Gradient and Hessian matrix of cumulative normal ditribution
- To: mathgroup at smc.vnet.net
- Subject: [mg67954] Gradient and Hessian matrix of cumulative normal ditribution
- From: "Pratim Vakish" <pratim_usc at hotmail.com>
- Date: Thu, 13 Jul 2006 06:55:40 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
Hello,
I am very new in Mathematica, and my question might be easy very easy.
My question is related to M Lejeune' question this June and to B. Hanlon and
R. Koopman's comments.
I am considering multivariate normal distributions.
I am interested in computing the gradient (vector of first-order partial
derivative) and Hessian matrix of the multivariate cumulative normal
distribution.
Could you indicate me how to proceed?
First, I would like to obtain the algebraic formulation of the gradient and
Hessian matrix (is thre a closed-form formulatyion for their components?),
and then, evaluate/compute the value of the gradient and Hessian at a given
point.
Taking the bivariate normal distribution and the examole discussed by M
Lejeune and B Hanlon,
r = {{1, 0.2}, {0.2, 1}};
ndist = MultinormalDistribution[{0, 0}, r])
cdf=CDF[ndist,{x1,x2}]
What is the gradient and Hessian matrix of cdf in algebraic formulation?
What is the values of the gradient and Hessian matrix of cdf at the point
x1=1, x2=0.8, for example?
Many thanks,
Pratim
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