# QuantLib_OneFactorStudentGaussianCopula man page

OneFactorStudentGaussianCopula — One-factor Student t — Gaussian Copula.

## Synopsis

`#include <ql/experimental/credit/onefactorstudentcopula.hpp>`

Inherits **OneFactorCopula**.

### Public Member Functions

**OneFactorStudentGaussianCopula** (const **Handle**< **Quote** > &**correlation**, int nm, **Real** maximum=10, **Size** integrationSteps=200)**Real density** (**Real** m) const

Density function of M. **Real cumulativeZ** (**Real** z) const

Cumulative distribution of Z.

### Additional Inherited Members

## Detailed Description

One-factor Student t - Gaussian Copula.

The copula model [ Y_i = a_iM+sqrt{1-a_i^2}Z_i ] is specified here by setting the probability density functions for $ Z_i $ ( $ D_Z $) to a Gaussian and for $ M $ ( $ D_M $) to a Student t-distribution with $ N_m $ degrees of freedom.

The variance of the Student t-distribution with $ 0 $ degrees of freedom is $ 0 / (0 - 2) $. Since the copula approach requires zero mean and unit variance distributions, $ M $ is scaled by $ sqrt{(N_m - 2) / N_m}. $

## Member Function Documentation

### Real density (Real m) const [virtual]

Density function of M. Derived classes must override this method and ensure zero mean and unit variance.

Implements **OneFactorCopula**.

### Real cumulativeZ (Real z) const [virtual]

Cumulative distribution of Z. Derived classes must override this method and ensure zero mean and unit variance.

Implements **OneFactorCopula**.

## Author

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## Referenced By

The man page OneFactorStudentGaussianCopula(3) is an alias of QuantLib_OneFactorStudentGaussianCopula(3).