A multivariate Student’s t-distribution is
derived by analogy to the derivation of a multivariate normal (Gaussian)
probability density function. This multivariate Student’s t-distribution can
have different shape parameters for the marginal probability density functions
of the multivariate distribution. Expressions for the probability density
function, for the variances, and for the covariances of the multivariate
t-distribution with arbitrary shape parameters for the marginals are given.
References
[1]
Kotz, S. and Nadarajah, S. (2004) Multivariate t-Distributions and Their Applications. Cambridge University Press, Cambridge.
[2]
Press, W.H., Teukolsky, S.A., Vetterling, W.T. and Flannery, B.P. (1992) Numerical Recipes in FORTRAN: The Art of Scientific Computing. 2nd Edition, Cambridge University Press, Cambridge, 89.
[3]
Cassidy, D.T. (2011) Describing n-Day Returns with Student’s t-Distributions. Physica A, 390, 2794-2802.
http://dx.doi.org/10.1016/j.physa.2011.03.019
[4]
Cassidy, D.T. (2012) Effective Truncation of a Student’s t-Distribution by Truncation of the Chi Distribution in a Mixing Integral. Open Journal of Statistics, 2, 519-525. http://dx.doi.org/10.4236/ojs.2012.25067
[5]
Cassidy, D.T. (2016) Student’s t Increments. Open Journal of Statistics, 6, 156-171.
http://dx.doi.org/10.4236/ojs.2016.61014
