What is a characteristic feature of a lognormal distribution?

A characteristic feature of a lognormal distribution is that it is defined as the distribution of a variable whose logarithm is normally distributed. This happens because while the lognormal distribution itself is not symmetric, its logarithmic transformation results in a normal distribution. This feature makes it particularly useful in fields such as finance and economics where the data can only take on positive values, such as stock prices and certain financial indices.

The lognormal distribution also exhibits positive skewness, meaning that it has a longer tail on the right side, which is important when modeling variables that cannot take on negative values. Additionally, the mean, median, and mode of a lognormal distribution do not equate, as the distribution is not symmetric; instead, the mean is greater than the median. Understanding this distinction helps in applying the lognormal distribution appropriately to real-world scenarios.