Merge branch 'master' of https://github.com/dmetivie/ExpectationMaxim…

…ization.jl

README.md

@@ -15,11 +15,30 @@ To work, the only requirements are that the `dist<:Distribution` considered has
 1. `logpdf(dist, y)` (used in the E-step)
 2. `fit_mle(dist, y, weigths)` (used in the M-step)
 
+In general 1. is easy, while 2. is only known explicitly for a few common distributions.
+In case 2. is not explicit known, you can always implement a numerical scheme, if it exists, for `fit_mle(dist, y)` see [`Gamma` distribution example](https://github.com/JuliaStats/Distributions.jl/blob/34a05d8a1671052624e7fa246b58484acc32cfe5/src/univariate/continuous/gamma.jl#L171).
+Or, when possible, represent your “difficult” distribution as a mixture of simple terms.
+(I had [this](https://stats.stackexchange.com/questions/63647/estimating-parameters-of-students-t-distribution) in mind, but it is not directly a mixture model.)
+Due to [Julia](https://julialang.org/) amazing [multiple dispatch](https://www.youtube.com/watch?v=kc9HwsxE1OY) systems and the [Distributions](https://juliastats.org/Distributions.jl/stable/) package, the code is very generic i.e., a lot of mixture should work:
+
+- Univariate continuous distributions
+- Univariate discrete distributions
+- Multivariate distributions (continuous or discrete).
+- Mixture of mixture (univariate or multivariate and continuous or discrete). Note that [Distributions](https://juliastats.org/Distributions.jl/stable/) currently does not allow `MixtureModel` to have discrete and continuous components (but who does that? Rain).
+
+**Have a look at the tests sections to see examples**.
+
+To work, the only requirements are that the `dist<:Distribution` considered has implanted
+
+1. `logpdf(dist, y)` (used in the E-step)
+2. `fit_mle(dist, y, weigths)` (used in the M-step)
+
 In general 1. is easy, while 2. is only known explicitly for a few common distributions.
 In case 2. is not explicit known, you can always implement a numerical scheme, if it exists, for `fit_mle(dist, y)` see [`Gamma` distribution example](https://github.com/JuliaStats/Distributions.jl/blob/34a05d8a1671052624e7fa246b58484acc32cfe5/src/univariate/continuous/gamma.jl#L171).
 Or, when possible, represent your “difficult” distribution as a mixture of simple terms.
 (I had [this](https://stats.stackexchange.com/questions/63647/estimating-parameters-of-students-t-distribution) in mind, but it is not directly a mixture model.)
 
+## TODO (feel free to contribute)
 ## TODO (feel free to contribute)
 
 - Add different variants for E-step and M-steps like stochastic EM and others.
@@ -70,4 +89,5 @@ isapprox(α, p[2][1]; rtol = rtol)
 isapprox(θ₂, p[2][2]; rtol = rtol)
 ```
 
+
 ![EM_mixture_example.svg](img/EM_mixture_example.svg)