Wakeby quantile-defined distribution
WakebyDistribution[α, β, γ, δ, μ]
Mean[WakebyDistribution[α, β, γ, δ, μ]]
→ Piecewise[{{α/(1 + β) + γ/(1 - δ) + μ, δ < 1}}, Indeterminate]Variance[WakebyDistribution[α, β, γ, δ, μ]]
→ Piecewise[{{α^2/((1 + β)^2*(1 + 2*β)) - γ^2/((-1 + δ)^2*(-1 + 2*δ)) - (2*α*γ)/((1 + β)*(-1 + δ)*(1 + β - δ)), δ < 1/2}}, Indeterminate]Quantile[WakebyDistribution[α, β, γ, δ, μ], q]
→ ConditionalExpression[Piecewise[{{((1 - (1 - q)^β)*α)/β - ((1 - (1 - q)^(-δ))*γ)/δ + μ, 0 < q < 1}, {μ, q <= 0}}, Infinity], 0 <= q <= 1]