Waring (two-parameter) and Yule (one-parameter) discrete distribution; supports PDF CDF Quantile and Mean
WaringYuleDistribution[α]
WaringYuleDistribution[α, β]
Mean[WaringYuleDistribution[α]]
→ Piecewise[{{(-1 + α)^(-1), α > 1}}, Indeterminate]PDF[WaringYuleDistribution[α], k]
→ Piecewise[{{α*Beta[1 + α, 1 + k], k >= 0}}, 0]Mean[WaringYuleDistribution[α, β]]
→ Piecewise[{{β/(-1 + α), α > 1}}, Indeterminate]