# what is quasibinomial distribution?

#### youngukoo

##### New Member
I've done some search, but still can't understand what quasibionmial distribution is. Can anyone give me an intuitive explanation? What is a difference between quasibinomial distribution and normal binomial distribution?

Thanks!

#### barrymorejennifer

##### New Member
The quasi-binomial distribution is a small perturbation of the binomial distribution. The mass
probability function is defined by
P(X = k) = C^k_np(p + k*phi)^(k-1)(1 -p - k*phi)^(n-k);
where k 0 to n; n; p usual parameters and phi elememt of -p/n , (1-p)/n
Of course, we retrieve the binomial
distribution with phi set to 0.

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#### hamilthj

##### New Member
The quasi-binomial distribution is a small perturbation of the binomial distribution. The mass
probability function is defined by
P(X = k) = C^k_np(p + k*phi)^(k-1)(1 -p - k*phi)^(n-k);
where k 0 to n; n; p usual parameters and phi elememt of -p/n , (1-p)/n
Of course, we retrieve the binomial
distribution with phi set to 0.
Does this essentially mean that the pmf of the quasi-binomial distribution includes a dispersion parameter (rather than the binomial pmf that assumes it is 1?). Would it be appropriate to use a quasi-binomial distribution to better describe data that are overdispersed?