A random variable which is log-normally distributed takes only positive real values. Relation between normal and lognormal distribution. This relationship is true regardless of the base of the logarithmic or find pdf of normal distribution online function. The last is related to the fact that the lognormal distribution is not uniquely determined by its moments.

In consequence, the characteristic function of the log-normal distribution cannot be represented as an infinite convergent series. That is, there exist other distributions with the same set of moments. In fact, there is a whole family of distributions with the same moments as the log-normal distribution. Contrary to the arithmetic standard deviation, the arithmetic coefficient of variation is independent of the arithmetic mean. The derivation of the formula is provided in the discussion of this Wikipedia entry. The log-normal distribution is important in the description of natural phenomena.

This follows, because many natural growth processes are driven by the accumulation of many small percentage changes. These become additive on a log scale. If the rate of accumulation of these small changes does not vary over time, growth becomes independent of size. Even if that’s not true, the size distributions at any age of things that grow over time tends to be log-normal. The length of comments posted in Internet discussion forums follows a log-normal distribution. Onset durations of acoustic comparison stimuli that are matched to a standard stimulus follow a log-normal distribution.