PERT project-management distribution on an interval with a mode (modified Beta)
PERTDistribution[{min, max}, c]
PERTDistribution[{min, max}, c, λ]
Mean[PERTDistribution[{min, max}, c]]
→ (4*c + max + min)/6PDF[PERTDistribution[{min, max}, c], x]
→ Piecewise[{{((max - x)^((4*(-c + max))/(max - min))*(-min + x)^((4*(c - min))/(max - min)))/((max - min)^5*Beta[1 + (4*(c - min))/(max - min), 1 + (4*(-c + max))/(max - min)]), min < x < max}}, 0]CDF[PERTDistribution[{min, max}, c], x]
→ Piecewise[{{BetaRegularized[(-min + x)/(max - min), 1 + (4*(c - min))/(max - min), 1 + (4*(-c + max))/(max - min)], min < x < max}, {1, x >= max}}, 0]