 Feller defines a Pareto variable by transformation "U" = "Y"−1 − 1 of a beta random variable "Y", whose probability density function is

where "B"( ) is the beta function.If

then "W" has a Feller–Pareto distribution FP("μ", "σ", "γ", "γ"1, "γ"2).If formula_43 and formula_44 are independent Gamma variables, another construction of a Feller–Pareto (FP) variable is

and we write "W" ~ FP("μ", "σ", "γ", "δ"1, "δ"2).