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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