {2\pi }}}}\ e^{-{\frac {\left(\ln x-\mu \right)^{2}}{2\sigma ^{2}}}}$

#### Log-normal distribution

Digits after the decimal point: 5
Probability density function value

Cumulative distribution function value

PDF Graph
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CDF Graph
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Cumulative density function (CDF) of the lognormal distribution formula:
${\frac {1}{2}}+{\frac {1}{2}}\operatorname {erf} {\Big [}{\frac {\ln x-\mu }{{\sqrt {2}}\sigma }}{\Big ]}$

To calculate log-normal distribution quantiles, you can use the following calculator:

#### Log-normal distribution quantile function

Digits after the decimal point: 2
Quantile

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PLANETCALC, Log-normal distribution