.- help for skewed normal generator .-Skewed normal generator ------------------------

^sknor^ [obs] [seednum] [mean] [var] [sk] [ku]

Description -----------

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 differ > ence 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 -------

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 Di > stribution 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 pape > r. 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 oppos > ite values of the ones listed above)

Examples --------

. ^sknor^ . ^sknor 10000^ . ^sknor 10000 123^ . ^sknor 10000 123 0.5 2 2 9^ . ^sknor 5000 123 5 1 -0.5 3^

Keywords -------- normal, distribution, skewness (skew, skewed), kurtosis

Author -------

Evangelos Kontopantelis National Primary Care Reserch and Development Centre University of Manchester M13 9PL e.kontopantelis@manchester.ac.uk

Also see -------- Ramberg et al paper: http://www.jstor.org/view/00401706/ap040083/04a00080/0 STB: STB-41 sg44.1, STB-28 sg44