Class EstimateByLogLikelihood
- java.lang.Object
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- dev.nm.stat.evt.evd.univariate.fitting.EstimateByLogLikelihood
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public class EstimateByLogLikelihood extends Object
Result from maximum likelihood fitting algorithm, which contains:- the log-likelihood function,
- the fitted parameters for the target model,
- the variance-covariance matrix,
- the standard errors,
- the confidence intervals.
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Constructor Summary
Constructors Constructor Description EstimateByLogLikelihood(Vector fittedParameters, RealScalarFunction logLikelihoodFunction)
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Method Summary
All Methods Instance Methods Concrete Methods Modifier and Type Method Description ConfidenceIntervalconfidenceInterval(double confidenceLevel)Compute the \((1 - \alpha)100\%\) confidence intervals for each element of the fitted parameter, given the required confidence level.MatrixcovarianceMatrix()Get the covariance matrix, which is estimated as the inverse of negative Hessian matrix of the log-likelihood function valued at the fitted parameter.ImmutableVectorgetFittedParameters()Get the fitted parameters.RealScalarFunctiongetLogLikelihoodFunction()Get the log-likelihood function.doublelogLikelihood()Compute the log-likelihood at the fitted value.VectorstandardError()Get the standard errors of the fitted parameters.
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Constructor Detail
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EstimateByLogLikelihood
public EstimateByLogLikelihood(Vector fittedParameters, RealScalarFunction logLikelihoodFunction)
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Method Detail
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getFittedParameters
public ImmutableVector getFittedParameters()
Get the fitted parameters. That is, the parameters that evaluate to the maximum log-likelihood.- Returns:
- the fitted parameters for the model
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getLogLikelihoodFunction
public RealScalarFunction getLogLikelihoodFunction()
Get the log-likelihood function. That is, \[ \ell(\theta | X_1,\ldots,X_n) = \sum_{i=1}^n \log f(X_i| \theta) \] where \(\theta\) is the parameter, \(X_i\) are the observations, \(f(.)\) is the probability density function.- Returns:
- the log-likelihood function
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logLikelihood
public double logLikelihood()
Compute the log-likelihood at the fitted value. That is, the maximum log-likelihood.- Returns:
- the maximum log-likelihood computed at the fitted value
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covarianceMatrix
public Matrix covarianceMatrix()
Get the covariance matrix, which is estimated as the inverse of negative Hessian matrix of the log-likelihood function valued at the fitted parameter.- Returns:
- the covariance matrix
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standardError
public Vector standardError()
Get the standard errors of the fitted parameters.- Returns:
- the standard errors
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confidenceInterval
public ConfidenceInterval confidenceInterval(double confidenceLevel)
Compute the \((1 - \alpha)100\%\) confidence intervals for each element of the fitted parameter, given the required confidence level. That is, \[ CI = (\hat{\theta} \pm z_{\alpha/2} \hat{\sigma}_{\hat{\theta}}) \] where \(\hat{\theta}\) is the fitted parameter, \(\hat{\sigma}_{\hat{\theta}}\) is the standard error of the estimate.- Parameters:
confidenceLevel- the required confidence level- Returns:
- the confidence interval
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