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·       Format:

Negbinomial(p, s)

·       Probability mass function:

LaTeX Math Block
alignmentleft
f(x)=\left(
    \begin{array}{c}
      x-1 \\
      x-s
    \end{array}
	 \right)
	 p^s(1-p)^{x-s}

·       Cumulative distribution function:

LaTeX Math Block
alignmentleft
F(x)=\displaystyle\sum_{i=s}^{\lfloor x \rfloor} \left(
    \begin{array}{c}
      x-1 \\
      i-s
    \end{array}
	 \right)
	 p^s(1-p)^{i-s}

·       Parameter restrictions:

s > 0, s is an integer, 0 < p ≤ 1

·       Domain: 

x = {s, s+1, s+2,...}

·       Mean:

LaTeX Math Inline
body\frac{s}{p}

·       Mode: 

z, z +1

if z is an integer

|z|+ 1

otherwise

where z = (s - 1)/ p

·       Variance:

LaTeX Math Block
alignmentleft
\frac{s(1-p)}{p^2}