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# NTRANDJOHNSONSU

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

## Syntax

NTRANDJOHNSONSU(

• Size,
• Gamma,
• Delta,
• Lambda,
• Xi,
• Algorithm,
• Random seed1,
• Random seed2,
• Use invert func,
• Use antithetic,
• Use resampling

)

#### Parameters

• Size is # of random numbers (Positive integer).
• Gamma is a parameter of the distribution $\gamma$.
• Delta is a parameter of the distribution $\delta\;(>0)$.
• Lambda is a parameter of the distribution $\lambda\;(>0)$.
• Xi is a parameter of the distribution $\xi$.
• 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.

## Remarks

• The distribution has infinite support $(-\infty,+\infty)$.
• The distribution is leptokurtic.

## 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
Data Description
0.8 Value of parameter Gamma
2 Value of parameter Delta
2.5 Value of parameter Lambda
1.2 Value of parameter Xi
Formula Description (Result)
=NTRANDJOHNSONSU(100,A2,A3,A4,A5,0) 100 Johnson SU deviates based on Mersenne-Twister algorithm for which the parameters 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 A2:A101 starting with the formula cell. Press F2, and then press CTRL+SHIFT+ENTER.