Skewness & Kurtosis
in [Matlab]
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From: apr on 23 Feb 2005 09:56 hi , can i plot charts in matlab by randomly generating some points with a specific Skewness and Kurtosis ? In "randn" function one can specify mean and variance ,is there a way you can specify skewness and kurtosis too ? thanks
From: Salomon on 23 Feb 2005 10:50 <http://www.mathworks.com/support/solutions/data/1-18CK0.html?solution=1-18CK0>
From: apr on 23 Feb 2005 13:16 Salomon wrote: > > > <http://www.mathworks.com/support/solutions/data/1-18CK0.html?solution=1-18CK0> > Thanks for your reply Salomon. So there is no way i can plot a chart in MATLAB with some specific values of Skewness & Kurtosis so it doesnot look like a normal distribution ?
From: StephenLL on 23 Feb 2005 13:27 apr wrote: > > > Salomon wrote: >> >> >> <http://www.mathworks.com/support/solutions/data/1-18CK0.html?solution=1-18CK0> >> > > Thanks for your reply Salomon. > So there is no way i can plot a chart in MATLAB with some specific > values of Skewness & Kurtosis so it doesnot look like a normal > distribution ? Since Skewness and Kurtosis is just a play on different Moments, use the method of moments to solve for parameters of the distributin so that they match your skewness and kurtosis. Obviously pick a distribution where the skewness and/or kurtosis is not fixed like the normal. Isn't skewness defined at E((x-mu)^3)/sigma^3 where mu is the mean and sigma is the standard deviation (unrelated to normal) and isn't the kurtosis E((x-mu)^4)/sigma^4. there are many different ways to do this. i suggest going back to your basic stats books for this. Once you find the distribution and parameters it is very easy in matlab to plot any information about that distribution.
From: "AJ "no z" johnson" on 24 Feb 2005 05:05
"apr" <aparna_raja(a)gse.harvard.edu> wrote in message news:eefcdaa.-1(a)webx.raydaftYaTP... > hi , > can i plot charts in matlab by randomly generating some points with a > specific Skewness and Kurtosis ? > In "randn" function one can specify mean and variance ,is there a way > you can specify skewness and kurtosis too ? > thanks The problem is, most distributions are defined by one or two parameters. Thus if you fix the first and second moments, you uniquely define the parameters, and so the skewness and kurtosis are inherently already defined as well. My thought is take a bimodal distributnion which is the sum of two normal distributions with different means, variances, and magnitudes. I think that by appropriately choosing these, you can get your desired properties. Maybe. Hope you are good at integrals! The problem might be easier if you are willing to use a finite sample space with discrete probabilities. (instead of a continuous distribution) I do recall these is some theorem that state that a distribution with a certain variance, there is an upper bound on the higher order moments, so you selection of skewness and kurtosis can't be completely arbitrary. Hope this helps, Aj |