Convert docstring references to the right format and add a few more

Fixes #88

joss/paper.bib

@@ -88,6 +88,14 @@ @book{joe2014
   file = {C:\Users\lrnv\Zotero\storage\VMB6EMI8\Joe - 2014 - Dependence modeling with copulas.pdf}
 }
 
+@book{johnson1987multivariate,
+  title={Multivariate statistical simulation: A guide to selecting and generating continuous multivariate distributions},
+  author={Johnson, Mark E},
+  volume={192},
+  year={1987},
+  publisher={John Wiley \& Sons}
+}
+
 @book{durantePrinciplesCopulaTheory2015,
   title = {Principles of Copula Theory},
   author = {Durante, Fabrizio and Sempi, Carlo},
@@ -222,4 +230,5 @@ @software{BivariateCopulas
   version      = {v0.1.5},
   doi          = {10.5281/zenodo.10412898},
   url          = {https://doi.org/10.5281/zenodo.10412898}
-}
+}
+

src/EllipticalCopula.jl

@@ -31,6 +31,9 @@ Recall that spherical random vectors are random vectors which characteristic fun
 We can therefore express this characteristic function as ``\\phi(\\bm t) = \\psi(\\lVert \\bm t \\rVert_2^2)``, where ``\\psi`` is a function that characterizes the spherical family, called the *generator* of the family. Any characteristic function that can be expressed as a function of the norm of its argument is the characteristic function of a spherical random vector, since ``\\lVert \\bm A \\bm t \\rVert_2 = \\lVert \\bm t \\rVert_2`` for any orthogonal matrix ``\\bm A``. 
 
 However, note that this is not how the underlying code is working, we do not check for validity of the proposed generator (we dont even use it)
+
+References:
+* [nelsen2006](@cite) Nelsen, Roger B. An introduction to copulas. Springer, 2006.
 """
 abstract type EllipticalCopula{d,MT} <: Copula{d} end
 Base.eltype(C::CT) where CT<:EllipticalCopula = Base.eltype(N(CT)(C.Σ))

src/EllipticalCopulas/GaussianCopula.jl

@@ -32,6 +32,9 @@ And yo can fit the distribution via :
 ```julia
 fit(GaussianCopula,data)
 ```
+
+References:
+* [nelsen2006](@cite) Nelsen, Roger B. An introduction to copulas. Springer, 2006.
 """
 struct GaussianCopula{d,MT} <: EllipticalCopula{d,MT}
     Σ::MT

src/EllipticalCopulas/TCopula.jl

@@ -35,6 +35,9 @@ fit(TCopula,data)
 ```
 
 Except that currently it does not work since `fit(Distributions.MvTDist,data)` does not dispatch. 
+
+References:
+* [nelsen2006](@cite) Nelsen, Roger B. An introduction to copulas. Springer, 2006.
 """
 struct TCopula{d,df,MT} <: EllipticalCopula{d,MT}
     Σ::MT

src/Generator/UnivariateGenerator/AMHGenerator.jl

@@ -17,6 +17,9 @@ The [AMH](https://en.wikipedia.org/wiki/Copula_(probability_theory)#Most_importa
 
 It has a few special cases: 
 - When θ = 0, it is the IndependentCopula
+
+References:
+* [nelsen2006](@cite) Nelsen, Roger B. An introduction to copulas. Springer, 2006.
 """
 struct AMHGenerator{T} <: UnivariateGenerator
     θ::T

src/Generator/UnivariateGenerator/ClaytonGenerator.jl

@@ -19,6 +19,9 @@ It has a few special cases:
 - When θ = -1/(d-1), it is the WCopula (Lower Frechet-Hoeffding bound)
 - When θ = 0, it is the IndependentCopula
 - When θ = ∞, is is the MCopula (Upper Frechet-Hoeffding bound)
+
+References:
+* [nelsen2006](@cite) Nelsen, Roger B. An introduction to copulas. Springer, 2006.
 """
 struct ClaytonGenerator{T} <: UnivariateGenerator
     θ::T

src/Generator/UnivariateGenerator/FrankGenerator.jl

@@ -19,6 +19,9 @@ It has a few special cases:
 - When θ = -∞, it is the WCopula (Lower Frechet-Hoeffding bound)
 - When θ = 1, it is the IndependentCopula
 - When θ = ∞, is is the MCopula (Upper Frechet-Hoeffding bound)
+
+References:
+* [nelsen2006](@cite) Nelsen, Roger B. An introduction to copulas. Springer, 2006.
 """
 struct FrankGenerator{T} <: UnivariateGenerator
     θ::T

src/Generator/UnivariateGenerator/GumbelBarnettGenerator.jl

@@ -15,12 +15,12 @@ The Gumbel-Barnett copula is an archimdean copula with generator:
 \\phi(t) = \\exp{θ^{-1}(1-e^{t})}, 0 \\leq \\theta \\leq 1.
 ```
 
-More details about Gumbel-Barnett copula are found in:
-
-    Joe, H. (2014). Dependence modeling with copulas. CRC press, Page.437
-
 It has a few special cases: 
 - When θ = 0, it is the IndependentCopula
+
+References:
+* [joe2014](@cite) Joe, H. (2014). Dependence modeling with copulas. CRC press, Page.437
+* [nelsen2006](@cite) Nelsen, Roger B. An introduction to copulas. Springer, 2006.
 """
 struct GumbelBarnettGenerator{T} <: UnivariateGenerator
     θ::T

src/Generator/UnivariateGenerator/GumbelGenerator.jl

@@ -18,6 +18,9 @@ The [Gumbel](https://en.wikipedia.org/wiki/Copula_(probability_theory)#Most_impo
 It has a few special cases: 
 - When θ = 1, it is the IndependentCopula
 - When θ = ∞, is is the MCopula (Upper Frechet-Hoeffding bound)
+
+References:
+* [nelsen2006](@cite) Nelsen, Roger B. An introduction to copulas. Springer, 2006.
 """
 struct GumbelGenerator{T} <: UnivariateGenerator
     θ::T

src/Generator/UnivariateGenerator/InvGaussianGenerator.jl

@@ -21,6 +21,9 @@ More details about Inverse Gaussian Archimedean copula are found in :
 
 It has a few special cases:
 - When θ = 0, it is the IndependentCopula
+
+References:
+* [nelsen2006](@cite) Nelsen, Roger B. An introduction to copulas. Springer, 2006.
 """
 struct InvGaussianGenerator{T} <: UnivariateGenerator
     θ::T

src/Generator/UnivariateGenerator/JoeGenerator.jl

@@ -18,6 +18,9 @@ The [Joe](https://en.wikipedia.org/wiki/Copula_(probability_theory)#Most_importa
 It has a few special cases: 
 - When θ = 1, it is the IndependentCopula
 - When θ = ∞, is is the MCopula (Upper Frechet-Hoeffding bound)
+
+References:
+* [nelsen2006](@cite) Nelsen, Roger B. An introduction to copulas. Springer, 2006.
 """
 struct JoeGenerator{T} <: UnivariateGenerator
     θ::T

src/Generator/ZeroVariateGenerator/IndependentGenerator.jl

@@ -18,6 +18,9 @@ It happends to be an Archimedean Copula, with generator :
 ```math
 \\phi(t) = \\exp{-t}
 ```
+
+References:
+* [nelsen2006](@cite) Nelsen, Roger B. An introduction to copulas. Springer, 2006.
 """
 struct IndependentGenerator <: ZeroVariateGenerator end
 max_monotony(::IndependentGenerator) = Inf

src/Generator/ZeroVariateGenerator/MGenerator.jl

@@ -15,6 +15,9 @@ W(\\mathbf{u}) \\le C(\\mathbf{u}) \\le M(\\mathbf{u})
 ```
 
 The two Frechet-Hoeffding bounds are also Archimedean copulas.
+
+References:
+* [nelsen2006](@cite) Nelsen, Roger B. An introduction to copulas. Springer, 2006.
 """
 struct MGenerator <: ZeroVariateGenerator end
 max_monotony(::MGenerator) = Inf

src/Generator/ZeroVariateGenerator/WGenerator.jl

@@ -13,6 +13,9 @@ W(\\mathbf{u}) \\le C(\\mathbf{u}) \\le M(\\mathbf{u})
 ```
 
 The two Frechet-Hoeffding bounds are also Archimedean copulas.
+
+References:
+* [nelsen2006](@cite) Nelsen, Roger B. An introduction to copulas. Springer, 2006.
 """
 struct WGenerator <: ZeroVariateGenerator end
 max_monotony(G::WGenerator) = 2

src/MiscellaneousCopulas/EmpiricalCopula.jl

@@ -15,6 +15,9 @@ C(\\mathbf x) = \\frac{1}{N}\\sum_{i=1}^n \\mathbf 1_{\\mathbf u_i \\le \\mathbf
 ```
 
 This function is very practical, be be aware that this is not a true copula (since ``\\mathbf u`` are only pseudo-observations). The constructor allows you to pass dirctly pseudo-observations (the default) or will compute them for you. You can then compute the `cdf` of the copula, and sample it through the standard interface.
+
+References:
+* [nelsen2006](@cite) Nelsen, Roger B. An introduction to copulas. Springer, 2006.
 """
 struct EmpiricalCopula{d,MT} <: Copula{d}
     u::MT

src/MiscellaneousCopulas/FGMCopula.jl

@@ -26,6 +26,9 @@ We use the stochastic representation of the copula to obtain random samples.
 
 It has a few special cases:
 - When d=2 and θ = 0, it is the IndependentCopula.
+
+References:
+* [nelsen2006](@cite) Nelsen, Roger B. An introduction to copulas. Springer, 2006.
 """
 struct FGMCopula{d, Tθ} <: Copula{d}
     θ::Tθ

src/MiscellaneousCopulas/PlackettCopula.jl

@@ -22,18 +22,12 @@ C_{1}(u,v) = uv
 It has a few special cases: 
 - When θ = 0, is is the MCopula (Upper Frechet-Hoeffding bound)
 - When θ = 1, it is the IndependentCopula
-- When θ = ∞, is is the WCopula (Lower Frechet-Hoeffding bound)
+- When θ = ∞, is is the WCopula (Lower Frechet-Hoeffding bound) 
 
-More details about Plackett Copula are found in:
-
-    Joe, H. (2014). Dependence modeling with copulas. CRC press, Page.164
-
-Details about the algorithm to generate copula samples can be seen in the following references:
-    
-    Johnson, Mark E. Multivariate statistical simulation:
-    A guide to selecting and generating continuous multivariate distributions.
-    Vol. 192. John Wiley & Sons, 1987. Page 193.
-    Nelsen, Roger B. An introduction to copulas. Springer, 2006. Exercise 3.38.
+References:
+* [joe2014](@cite) Joe, H. (2014). Dependence modeling with copulas. CRC press, Page.164
+* [johnson1987multivariate](@cite) Johnson, Mark E. Multivariate statistical simulation: A guide to selecting and generating continuous multivariate distributions. Vol. 192. John Wiley & Sons, 1987. Page 193.
+* [nelsen2006](@cite) Nelsen, Roger B. An introduction to copulas. Springer, 2006. Exercise 3.38.
 """
 struct PlackettCopula{P} <: Copula{2} # since it is only bivariate.
     θ::P  # Copula parameter

src/MiscellaneousCopulas/SurvivalCopula.jl

@@ -11,7 +11,10 @@ Computes the survival version of any copula on given indices. From a copula ``C`
 S(u_1,...u_4) = C(u_1,1-u_2,1-u3,u_4)
 ```
 
-This constructor allows to derive new "survival" families. For exemple, in bivariate cases, this allows to do "rotations". The obtained models can be treated as the starting one, i.e. as a random vector in [0,1]^d with uniforms marginals. 
+This constructor allows to derive new "survival" families. For exemple, in bivariate cases, this allows to do "rotations". The obtained models can be treated as the starting one, i.e. as a random vector in [0,1]^d with uniforms marginals.
+
+References:
+* [nelsen2006](@cite) Nelsen, Roger B. An introduction to copulas. Springer, 2006.
 """
 struct SurvivalCopula{d,CT,VI} <: Copula{d}
     C::CT

src/SklarDist.jl

@@ -37,6 +37,7 @@ D̂ = fit(SklarDist{FrankCopula,Tuple{Gamma,Normal,LogNormal}}, simu)
 
 References: 
 * [sklar1959](@cite) Sklar, M. (1959). Fonctions de répartition à n dimensions et leurs marges. In Annales de l'ISUP (Vol. 8, No. 3, pp. 229-231).
+* [nelsen2006](@cite) Nelsen, Roger B. An introduction to copulas. Springer, 2006.
 """
 struct SklarDist{CT,TplMargins} <: Distributions.ContinuousMultivariateDistribution
     C::CT