# Multivariate Normal Distribution

```@article{Tong1989MultivariateND,
title={Multivariate Normal Distribution},
author={Yung Liang Tong},
journal={The SAGE Encyclopedia of Research Design},
year={1989}
}```
• Y. Tong
• Published 18 December 1989
• Mathematics
• The SAGE Encyclopedia of Research Design
In this chapter we generalize the normal distribution to the multivariate case. The multivariate normal or Gaussian distribution is one of the most important multivariate distributions encountered in applied probability. One of the reasons is that this distribution is fundamental in the definition of a normal or Gaussian random process. A random process is a time — varying random variable; i.e., a random waveform. The Gaussian random process arises in a multitude of applications, both because…

### Evaluating the cdf of the Skew Normal distribution

• Mathematics
• 2020
In this paper, we consider various methods for evaluating the cdf of the Skew Normal distribution. This distribution arises in the stochastic frontier model because it is the distribution of the

### EVALUATION OF MULTIVARIATE NORMAL PROBABILITY INTEGRALS USING A LOW VARIANCE SIMULATOR

This paper describes a low variance simulator of the normal distribution function. The probability integral is evaluated exactly at an initial point specified with a factor analytic covariance

### A note on finding peakedness in bivariate normal distribution using Mathematica

• Mathematics
• 2007
Peakedness measures the concentration around the central value. A classical standard measure of peakedness is kurtosis which is the degree of peakedness of a probability distribution. In view of

### Transforming Gaussian correlations. Applications to generating long-range power-law correlated time series with arbitrary distribution.

• Computer Science
Chaos
• 2020
This work studies analytically and numerically how the Pearson's correlation of two Gaussian variables changes when the variables are transformed to follow a different destination distribution, and proposes how to generalize standard algorithms producing a Gaussian power-law correlated time series in order to create a synthetic time series with an arbitrary distribution and controlled power- law correlations.

### Convergence of series of moments on general exponential inequality

• Mathematics
Statistics
• 2022
For an array of random variables and a sequence of positive numbers, sufficient conditions are given under which, for all , where denotes the positive part of x and , . Our statements are announced

### APPROXIMATING THE MEAN SQUARED PREDICTION ERROR IN LINEAR MODELS UNDER THE FAMILY OF EXPONENTIAL CORRELATIONS

We investigate approximations for the mean squared prediction error in a linear regression model with correlated errors. The correlation structure is assumed to be the family of exponential

### Sequential estimation via replicated piecewise stopping number in a tow—parameter exponential family of distributions

• Mathematics
• 1994
In a certain class of two—parameter exponential distributions, we consider minimum risk point estimation problems for one of the parameters. We propose to implement the sequential procedure of Bose

### The effect of discretization on the mean geometry of a 2D random field

• Mathematics
Annales Henri Lebesgue
• 2021
The study of the geometry of excursion sets of 2D random fields is a question of interest from both the theoretical and the applied viewpoints. In this paper we are interested in the relationship

### Modeling maxima of longitudinal contralateral observations

Abstract The paper gives the joint distribution of maxima of contralateral observations taken from the same individual at several occasions, when the data are normal with given constraints on the

## References

SHOWING 1-6 OF 6 REFERENCES

### Measures of multivariate skewness and kurtosis with applications

SUMMARY Measures of multivariate skewness and kurtosis are developed by extending certain studies on robustness of the t statistic. These measures are shown to possess desirable properties. The

### Simultaneous Confidence Regions for the Frequency Analysis of Multiple Time Series

• Mathematics
• 1987
Abstract In the frequency analysis of several time series observed simultaneously, it is often necessary to adapt classical results of linear models and multiple regression to situations involving

### Stochastic simulation of daily precipitation, temperature, and solar radiation

Long samples of weather data are frequently needed to evaluate the long-term effects of proposed hydrologic changes. The evaluations are often undertaken using deterministic mathematical models that

### Mathematical assessment of synthetic hydrology

To generate multivariate synthetic sequences that will resemble multivariate historic sequences in terms of means, standard deviations, skewnesses, lag-one serial correlation, and lag-zero