Sampling the Multivariate Standard Normal Distribution under a Weighted Sum Constraint

Screening for a Multivariate Mixture Normal Distribution

Estimating Sum by Weighted Sampling

We study the classic problem of estimating the sum of n variables. The traditional uniform sampling approach requires a linear number of samples to provide any non-trivial guarantees on the estimated sum. In this paper we consider various sampling methods besides uniform sampling, in particular sampling a variable with probability proportional to its value, referred to as linear weighted sampli...

Values for the Cumulative Distribution Function of the Standard Multivariate Normal Distribution

This paper provides cumulative distribution function values for the standard multivariate normal distribution. The values are derived from a simulation model for the multivariate normal distribution, which can be run on any standard personal computer. Utilizing user-input distribution parameters, the model simulates the actual standard multivariate normal distribution. Since approximations of t...

screening for a multivariate mixture normal distribution

Sampling According to the Multivariate Normal Density

This paper 1 deals with the normal density of n dependent random variables. This is a function of the form : ce ?x T Ax where A is an n n positive deenite matrix, x is the n?vector of the random variables and c is a suitable constant. The rst problem we consider is the (approximate) evaluation of the integral of this function over the positive orthant Z 1 x1=0 Z 1 x2=0 ... Z 1 xn=0 ce ?x T Ax :...