be obtained by multiplying the mode and mean in the above infobox by q and the variance by q2. Properties If then . If then . If and two iid variables, then with and , as the beta prime distribution is infinitely divisible. More generally, let iid variables following the same beta prime distribution, i.e. , then the sum with and . Related distributions If has an F-distribution, then , or equivalently, . If then . If and are independent, then . Parametrization 1: If are independent, then . Parametrization 2: If are independent, then . the Dagum distribution the Singh–Maddala distribution. the log logistic distribution. The beta prime distribution is a special case of the type 6 Pearson distribution. If X has a Pareto distribution with minimum and shape parameter , then . If X has a Lomax distribution, also known as a Pareto Type II distribution, with shape parameter and scale parameter , then . If X has a standard Pareto Type IV distribution with shape parameter and inequality parameter , then , or equivalently, . The inverted Dirichlet distribution is a generalization of the beta prime distribution. If , then has a generalized logistic distribution. Notes References Johnson, N.L., Kotz, S., Balakrishnan, N. (1995). Continuous Univariate Distributions, Volume 2 (2nd Edition), Wiley. MathWorld article Continuous distributions Compound probability distributions