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#1 2007-08-07 06:56:32

jimc52
Member
Registered: 2007-08-07
Posts: 2

Kurtosis - Stat Calulation, Need HELP Please :)

Ok, hope people have PATIENCE with me here...I am doing some stat calculations, but I am NOT a statistician, so please bear with me. Please don't expect me to know exactly what I am doing, I'm not a mathematician either. I need to calculate the kertosis. I have been all over the internet and found many examples of the FORMULA only. I have not found one example, that leads me thru the cryptic formula calculation. I have tried plugging in what I THINK are the right numbers, but I cannot seem to get the right answer. So I am lost here and just need one example to help me figure things out.

Essentially, the formula for kurtosis is:

This is the formula using BASIC language, the carat "^" means to raise to the power in computer jargon:

             kurtosis=(sum(x-m)^4/Sigma^4)/n - using the population statistic N

This is the same forumla from a different site and is a little bit more crytic to me, but essentially is the same as above:

             kurtosis = ∑(xn - MeanX)4 / (StdX[N-1]4 * (N-1)) - using the sample statisic N

I understand n is the population total and not a sample total, and I have found some forms of the equation as using n-1, sample statistic.

I have used Excel statistical functions to solve the problem for me and I am writing a little BASIC program to help me in some other software outside Excel. Therefore, just relying on Excel is not what I am trying to do to get answers. I need to write the kertosis equation into a BASIC program.

Here is my problem:

N=5

Input numbers:

6
7
8
9
10

Mean = 8
Sum = 40
Stdev = 1.581139 (sample stdev)
Stdev = 1.414214 (population stdev)
Kurtosis = -1.2

Given these parameters, can someone please just PLUG the right values into the above equation (show me please!) and get a kurtosis of -1.2?

I think I am just having a little bit of difficulty understand exactly what gets plugged in where. Please just use my example here with these values and show me what to plug in using the kurtosis equation above.

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#2 2007-08-07 15:02:41

George,Y
Member
Registered: 2006-03-12
Posts: 1,379

Re: Kurtosis - Stat Calulation, Need HELP Please :)

Kurtosis = -1.2

Wrong-a kurtosis cannot be negative


X'(y-Xβ)=0

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#3 2007-08-08 04:05:12

jimc52
Member
Registered: 2007-08-07
Posts: 2

Re: Kurtosis - Stat Calulation, Need HELP Please :)

Ok, but this is what Excel generated.  I guess you are telling me that Excel is incorrectly calculating the Kurtosis value.
It would be helpful to me, if you would use my example above, and show me how to calculate the correct Kurtosis value.

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#4 2007-08-08 23:27:15

George,Y
Member
Registered: 2006-03-12
Posts: 1,379

Re: Kurtosis - Stat Calulation, Need HELP Please :)

Guess you have some error in using Excel.

It's simpler than you thought:

kurtosis = ∑(xn - MeanX)[sup]4[/sup] / (StdX[N-1][sup]4[/sup]* (N-1))

∑(xn - MeanX)[sup]4[/sup] =16+1+0+1+16=34
Var[5-1]= (4+1+0+1+4)/4=10/4 (=1.581139[sup]2[/sup])
Stdev[5-1][sup]4[/sup](5-1)= (10/4)[sup]2[/sup]*4=10*10/4=25

So Kurtosis=34/25=1.36

Last edited by George,Y (2007-08-08 23:30:21)


X'(y-Xβ)=0

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