Question

Explain why overdispersion cannot be detected in the Bernoulli model.

Answer 1

The over dispersion can be defined as the situation in statistics when the observed variance is greater than expected variance of given data set belonging to the given distribution. In binomial distribution, we see the concept of overdispersion makes sense only when n>1 so it cannot be detected in bernoulli distribution.

In case of bernoulli distribution,

Variance =p(1-p). While mean =p

Thus, mean > variance always,

The variance depends only on sigle parameter p.

If we look at poisson distribution, mean=l=variance, so greater the rate greater will be variation seen. But this could not be the case with bernoulli where mean will always be greater than variance.

Thanks