Reprinted: https://blog.csdn.net/donggui8650/article/details/101556041
In probability theory, the lognormal distribution is a continuous probability distribution for the number of random variables that follow a normal distribution.
From a statistical point of understanding lognormal distribution is such that there are a lot of things in nature have very slow growth, or even negligible (small percentage changes), but the effect is the impact on the whole thing, that is, each growth has it is a front-growing product operation, but if we put him on several domain, you can magnify the effect of their growth.
Assumptions: x1, x2, ..., xk denotes the i-th unit growth per unit time, the x1, x2, ... xk greater than or equal to 0, so zi = log (xi) denotes the logarithm of xi, clearly :
Because x1, x2, ... xk independent and identically distributed, apparently z1, z2 ... zk is independent and identically distributed, according to the central limit theorem is slow (when the sample size is large enough, the distribution of the sample mean (variable and distribution) slowly become a normal distribution) are: