Multinomial Distribution
The multinomial scheme extends the Bernoulli trial in cases with more than two outcomes. A multinomial scheme refers to a situation where you have multiple categories or outcomes and are interested in studying the probabilities of each outcome occurring. A probability distribution that models the number of successes in a fixed number of independent trials with multiple categories is called multinomial distribution.
Example
A company is surveying to gather feedback from its customers.
The survey has three possible responses: "Satisfied," "Neutral," and "Dissatisfied." The company randomly selects 50 customers and records their responses.
Assume that each customer is satisfied with a probability 0.3, neutral with a probability 0.4, and dissatisfied with a probability 0.3.
Calculate the probability that there will be 25 "Satisfied" responses, 15 "Neutral," and 10 "Dissatisfied".
To solve this task multinomial distribution is used:
123456789101112import numpy as np from scipy.stats import multinomial # Define the probabilities of each response category probabilities = [0.3, 0.4, 0.3] # Satisfied, Neutral, Dissatisfied # Specify the number of responses for which we calculate probability response = [25, 15, 10] # 25 satisfied, 15 neutral, 10 dissatisfied responses out of 50 total responses # Calculate the probability mass function (pmf) using multinomial distribution pmf = multinomial.pmf(response, n=50, p=probabilities) print(f'Probability of {response}: {pmf:.4f}')
In the code above, we used .pmf() method of scipy.stats.multinomial class with parameters n (number of trials) and p (probabilities of each outcome) to calculate probability that we will have certain response (the first argument of the .pmf() method.
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The multinomial scheme extends the Bernoulli trial in cases with more than two outcomes. A multinomial scheme refers to a situation where you have multiple categories or outcomes and are interested in studying the probabilities of each outcome occurring. A probability distribution that models the number of successes in a fixed number of independent trials with multiple categories is called multinomial distribution.
Example
A company is surveying to gather feedback from its customers.
The survey has three possible responses: "Satisfied," "Neutral," and "Dissatisfied." The company randomly selects 50 customers and records their responses.
Assume that each customer is satisfied with a probability 0.3, neutral with a probability 0.4, and dissatisfied with a probability 0.3.
Calculate the probability that there will be 25 "Satisfied" responses, 15 "Neutral," and 10 "Dissatisfied".
To solve this task multinomial distribution is used:
123456789101112import numpy as np from scipy.stats import multinomial # Define the probabilities of each response category probabilities = [0.3, 0.4, 0.3] # Satisfied, Neutral, Dissatisfied # Specify the number of responses for which we calculate probability response = [25, 15, 10] # 25 satisfied, 15 neutral, 10 dissatisfied responses out of 50 total responses # Calculate the probability mass function (pmf) using multinomial distribution pmf = multinomial.pmf(response, n=50, p=probabilities) print(f'Probability of {response}: {pmf:.4f}')
In the code above, we used .pmf() method of scipy.stats.multinomial class with parameters n (number of trials) and p (probabilities of each outcome) to calculate probability that we will have certain response (the first argument of the .pmf() method.
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