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Consider a data set X = (X1, X2, . . . , XI) having mean value μ and standard deviation σ.
The one element data set (μ) has the same mean value as the big data set X.
The two element data set (μ-σ, μ+σ) has the same mean value and the same standard deviation as the big data set X.
I want to generalize this.
What is the three-element data set (A, B, C) having the same mean value and the same standard deviation and the same skewness as X?
What is the four-element data set (A, B, C, D) having the same mean value and the same standard deviation and the same skewness and the same kurtosis as X?
and so on.
Bo Jacoby ( talk) 22:05, 15 June 2015 (UTC).
where
are the moments that are known. So, you can directly write down the logarithm of the polynomial using the known moments, exponentiation is easy using most computer algebra systems (I'm sure Bo can write a compact J program for this :) ) and then the can be extracted from the zeros (and I think there is a simple J routine for that too.) So, I wouldn't be surprised if Bo can come up with a one line J program that will do the job. Count Iblis ( talk) 15:17, 16 June 2015 (UTC)
This is a one line J program implementing RDBury's method for two elements. (Oops: the double apostrophes around p q are changed to italics by the WP editor!)
simplify=. 3 : '|.>{:p.(-:q-*:p),p,_1[''p q''=.2*}.(%{.)+/y^/i.3' simplify 1 2 2 2 3 1.36754 2.63246 simplify simplify 1 2 2 2 3 1.36754 2.63246
Bo Jacoby ( talk) 10:38, 17 June 2015 (UTC).
This 6-liner implements RDBury's method for computing three elements and four elements etc. As predicted the roots are sometimes complex.
simplify=. 4 : 0 y=.x*}.(%{.)+/y^/i.>:x x=.1 for.y do.x=.((-/x*(#x){.y)%#x),x end. -|.>{:p.x )
Examples:
1 simplify 1 2 2 2 3 2 2 simplify 1 2 2 2 3 1.36754 2.63246 3 simplify 1 2 2 2 3 1.2254 2 2.7746 4 simplify 1 2 2 2 3 1.05666 2j0.29983 2j_0.29983 2.94334 5 simplify 1 2 2 2 3 1 2 2 2 3 10 simplify 1 2 2 2 3 1 1 2 2 2 2 2 2 3 3
Thank you everybody. The problem is solved. -- Bo Jacoby ( talk) 20:37, 18 June 2015 (UTC).
Mathematics desk | ||
---|---|---|
< June 14 | << May | June | Jul >> | June 16 > |
Welcome to the Wikipedia Mathematics Reference Desk Archives |
---|
The page you are currently viewing is a transcluded archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages. |
Consider a data set X = (X1, X2, . . . , XI) having mean value μ and standard deviation σ.
The one element data set (μ) has the same mean value as the big data set X.
The two element data set (μ-σ, μ+σ) has the same mean value and the same standard deviation as the big data set X.
I want to generalize this.
What is the three-element data set (A, B, C) having the same mean value and the same standard deviation and the same skewness as X?
What is the four-element data set (A, B, C, D) having the same mean value and the same standard deviation and the same skewness and the same kurtosis as X?
and so on.
Bo Jacoby ( talk) 22:05, 15 June 2015 (UTC).
where
are the moments that are known. So, you can directly write down the logarithm of the polynomial using the known moments, exponentiation is easy using most computer algebra systems (I'm sure Bo can write a compact J program for this :) ) and then the can be extracted from the zeros (and I think there is a simple J routine for that too.) So, I wouldn't be surprised if Bo can come up with a one line J program that will do the job. Count Iblis ( talk) 15:17, 16 June 2015 (UTC)
This is a one line J program implementing RDBury's method for two elements. (Oops: the double apostrophes around p q are changed to italics by the WP editor!)
simplify=. 3 : '|.>{:p.(-:q-*:p),p,_1[''p q''=.2*}.(%{.)+/y^/i.3' simplify 1 2 2 2 3 1.36754 2.63246 simplify simplify 1 2 2 2 3 1.36754 2.63246
Bo Jacoby ( talk) 10:38, 17 June 2015 (UTC).
This 6-liner implements RDBury's method for computing three elements and four elements etc. As predicted the roots are sometimes complex.
simplify=. 4 : 0 y=.x*}.(%{.)+/y^/i.>:x x=.1 for.y do.x=.((-/x*(#x){.y)%#x),x end. -|.>{:p.x )
Examples:
1 simplify 1 2 2 2 3 2 2 simplify 1 2 2 2 3 1.36754 2.63246 3 simplify 1 2 2 2 3 1.2254 2 2.7746 4 simplify 1 2 2 2 3 1.05666 2j0.29983 2j_0.29983 2.94334 5 simplify 1 2 2 2 3 1 2 2 2 3 10 simplify 1 2 2 2 3 1 1 2 2 2 2 2 2 3 3
Thank you everybody. The problem is solved. -- Bo Jacoby ( talk) 20:37, 18 June 2015 (UTC).