pythonstatistics

Sample from a multivariate t distribution python


I am wondering if there is a function for sampling from a multivariate student t-distribution in Python. I have the mean vector with 14 elements, the 14x14 covariance matrix and the degrees of freedom and I want to sample a vector from this t-distribution. For the one dimensional case I used stats.t.rvs(df,loc,scale) and I was wondering if there is something similar for the multivariate case. Any help would be very much appreciated.

Thanks


Solution

  • You can find this function into sandbox directory of statsmodels GitHub repo. Link to the function: https://github.com/statsmodels/statsmodels/blob/master/statsmodels/sandbox/distributions/multivariate.py#L90

    Source code of the function:

    #written by Enzo Michelangeli, style changes by josef-pktd
    # Student's T random variable
    def multivariate_t_rvs(m, S, df=np.inf, n=1):
        '''generate random variables of multivariate t distribution
        Parameters
        ----------
        m : array_like
            mean of random variable, length determines dimension of random variable
        S : array_like
            square array of covariance  matrix
        df : int or float
            degrees of freedom
        n : int
            number of observations, return random array will be (n, len(m))
        Returns
        -------
        rvs : ndarray, (n, len(m))
            each row is an independent draw of a multivariate t distributed
            random variable
        '''
        m = np.asarray(m)
        d = len(m)
        if df == np.inf:
            x = np.ones(n)
        else:
            x = np.random.chisquare(df, n) / df
        z = np.random.multivariate_normal(np.zeros(d), S, (n,))
        return m + z/np.sqrt(x)[:,None]   # same output format as random.multivariate_normal