Sebaran binomial négatip: Béda antarrépisi

The sum of independent negative-binomially distributed random variables with the same value of the parameter ''p'' but the "''r''-values" ''r''₁ and ''r''₂ is negative-binomially distributed with the same ''p'' but with "''r''-value" ''r''₁ + ''r''₂.

 

 

If we follow the convention that the negative binomial distribution is the probability distribution of the number of failures before the ''r''th success, then any negative binomial distribution is [[infinite divisibility|infinitely divisible]], i.e., if ''X'' has a negative binomial distribution, then for any positive integer ''n'', there exist independent identically distributed random variables ''X''₁, ..., ''X''_''n'' whose sum has the same distribution that ''X'' has. These will not be negative-binomially distributed in the sense defined above unless ''n'' is a divisor of ''r'', but see the "third convention" below.