VoseLLH

See also:  MLE, Distribution_Fit, Information_criteria

VoseLLH(FitObject)

 

 

 

Example model

The Vose LLH function calculates the natural log of the joint likelihood of observed data coming from the fitted model.  The parameter FitObject can be any ModelRisk distribution, copula or time series object fitted to data.

For example, in the model below a gamma distribution is fitted to a data set. Cell E1 contains the formula for a fitted gamma distribution object, and cell E3 returns the log likelihood associated with this fit. Since ModelRisk fits probability models using maximum likelihood estimation techniques, the VoseLLH function is returning the maximised log likelihood value.

Cell E4 gives a check on the value returned by VoseLLH in this example. The formula calculates the joint probability density of the dataset were they to come from the fitted distribution. Multiplying by LN(10) converts from log base 10 to log base e.

 

The example model provides other examples of the VoseLLH function with copula and time series fitted objects.

Fitted probability model objects can be nested within the VoseLLH function in the usual Excel notation so, for example, the formula in cell E3 for the example model above could also be:

=VoseLLH(VoseGammaFitObject(B2:B14))

Uses

VoseLLH is useful for comparing fits between different models on a likelihood basis. It can be used to select the most appropriate fitted model automatically within the spreadsheet, as this example shows. VoseLLH is closely connected to VoseAIC,  VoseSIC, and VoseHQIC, which return information criteria for a fitted probability model object. Information criteria are essentially log-likelihood value modified to penalise a fitted model according to the number of parameters within the model. Information criteria balance the goodness of fit of a model against its parsimony.

 

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