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# NTRANDMULTINORM

Returns multivariate normal pseudo random number(s) based on Mersenne Twister Algorithm which has long period (219937-1), high order of equidistribution (623 dimensions).

## Syntax

NTRANDMULTINORM(

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

)

#### Parameters

• Size is # of random numbers (Positive integer).
• Cov is a covariance matrix.
• Mean is a vector of the arithmetic means of each variable.
• Algorithm is a integer value that determines a method to generate uniform random number.
• 0: Mersenne Twister(2002)
• 1: Mersenne Twister(1998)
• 2: Numerical Recipes
ran2()
• Random seed1 is 1st. random seed.
• Random seed2 is 2nd. random seed.
• Use invert func 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 antithetic 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 resampling 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.

## Example

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

How to copy an example

1. Create a blank workbook or worksheet.
2. Select the example in the Help topic.

Note  Do not select the row or column headers.

Selecting an example from Help

3. Press CTRL+C.
4. In the worksheet, select cell A1, and press CTRL+V.
5. 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.

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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.

• See tutorial video