Singh-Maddala (Burr XII) distribution on positive reals
SinghMaddalaDistribution[q, a, b]
Mean[SinghMaddalaDistribution[q, a, b]]
→ Piecewise[{{(b*Gamma[1 + a^(-1)]*Gamma[-a^(-1) + q])/Gamma[q], a*q > 1}}, Indeterminate]PDF[SinghMaddalaDistribution[q, a, b], x]
→ Piecewise[{{(a*q*x^(-1 + a)*(1 + (x/b)^a)^(-1 - q))/b^a, x > 0}}, 0]CDF[SinghMaddalaDistribution[q, a, b], x]
→ Piecewise[{{1 - (1 + (x/b)^a)^(-q), x > 0}}, 0]