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Which distribution is a particular case of multinomial distribution?
The more widely known binomial distribution is a special type of multinomial distribution in which there are only two possible outcomes, such as true/false or heads/tails. In finance, analysts use the multinomial distribution to estimate the probability of a given set of outcomes occurring.
What are the characteristics of a multinomial experiment?
Multinomial experiments
- The experiment consists of k repeated trials.
- Each trial has a discrete number of possible outcomes.
- On any given trial, the probability that a particular outcome will occur is constant.
- The trials are independent; that is, the outcome on one trial does not affect the outcome on other trials.
What is the definition of the multinomial distribution?
The multinomial distribution arises from an extension of the binomial experiment to situations where each trial has k ≥ 2 possible outcomes. each trial produces exactly one of the events E 1, E 2, …, E k (i.e. these events are mutually exclusive and collectively exhaustive), and
What is the PMF of the multinomial distribution?
If the dice is fair, then p i = 1 6 for all i. The PMF of the multinomial distribution is given by where ∑ ki = 1x i = n. If k = 2, the multinomial distribution becomes a binomial distribution with n trials and success probability p1.
Which is the maximum likelihood estimate for a multinomial distribution?
The covariance between Xi and Xj is − npipj. The maximum likelihood estimate of pi for a multinomial distribution is the ratio of the sample mean of xi ‘s and n.
Which is an example of a multinomial random variable?
An example where a multinomial random variable could occur is during the throw of a dice. Let Xi, i = 1, 2, … , 6, denote the number of times i is observed in n throws of a dice. Then X = ( X1, X2, … , X6) has a multinomial distribution. If the dice is fair, then p i = 1 6 for all i.