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



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




  • 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
  • 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.


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

    click to open
    click to close
    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

      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.
    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



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