This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

Likelihood

 Likelihood gives the likelihood function for observations , , ... from the distribution dist.
• The likelihood function Likelihood is given by , where is the probability density function at , PDF.
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:
 Out[1]=

Compute a likelihood for numeric data:
 Out[2]=
Plot likelihood contours as a function of and on a log scale:
 Out[3]=

Compute the likelihood for multivariate data:
 Out[2]=
 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:
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:
New in 8