for the m and sd ... simple ... for skewness and kurtosis ... i am not sure ... of course, if you already have a distribution with the amount of skewness and kurtosis you want ... again, no problem
in minitab, changing a given distribution (any one) to one with different m and sd ... is easy
say we have the following data ... 1 to 10 ...
MTB > set c50
DATA> 1 2 3 4 5 6 7 8 9 10 <<<< just input the data ... you could make this ANY data set you want
DATA> end
MTB > name c50='X'
MTB > desc c50
Descriptive Statistics: X
Variable N Mean Median TrMean StDev SE Mean X 10 5.500 5.500 5.500 3.028 0.957
Variable Minimum Maximum Q1 Q3 X 1.000 10.000 2.750 8.250
m=5.5 and sd=3.028
say you want to have a set of data where m=32 and sd=4.6?
MTB > cent c50 c51 <<< convert to z scores
MTB > name c51='zX'
MTB > let c52=c51*4.6 + 32 <<< use linear transformation to new scale ... z * new sd + new m
MTB > name c52='newX'
MTB > prin c50-c52 <<< here are the data columns
Data Display
Row X zX newX
1 1 -1.48630 25.1630 2 2 -1.15601 26.6823 3 3 -0.82572 28.2017 4 4 -0.49543 29.7210 5 5 -0.16514 31.2403 6 6 0.16514 32.7597 7 7 0.49543 34.2790 8 8 0.82572 35.7983 9 9 1.15601 37.3177 10 10 1.48630 38.8370
MTB > desc c50-c52
Descriptive Statistics: X, zX, newX
Variable N Mean Median TrMean StDev SE Mean X 10 5.500 5.500 5.500 3.028 0.957 zX 10 0.000 0.000 0.000 1.000 0.316 newX 10 32.00 32.00 32.00 4.60 1.45
note newX has m=32 and sd=4.6
now, IF the original data had the desired skewness ... and kurtosis ... the newX set would too
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