Add basic location-scale family support

[johnmyleswhite]

This adds an initial draft of support for location-scale families of univariate distribution. This makes it possible to rescale and relocate univariate distributions using scalar arithmetic, giving things like d1 = Normal(0, 1) + 3 and d2 = 3 * Uniform(0, 1) + 11.

The basic principle is simple: unless there is a clear way in which changing the location or scale of a distribution produces another distribution of the same type, we create an ad hoc UnivariateLocationScaleFamily type, which maintains a separate location and scale parameter. Thus, one has two ways of writing some distributions. for example, the two distributions below are meant to be identical:

• UnivariateLocationScaleFamily(Normal(0, 1), 2.0, 2.0)
• Normal(2.0, 2.0)

But special cases are handled as needed, so that 3 * Normal(0, 1) gives Normal(0, 3) rather than the less efficient UnivariateLocationScaleFamily(Normal(0, 1), 0.0, 3.0).

[patrickeganfoley]

Hello,

Is this doing something similar to this code https://github.com/patrickeganfoley/Distributions.jl/blob/master/src/relationships.jl ?

It doesn't seem like it, or maybe this was never pulled and was decided against, since right now you get:

julia> ef = 3*Normal(0,1)
ERROR: no method *(Int64, Normal)

Do we not want that? Or stuff like exp( Normal(0,1) ) = LogNormal(0,1) ?

[lindahua]

There hasn't been much progress along this line, probably because of there are more important things. No one is against this. It is just a matter of time before this happens.

[patrickeganfoley]

Cool.

If I were to do it, should I have it all on one file?

[lindahua]

There's no rule governing about what should go in one file.

The general practice is that you start from one file, and if the file gets too long or too complicated, break it into smaller files.

[johnmyleswhite]

Now that I'm thinking about getting the bare minimum in place and worrying about efficiency optimizations later, I'm wondering if we should have the parametric type be LocationScaleFamily and let that vary with variate type.

[matbesancon]

Closing this for #635
@kleinschmidt same here :)