The Pearson Type III, or Gamma, distribution describes the probability of occurrence of a given event in a Poisson process. When the population of events are very positively skewed, the data are usually log-transformed and the distribution called the Log Pearson Type III Distribution. The Pearson Type III probability density function is
where Υ is the lower bound of the distribution, β is a scale parameter, α a shape parameter, and Γ () the gamma function. Theses three parameters are related to the mean μ, variance σ2, and skewness gx of the distribution as
μ = γ+ αβ, σ2 = α, gx = 2/√α
The Pearson Type III Distribution was first applied in hydrology to describe the distribution of annual maximum discharges (Foster, 1924). The Log Pearson Type III Distribution is widely used in the U.S. to calculate flood recurrences because it has been recommended by the U.S. Interagency Advisory Committee on Water Data. It is the default distribution used by the U.S. Geological Survey for flood studies.