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help for skewed normal generator
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Skewed normal generator
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^sknor^ [obs] [seednum] [mean] [var] [sk] [ku]
Description
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The program generates random numbers from a skewed normal distribution (right-
skew being the default).
[obs]: number of observations to be generated (optional; set to current
dataset size if omitted)
[seednum]: seed number to be used for drawing 'random' numbers - makes a difference if your simulations occur
on the same second (i.e. running a batch of simulations)
[mean]: mean of the simulated distribution (optional; set to 0 if omitted)
[var]: variance (optional; set to 1 if omitted)
[sk]: skewness (optional; set to 0 if omitted)
[ku]: kurtosis (optional; set to 3 if omitted)
Remarks
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For sk=0 and ku=3 (the default values) the generated distribution is normal.
The program is based on a method described in "Ramberg et al, A probability Distribution
and its uses in fitting data, Technometrics, 1979".
The method uses a formula with 4 parameters and parameter values which generate
data of various degrees of skewness and kurtosis have been provided in the paper.
Only a few of those have been included in this program the command, but it can
easily be updated with more.
The included pairs of values are (sk,ku): (0,1.75), (0,3), (0,3.2), (0,3.3), (0,3.4),
(0,3.6), (0,4), (0,4.4), (0,5), (0,6), (0,7), (0,8), (0,9), (0.5,3), (0.5,4), (0.5,5),
(0.5,6), (0.5,7), (0.5,8), (0.5,9), (1,4), (1,5), (1,6), (1,7), (1,8), (1,9), (1,10),
(1.5,6), (1.5,7), (1.5,8), (1.5,9), (1.5,10), (1.5,11), (1.5,12), (2,9), (2,10), (2,11),
(2,12), (2,13), (2,14), (2,15),
For sk=2 and ku=9 the most extreme distribution is generated.
Negative skewness values can be inputted for left-skew distributions (the opposite values
of the ones listed above)
Examples
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. ^sknor^
. ^sknor 10000^
. ^sknor 10000 123^
. ^sknor 10000 123 0.5 2 2 9^
. ^sknor 5000 123 5 1 -0.5 3^
Keywords
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normal, distribution, skewness (skew, skewed), kurtosis
Author
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Evangelos Kontopantelis
National Primary Care Reserch and Development Centre
University of Manchester
M13 9PL
e.kontopantelis@manchester.ac.uk
Also see
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Ramberg et al paper: http://www.jstor.org/view/00401706/ap040083/04a00080/0
STB: STB-41 sg44.1, STB-28 sg44