Loss Models: From Data to Decisions, 4th Edition

A.2 Transformed beta family

A.2.1 Four-parameter distribution

A.2.1.1 Transformed beta—α, θ, γ, τ (generalized beta of the second kind, Pearson Type VI)²

A.2.2 Three-parameter distributions

A.2.2.1 Generalized Pareto—α, θ, τ (beta of the second kind)

A.2.2.2 Burr—α, θ, γ (Burr Type XII, Singh—Maddala)

A.2.2.3 Inverse Burr—τ, θ, γ, (Dagum)

A.2.3 Two-parameter distributions

A.2.3.1 Pareto—α, θ (Pareto Type II, Lomax)

A.2.3.2 Inverse Pareto—τ, θ

A.2.3.3 Loglogistic—γ, θ (Fisk)

A.2.3.4 Paralogistic—α, θ This is a Burr distribution with γ = α.

Starting values can use estimates from the loglogistic (use γ for α) or Pareto (use α) distributions.

A.2.3.5 Inverse paralogistic—τ, θ This is an inverse ...