LIKELIHOOD FUNCTION Meaning and
Definition
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The likelihood function can be defined as a fundamental concept in statistical inference. It is a function that quantifies the probability of observing certain data, given a specific set of parameters in a statistical model. In simpler terms, the likelihood function measures how likely a particular set of data points is based on the values of the unknown parameters in a statistical model.
The likelihood function is usually denoted as L(θ|x), where θ represents the parameters of the model and x represents the observed data. It functions as a measure of how well the observed data fits the hypothesized model. In other words, it provides a way to assess the plausibility of different parameter values by calculating the probability of obtaining the observed data under those values.
The likelihood function is often used in maximum likelihood estimation, a common method for estimating the parameters of a statistical model. By maximizing the likelihood function with respect to the parameters, we can find the values that are most likely to have generated the observed data.
Furthermore, the likelihood function has several important properties, such as its invariance under reparameterization and its relationship to other statistical concepts like the log-likelihood function. It plays a crucial role in statistical modeling and inference, serving as the foundation for many statistical techniques and computational methods.
Common Misspellings for LIKELIHOOD FUNCTION
- Likelihood Functioo
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- likelihood f unction
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Etymology of LIKELIHOOD FUNCTION
The word "likelihood" originates from the Middle English term "liklihede", which means "appearance or attractiveness". It further developed from the Old English word "gelīc" meaning "like" and the suffix "-hede" denoting "state or quality". The term "function" stems from the Latin word "functionem", meaning "performance" or "execution". Therefore, when combined, the term "likelihood function" refers to the function that assesses the resemblance or similarity of an event occurring based on given data or observations.
