Loss Models: From Data to Decisions, 4th Edition

A.5 Other distributions

A.5.1.1 Lognormal—μ, σ (μ can be negative)

A.5.1.2 Inverse Gaussian—μ, θ

A.5.1.3 log-t—r, μ, σ (μ can be negative) Let Y have a t distribution with r degrees of freedom. Then X = exp(σY + μ) has the log-t distribution. Positive moments do not exist for this distribution. Just as the t distribution has a heavier tail than the normal distribution, this distribution has a heavier tail than the lognormal distribution.

A.5.1.4 Single-parameter Pareto—α, θ

Note: Although there appear to be two parameters, only α is a true parameter. The value of θ must be set in advance.