BUILT-IN MATHEMATICA SYMBOL

LogLikelihood

gives the log-likelihood function for observations

,

, ... from the distribution dist.

MORE INFORMATION

The log-likelihood function LogLikelihood is given by , where is the probability density function at , PDF.

EXAMPLES

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Basic Examples (3)

Get the log-likelihood function for a normal distribution:

Compute a log-likelihood for numeric data:

Plot log-likelihood contours as a function of

and

:

Compute the log-likelihood for multivariate data:

Get the log-likelihood function for a normal distribution:

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Compute a log-likelihood for numeric data:

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Plot log-likelihood contours as a function of

and

:

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Compute the log-likelihood for multivariate data:

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Scope (9)

Compute the log-likelihood for a continuous distribution:

Compute the log-likelihood for a discrete distribution:

Plot the log-likelihood, assuming

is unknown:

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

Visualize the log-likelihood surface, assuming

:

For a multivariate discrete distribution with known parameters:

Compute the log-likelihood for a truncated standard normal:

Plot the log-likelihood contours as a function of the truncation points:

Compute the log-likelihood for a constructed distribution:

Compute the log-likelihood for a product distribution:

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

Compute the log-likelihood for a copula distribution:

Plot the log-likelihood as a function of the kernel parameter:

Compute the log-likelihood for a component mixture:

Applications (2)

Visualize the log-likelihood surface for a distribution of two parameters:

Visualize as contours of equal log-likelihood:

Show log-likelihood functions with mixed continuous and discrete parameters:

Properties & Relations (3)

LogLikelihood is the log of Likelihood:

LogLikelihood is the sum of logs of PDF values for data:

EstimatedDistribution estimates parameters by maximizing the log-likelihood:

FindDistributionParameters gives the parameter estimates as rules:

Visualize the log-likelihood function near the optimal value:

Neat Examples (2)

Visualize isosurfaces for an exponential power log-likelihood:

Visualize isosurfaces for a bivariate normal log-likelihood: