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In statistics, the likelihood-ratio test is a hypothesis test that involves comparing the goodness of fit of two competing statistical models, typically one found by maximization over the entire parameter space and another found after imposing some constraint, based on the ratio of their likelihoods.
18 lip 2022 · The Likelihood-Ratio Test (LRT) is a statistical test used to compare the goodness of fit of two models based on the ratio of their likelihoods. This article will use the LRT to compare two models…
Learn how to use the likelihood ratio test to verify null hypotheses that can be written in the form . See the test statistic, its asymptotic distribution, and an example application.
Likelihood Ratio Test for Simple Hypotheses. Let X1, X2, X3, ..., Xn be a random sample from a distribution with a parameter θ. Suppose that we have observed X1 = x1, X2 = x2, ⋯, Xn = xn. To decide between two simple hypotheses. H0: θ = θ0, H1: θ = θ1, we define λ(x1, x2, ⋯, xn) = L(x1, x2, ⋯, xn; θ0) L(x1, x2, ⋯, xn; θ1).
Learn how to use the likelihood ratio test statistic to test hypotheses about the parameters of a population distribution. See examples from normal and exponential distributions and the relation to MLE and supremum.
The method, called the likelihood ratio test, can be used even when the hypotheses are simple, but it is most commonly used when the alternative hypothesis is composite.
A likelihood ratio greater than 1 indicates that the test result is associated with the presence of the disease, whereas a likelihood ratio less than 1 indicates that the test result is associated with the absence of disease.
