LIKELIHOOD FUNCTIONS Meaning and
Definition
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Likelihood functions, in the context of statistics and probability, refer to a fundamental concept used to estimate unknown parameters based on observed data. Specifically, a likelihood function is a mathematical function that quantifies the likelihood or plausibility of different values for the parameters of a statistical model, given the observed data.
The likelihood function is constructed by evaluating the joint probability distribution function or probability mass function of the observed data, conditional on the values of the parameters of the statistical model. The fundamental assumption underlying the construction of the likelihood function is that the observed data are independent and identically distributed (IID) random variables.
The likelihood function serves as a powerful tool for parameter estimation because it encapsulates the information contained in the observed data about the unknown parameters. By maximizing the likelihood function, statisticians and data analysts can obtain estimates of the parameter values that are most consistent with the observed data.
The concept of likelihood functions is closely related to the idea of maximum likelihood estimation (MLE), which aims to find the parameter values that maximize the likelihood function. MLE is widely used in various statistical methods and models, such as linear regression, logistic regression, and time series analysis.
In summary, a likelihood function is a mathematical function that quantifies the plausibility of different parameter values, given the observed data, and plays a crucial role in estimating unknown parameters in statistical models.
Common Misspellings for LIKELIHOOD FUNCTIONS
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Etymology of LIKELIHOOD FUNCTIONS
The term "likelihood function" originated from the field of statistics and probability. The word "likelihood" is derived from the Middle English word "liklihede", which means probability or chance. The addition of "function" to "likelihood" refers to the mathematical function used to express the probability distribution of a statistical model given a set of parameters.
