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# NTRANDGUMBEL

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

## Syntax

NTRANDGUMBEL(

• Size,
• Alpha,
• Beta,
• Algorithm,
• Random seed1,
• Random seed2

)

#### Parameters

• Size is # of random numbers (Positive integer).
• Alpha is a parameter of the distribution $\alpha$.
• Beta is a parameter of the distribution $\beta\;(>0)$.
• 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.

## Remarks

• The distribution has infinite support $(-\infty,+\infty)$
• The distribution has constant skewness 1.3139547….
• The distribution is leptokurtic (kurtosis is 2.4).

## 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
-3.5 Value of parameter Alpha
23 Value of parameter Beta
Formula Description (Result)
=NTRANDGUMBEL(100,A2,A3,0) 100 beta 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 A5:A104 starting with the formula cell. Press F2, and then press CTRL+SHIFT+ENTER.