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fix typo in docstring #101

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Dec 14, 2023
Merged

fix typo in docstring #101

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6 changes: 3 additions & 3 deletions src/EllipticalCopulas/GaussianCopula.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -9,12 +9,12 @@ Constructor
GaussianCopula(Σ)

The [Gaussian Copula](https://en.wikipedia.org/wiki/Copula_(probability_theory)#Gaussian_copula) is the
copula of a [Multivariate normal distribution](http://en.wikipedia.org/wiki/Multivariate_normal_distribution). It is constructed as :
copula of a [Multivariate normal distribution](http://en.wikipedia.org/wiki/Multivariate_normal_distribution). It is constructed as:

```math
C(\\mathbf{x}; \\boldsymbol{\\Sigma}) = F_{\\Sigma}(F_{\\Sigma,i}^{-1}(x_i),i\\in 1,...d)
```
where ``F_{\\Sigma}`` is a cdf of a gaussina random vector and `F_{\\Sigma,i}` is the ith marignal cdf, while ```\\Sigma`` is the covariance matrix.
where ``F_{\\Sigma}`` is a cdf of a gaussian random vector and `F_{\\Sigma,i}` is the ith marginal cdf, while ``\\Sigma`` is the covariance matrix.

It can be constructed in Julia via:
```julia
Expand Down Expand Up @@ -59,4 +59,4 @@ function _cdf(C::CT,u) where {CT<:GaussianCopula}
μ = zeros(T,d)
lb = repeat([T(-Inf)],d)
return MvNormalCDF.mvnormcdf(μ, C.Σ, lb, x)[1]
end
end