Probability distributions: location (i.e. shift) and scale variants

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The location and scale of any probability distribution can be adjusted by using the (linear) transform  where  and  are constants ( adjusts the location, i.e. shifts the distribution, whilst  adjusts its scale). This leaves the skew and (excess kurtosis) unaltered but alters the mean and variance as  and .


In some cases the typical distributional specification already includes such components. For example, the normal distribution  is the location and scale adjusted version of the unit normal distribution .


In other cases the standard distributional specification does not include such adjustments. For example, the (standard) Student’s t distribution depends one just one parameter, its degrees of freedom. The probability distribution orientated Nematrian web functions recognise location and/or scale adjusted variants of wide range of standard probability distributions.


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