How does matlab compute the contours of gaussian, student's t or clayton copulas?

I am trying to understand how Matlab computes the contours for Bivariate gaussian distributions, Student's t, or for example for a Clayton copula. I mean I am looking for the contour equations, I am wondering if there is an explicit contour equation. I know that there are functions to compute the contours and plot them, but I would like to know how they work to get the data and plot them in 2-D.

For example, what is the analytical expression for the Clayton copula contours?

Many thanks,

Answer 1

[Gautam]

Hi Juan,

MATLAB computes the contours of a probability distribution like a bivariate gaussian distribution by evaluating the probability density function to constant probability values.

For example, for a bivariate gaussian distribution, the equation of a contour is obtained by setting the exponent of the Gaussian function to a constant value. This gives the equation for the contour:

You can refer to the following MathWorks document to know more about evaluating the probability density function of a bivariate gaussian distribution

https://www.mathworks.com/help/stats/multivariate-normal-distribution.html