Multivariate-student-t
This repository contain functions based on Matlab to compute the Multivariate t distribution and conditional density and parameters.
MVT.m can only compute the Bivariate t distribution density for now
MVT_Con.m computes the Conditional distribution parameters X2|X1 based on Peng Ding(2016)[1] theory work on conditional distribution of multivariate t
MVTrand.m generates the p-dimensional random numbers which are multivariate t distributed
MLE_con_t.m estimates the Conditional X2|X1 parameters via Maximum likelihood Estimator and titer.m attributed to Prof. Paolella（Please use the mle method, as the titer.m is not included）
MVTpara.m returns the approximate parameters from a n-by-p sample assuming to be a p dimentional multivariate t distribution, by method Batch Approximation Algorithm attributed to Aeschliman, Park & Kak(2010)[2]
S_weighted_t.m returns non-zero weighted sum of the univariate margins distribution from a p dimensional multivariate t distribution via characteristic function
本程辑包中包含了计算多元T分布的概率密度和条件概率密度的各程序
MVT.m 目前仅能计算二元T分布的概率密度
MVT_Con.m 计算二元T分布的条件分布X2|X1的参数和概率密度 Peng Ding(2016)[1]
MVTrand.m 可生成p维的多元T分布随机数
MLE_con_t.m 使用最大似然估计估计X2｜X1的条件分布参数（注：titer.m 并未包含其中，请勿使用titer.m 函数）
MVTpara.m 使用Batch Approximation算法估计p维多元T分布的参数（Aeschliman, Park & Kak，2010)[2]
S_weighted_t.m 利用特征函数计算多元T分布的加权和的分布参数和概率密度
References
[1] Peng Ding. “On the Conditional Distribution of the Multivariate t Distribution”. In: The American Statistician 70.3 (July 2, 2016), pp. 293–295. issn: 0003-1305, 1537-2731. doi: 10.1080/00031305.2016.1164756. url: https://www.tandfonline.com/doi/full/ 10.1080/00031305.2016.1164756 (visited on 11/22/2021).
[2] David Hutchison et al. “A Novel Parameter Estimation Algorithm for the Multivariate t-Distribution and Its Application to Computer Vision”. In: Computer Vision – ECCV 2010. Ed. by Kostas Daniilidis, Petros Maragos, and Nikos Paragios. Vol. 6312. Series Title: Lecture Notes in Computer Science. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010, pp. 594–607. isbn: 978-3-642-15551-2 978-3-642-15552-9. doi: 10.1007/978-3-642- 15552-9_43. url: http://link.springer.com/10.1007/978-3-642-15552-9_43 (visited on 11/22/2021).