# NTRANDMULTINORM

Returns multivariate normal pseudo random number(s) based on Mersenne Twister Algorithm which has long period (2^{19937}-1), high order of equidistribution (623 dimensions).

## Syntax

**NTRANDMULTINORM**(

*Size,**Cov,**Mean,**Algorithm,**Random seed1,**Random seed2,**Use invert func,**Use antithetic,**Use resampling*

)

#### Parameters

is # of random numbers (Positive integer).**Size**is a covariance matrix.**Cov**is a vector of the arithmetic means of each variable.**Mean**is a integer value that determines a method to generate uniform random number.**Algorithm**- 0: Mersenne Twister(2002)
- 1: Mersenne Twister(1998)
- 2: Numerical Recipes

ran2()

is 1st. random seed.**Random seed1**is 2nd. random seed.**Random seed2**is a logical value that determines a method to generate normal random number. If Use invert func is TRUE, inverse function method is used; if FALSE, box-Muller method is used.**Use invert func**is a logical value that determines antithetic variant method is used or not. If Use antithetic is TRUE, antithetic variant method is used; if FALSE, antithetic variant method is not used.**Use antithetic**is a logical value that determines quadratic resampling method is used or not. If Use resampling is TRUE, quadratic resampling method is used; if FALSE, quadratic resampling method is not used.**Use resampling**

## Example

- The example may be easier to understand if you copy it to a blank worksheet

How to copy an example

- Create a blank workbook or worksheet.
- Select the example in the Help topic.
**Note**Do not select the row or column headers.Selecting an example from Help

- Press CTRL+C.
- In the worksheet, select cell A1, and press CTRL+V.
- To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the
**Tools**menu, point to**Formula Auditing**, and then click**Formula Auditing Mode**.

1 2 3 4 5 6 7 8

A B C D Data Data Data Description 1.44 0.48 -0.36 cov. matrix 0.48 0.64 0 cov. matrix -0.36 0 0.25 cov. matrix Data Data Data Description 1 2 3 mean vector Formula Description (Result) =NTRANDMULTINORM(100,A2:C4,A6:C6) 100 normal deviates (x 3 variables) for the terms above Note The formula in the example must be entered as an array formula. After copying the example to a blank worksheet, select the range A8:C107 starting with the formula cell. Press F2, and then press CTRL+SHIFT+ENTER.

- Download sample excel sheet
- See tutorial video

## See also

- Normal distribution (Multi variables)
- Choice of the random number generator algorithm
- Why I always see the same result even if I input formula into multiple cell?