Multinomial Distribution Vs Binomial Distribution. Multinoulli distribution whereas the binomial distribution generalises the bernoulli distribution across the number of trials the multinoulli distribution generalises it across the number of outcomes that is rolling a dice instead of tossing a coin. In probability theory the multinomial distribution is a generalization of the binomial distribution for example it models the probability of counts for each side of a k sided die rolled n times.
Suppose p x 1 θ. There is a fixed number n of observations. For fixed values of the mean and size n the variance is maximal when all success probabilities are equal and we have a binomial distribution.
Out of those probability distributions binomial distribution and normal distribution are two of the most commonly occurring ones in the real life.
Poisson and binomial multinomial models of contingency tables. With the poisson distribution we know the mean m but not the sample size. Multinoulli distribution whereas the binomial distribution generalises the bernoulli distribution across the number of trials the multinoulli distribution generalises it across the number of outcomes that is rolling a dice instead of tossing a coin. Since a poisson binomial distributed variable is a sum of n independent bernoulli distributed variables its mean and variance will simply be sums of the mean and variance of the n bernoulli distributions.
