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Statistics[ProfileLogLikelihood] - plot a profile of the log likelihood function
Calling Sequence
ProfileLogLikelihood(R, V, options, plotoptions)
ProfileLogLikelihood['interactive'](R, V)
Parameters
R
-
algebraic; a random variable or distribution
V
rtable; data sample
options
(optional) equation(s) of the form option=value where option is one of bounds, deviations, ignore, params, range, weights; specify options for the ProfileLogLikelihood command
plotoptions
options to be passed to the plots[display] command
Description
The ProfileLogLikelihood command plots a profile of the LogLikelihood command.
The first parameter R can be a distribution (see Statistics[Distribution]), a random variable, or an algebraic expression involving random variables (see Statistics[RandomVariable]).
The second parameter V is an Array of data samples used to calculate the log likelihood function.
Options
The options argument can contain one or more of the options shown below. All unrecognized options will be passed to the plots[display] command. See plot[options] for details.
bounds=none or range
If this option specifies a range, then ProfileLogLikelihood will attempt to calculate the maximum likelihood estimate within the given bounds. Otherwise the command will attempt to calculate the maximum likelihood estimate over the entire real line (default). Note that this option only applies if a range is not specified with the 'range' option.
deviations=realcons
This option specifies the radius of the region plotted around the maximum likelihood estimate, given option range=deduce. This option is 3 by default.
ignore=truefalse
This option is used to specify how to handle non-numeric data. If ignore is set to true all non-numeric items in data will be ignored.
params=list(name=realcons)
This option specifies any additional indeterminates in the likelihood expression that should be evaluated prior to plotting. The likelihood profile requires that there is only one indeterminate in the expression, so this provides a mechanism to specify the values of missing parameters.
range=deduce or range
If this option is set to 'deduce' (default), ProfileLogLikelihood will attempt to calculate the maximum likelihood estimate and plot the log likelihood function in an interval around it. Otherwise, this parameter can specify a range to plot the likelihood profile on.
weights=rtable
Vector of weights (one-dimensional rtable). If weights are given, the log likelihood function will be scaled so each data point has the given weight. Note that the weights provided must have type realcons and the results are floating-point, even if the problem is specified with exact values. Both the data array and the weights array must have the same number of elements.
Examples
Plot the profile of the log likelihood function of a Pareto distribution.
See Also
Statistics, Statistics[Computation], Statistics[Estimation][LogLikelihood]
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