9. Lognormal

Two British mathematicians, Francis Galton and Donald McAlister, introduced the lognormal distribution in 1879. The lognormal distribution is sometimes referred as the Galton distribution. The lognormal variable begins at zero, its density peaks soon after and thereafter tails down to higher x values. The variable x is lognormal distributed when another variable, y, formed by the logarithm of x, becomes normally distributed. The probability density of x is listed in the chapter, while the associated cumulative distribution function, F(x), is not since there is no closed–form solution. A method to compute the cumulative probability of any x is provided. When sample data is available, the measures from the sample are used to estimate the parameters of the lognormal. In the event no sample data is available and estimates of the lognormal variable are needed, two methods are described on how to compute the estimates. The lognormal distribution is not as popularly known as the normal, but applies easily in research studies of all kinds. It has applications in many disciplines, such as weather, engineering and economics.