Lognormal Distribution

A random variable X is said to have a lognormal distribution if ln(X) has a normal distribution with mean μ and standard deviation σ. Equivalently, X = eY where Y is normally distributed with mean μ and standard deviation σ. The lognormal distribution is used when the distribution is believed to be skewed.

The probability density function of the lognormal distribution with parameter μ and σ is given by the following equation:

, x > 0

The shape of the lognormal distribution is defined by three parameters. First, standard deviation for the lognormal (σ) also known as the shape parameter. It affects the general shape of the distribution without affecting the location or height of the graph. Second, mean (μ), the location parameter, which tells you where on the x-axis the graph is located. Third, is median, the scale parameter, which tells us whether the graph shrinks or stretches.