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Download a pdf copy of this help file here |
See also: Skew Normal distribution
Format:
VoseNormalMix(μ,σ,κ,
U )
The Normal Mix (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).
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.
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 from 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.
VoseNormalMix generates values from this distribution or calculates a percentile. Professional and Industrial editions only.
VoseNormalMixObject constructs a distribution object for this distribution. Professional and Industrial editions only.
VoseNormalMixlProb returns the probability density or cumulative distribution function for this distribution. Professional and Industrial editions only.
VoseNormalMixProb10 returns the log10 of the probability density or cumulative distribution function. Professional and Industrial editions only.
VoseNormalMixFit generates values from this distribution fitted to data, or calculates a percentile from the fitted distribution. Professional and Industrial editions only.
VoseNormalMixFitObject constructs a distribution object of this distribution fitted to data. Professional and Industrial editions only.
VoseNormalMixFitP returns the parameters of this distribution fitted to data. Professional and Industrial editions only.