The Multinomial distribution is a concept of probability that helps to get results in the form of 2 or more outcomes. It is not a complex part of probability and statistics, it is just a count in the mathematical concept of probability to get a satisfying outcome in multiple ways by computing all the samples of available products. Suppose, a dice is thrown multiple times, then it will give only 6 possible outcomes but no more expected results and if two dice are thrown multiple times, then it will give 36 possible outcomes but no more expected results.
Multinomial distribution Vs Binomial Distribution
Multinomial Distribution consists of binomial distribution or we can say that it is a generalization of the binomial distribution, it is the best method of binomial test in statistics which is shown happening by a single trial in which only two outcomes are possible such as head and tails.
The Multinomial distribution is different from binomial distribution due to variables and outcome quantity such as multiple variables in multinomial and single variables in a binomial distribution. These distributions are applied for getting accurate results with possibilities by experimental distribution.
Suppose you are a financial analyst and you have to calculate the company’s earnings, in that situation you have to acquire the probability concept of a given set of outcomes so that you can edit prepared reports if the reports do not schedule in a proper way. You will even give multiple trials for getting an outcome like dice is thrown multiple times but it gives some possible outcomes, not independent results and the one result does not impact the other result. Whenever you will do an experiment until you will get a new result or outcome but the binomial distribution is dependent, it gives only two possible outcomes, not more than 2.
Is it easy to calculate probability with Multinomial distribution?
To get profitability with statistics is different from the mathematical way because the multinomial distribution allows the analysts to calculate probability with a given set of outcomes. Analysts with multinomial distribution can get meaningful results with experiments in science, investing, finance, mathematics, economics, and many more.
The best part of these distributions, they generate two kinds of outcomes such as discrete and continuous.
Continuous outcomes are the outcomes that throw possible outcomes with infinity solutions or we can say that it can be uncountable by which analysts can satisfy easily. This outcome is wanted by everyone for getting more choice in every experiment. It is a time-consuming method of getting outcomes. It represents and shows with exponential, geometrical, and normal methods.
Discrete outcomes are the outcomes that throw possible outcomes with limited solutions or we can say that it can be countable. It can take prescribed values in between 1 to 6 integers. It can be distributed in a binomial or multinomial.
Advantages of the multinomial distribution
- Multinomial distribution has multiple outcomes when it deals with specific events but the binomial is different due to two outcomes of possibility.
- It works with continuous as well as discrete but in different situations such as when unlimited events in discrete outcomes and possible outcomes are gained from continuous events in high, medium, or low degrees.
- It is an expensive but managerial application.
- It has control over its process due to specific outcomes.
Example of Multinomial Distribution
(‘n’ indicates a number of events, n1 indicates a number of events 1, n2 indicates a number of events 2, and ‘nx’ indicates a number of events x).
(P1 indicates a probability that event 1 happens, P2 indicates a probability that event 2 happens, and Px indicates that event x happens).