# What is Log-Normal Distribution?

Log-Normal Distribution in probability theory is a continuous probability distribution of a random variable whose logarithm is normally distributed. Thus, if the random variable is log-normally distributed, then has a normal distribution. Likewise, if Y has a normal distribution, then X=exp(y) has a log-normal distribution. A random variable which is log-normally distributed takes only positive real values. The distribution is occasionally referred to as the Galton distribution or Galton’s distribution, after Francis Galton.A log-normal process is the statistical realization of the multiplicative product of many independent random variables, each of which is positive. This is justified by considering the central limit theorem in the log domain. The log-normal distribution is the maximum entropy probability distribution for a random variate for which the mean and variance of are specified.

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