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

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.

  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?