Mixed Normal distribution


Format: NormalMix(μ,σ,κ)

The Mixed Normal (NormalMix) distribution is a continuous unbounded distribution developed as a deviation to the Normal distribution to allow for a greater kurtosis by altering the κ parameter, as illustrated in the plot below. When κ=0 the distribution reduces to a Normal (μ,σ).

 

Uses

The NormalMix distribution can be used to fit to data that are approximately Normal but have a kurtosis > 3. i.e. greater than the Normal distribution. The NormalMix can readily be compared to a Normal since they share the same mean μ and standard deviation σ parameters.

Comments

The range of possible kurtosis values lies within [3,6] equating to excess kurtosis values of 0 and 3 respectively.

The Normal Mix distribution is constructed by taking the average of the distribution functions of two Normal distributions with the same mean μ but with different standard deviations to obtain the required kurtosis.


ModelRisk functions added to Microsoft Excel for the Normal Mix distribution

VoseNormalMix generates random values from this distribution for Monte Carlo simulation, or calculates a percentile if used with a U parameter.

VoseNormalMixObject constructs a distribution object for this distribution.

VoseNormalMixlProb returns the probability density or cumulative distribution function for this distribution.

VoseNormalMixProb10 returns the log10 of the probability density or cumulative distribution function.

VoseNormalMixFit generates values from this distribution fitted to data, or calculates a percentile from the fitted distribution.

VoseNormalMixFitObject constructs a distribution object of this distribution fitted to data.

VoseNormalMixFitP returns the parameters of this distribution fitted to data.

 

Mixed Normal distribution equations

 

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