Consider a four-parameter Pearson type VI distribution with shape parameters α1 and α2, sc...

Consider a four-parameter Pearson type VI distribution with shape parameters α₁ and α₂, scale parameter β, and location parameter γ. If α₁ = 1, γ = β = c > 0, then the resulting density is

which is the density function of a Pareto distribution with parameters c and α₂, denoted Pareto(c, α₂). Show that X ~ Pareto(c, α₂) if and only if Y = ln X ~ expo(ln c, 1/α₂), an exponential distribution with location parameter ln c and scale parameter 1/α₂.