When Should You Use Multinomial Distribution

Introduction

Binomial distribution may be useful when a number of independent trials may be performed and there are two categories of data. However, in case there are more than two categories of data, it may be helpful to make use of the process of multinomial distribution. There are four essential conditions that are necessary for a multinomial distribution. These are:

• Fixed number of trials
• Independent trials
• Several different classifications
• Probability for the classifications remains the same for all trials

It is necessary for all these conditions to be present in the process being investigated in order to make effective use of the formula of binomial probability distribution. Below is a more detailed look at each of these conditions.

Fixed Trials

The process that is under investigation must have a fixed number of trials and it is necessary that number of trials do not vary. The method for performing each trial must be the same; however there is a possibility that the results of the trials may vary.

Independent Trials

It is also important that each of the trials must be independent. This implies that each trial should not have any sort of effect on the other trials. Some of the best examples of independent trials are rolling two dices or flipping a number of coins. Due to the events being independent, the multiplication rule can be used to multiply all the probabilities together.

Several Classifications

The main point of difference between a binomial and multinomial distribution is the number of classifications that need to be considered. While binomial distribution involves only two classifications, a multinomial one involves a number of classifications. In a multinomial distribution, each of the trials is put under one of the multiple classifications that are possible. There are no limits to the number of categories that may be used. A good illustration of this can be the rolling of a dice. Since there are six possible results of the roll of dice, there can be six different categories. Another notable thing is that these possibilities do not overlap with each other as the same roll of dice cannot produce a two and a three.

Same Probabilities

Throughout the process of investigation, it is important for the probabilities of all different classifications to remain unchanged. The roll of dice can be a good example of this as well but it is not necessary for the probabilities to be similar. Another illustration of this can be the rolling of a roulette wheel. Irrespective of the number of occasions that the wheel may be spun, the probability for each of the results remains the same almost every time even though the red and green spaces have different respective probabilities.

Conclusion

Multinomial Distribution has a number of uses in various different fields such as ecology.

This article has been compiled by Evelyn, who is a writer on various academic topics.