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In probability theory, a lognormal distribution is a probability distribution of a random variable whose logarithm is normally distributed. If Y is a random variable with a normal distribution, then X = exp(Y) has a lognormal distribution; likewise, if X is lognormally distributed, then Y = log(X) is normally distributed. (This is true regardless of the base of the logarithmic function: if log_{a}(Y) is normally distributed, then so is log_{b}(Y), for any two positive numbers a, b ≠ 1.)
Lognormal is also written log normal or lognormal. It is occasionally referred to as the Galton distribution or Galton's distribution, after Francis Galton.
A variable might be modeled as lognormal if it can be thought of as the multiplicative product of many independent random variables each of which is positive. For example, in finance, a longterm discount factor can be derived from the product of shortterm discount factors. In wireless communication, the attenuation caused by shadowing or slow fading from random objects is often assumed to be lognormally distributed. See logdistance path loss model.
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