BUILT-IN MATHEMATICA SYMBOL

Likelihood

gives the likelihood function for observations

,

, ... from the distribution dist.

MORE INFORMATION

The likelihood function Likelihood is given by , where is the probability density function at , PDF.

EXAMPLES

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Basic Examples (3)

Get the likelihood function for a normal distribution:

Compute a likelihood for numeric data:

Plot likelihood contours as a function of

and

on a log scale:

Compute the likelihood for multivariate data:

Get the likelihood function for a normal distribution:

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Compute a likelihood for numeric data:

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Plot likelihood contours as a function of

and

on a log scale:

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Compute the likelihood for multivariate data:

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Scope (9)

Compute the likelihood for a continuous distribution:

Compute the likelihood for a discrete distribution:

Plot the likelihood, assuming

is unknown:

Obtain the log-likelihood for a continuous multivariate distribution with unknown parameters:

Visualize the log of the likelihood surface, assuming

:

For a multivariate discrete distribution:

Compute the likelihood for a truncated standard normal:

Compute the likelihood for a constructed distribution:

Visualize the likelihood contours as a function of the lower bound and

:

Compute the likelihood for a product distribution:

Obtain the result as a product of the independent component-wise likelihoods:

Compute the likelihood for a copula distribution:

Plot the likelihood as a function of the kernel parameter:

Compute the likelihood for a component mixture:

Properties & Relations (3)

Likelihood is a product of PDF values for the data:

The log of Likelihood is LogLikelihood:

EstimatedDistribution estimates parameters by maximizing the likelihood:

FindDistributionParameters gives the parameter estimates as rules:

Visualize the likelihood function near the optimal value: