Pascal distribution (number of trials until n successes)
PascalDistribution[n, p]
Mean[PascalDistribution[n, p]]
→ n/pPDF[PascalDistribution[n, p], x]
→ Piecewise[{{(1 - p)^(-n + x)*p^n*Binomial[-1 + x, -1 + n], x >= n}}, 0]CDF[PascalDistribution[n, p], x]
→ Piecewise[{{BetaRegularized[p, n, 1 - n + Floor[x]], x >= n}}, 0]