About types and estimation of probability distributionsAbout types and estimation of probability distributions

This is an article about the types and estimation of probability distributions.

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Today we will learn about the types and estimation of probability distributions.

A probability distribution is a function that provides information about the values ​​that a random variable can have and the probability that those values ​​will occur.

We will explain the types of probability distributions and their estimation below.

Types of probability distributions

Discrete Probability Distribution

A discrete probability distribution defines the values ​​that a discrete random variable can take and the probability that those values ​​will occur.

Representative examples include binomial distribution and Poisson distribution.

Continuous Probability Distribution

A continuous probability distribution defines the probability that a continuous random variable falls within a certain interval.

Representative examples include normal distribution, exponential distribution, and uniform distribution.

Estimation of probability distribution

Estimation of probability distribution refers to the process of estimating the shape or parameters of a probability distribution based on given data.

This allows you to estimate a probability distribution based on data without knowing the actual distribution.

Representative methods include the following:

Maximum Likelihood Estimation (MLE)

MLE is a method of finding the parameter with which the given data has the highest probability, and is mainly used to find the parameter that best fits the given data.

Least Squares Estimation (LSE)

LSE is a method of estimating parameters by minimizing the sum of squares of residuals (errors) between given data and a model, and is widely used in regression analysis.

Bayesian Estimation

Bayesian estimation is a method of estimating parameters by obtaining a prior distribution and a posterior distribution based on data, and is used to deal with uncertainty probabilistically.

Conclusion

The type and estimation of probability distributions are important factors in analyzing and modeling data and are used to effectively interpret and model data.

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