The multinomial distribution is a type of probability distribution used in finance to determine the likelihood of a certain set of outcomes.

Aldous and Shepp recently proved that the Erlang distribution of a given order is the least variable phase-type distribution of that order, in the sense of minimizing the coefficient of variation.

The COV is equal to the ratio between the standard deviation and the mean. Although COV is most commonly used in comparing relative risk, it may be applied to many types of probability distribution.

Journal of Applied Probability, Vol. 29, No. 1 (Mar., 1992), pp. 92-103 (12 pages) We characterise the classes of continuous and discrete phase-type distributions in the following way. They are known ...