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-   -   How to calculate the moments of a new pdf? (http://mymathforum.com/advanced-statistics/344034-how-calculate-moments-new-pdf.html)

 consuli April 16th, 2018 10:39 AM

How to calculate the moments of a new pdf?

Hello!

I have developed the PDF (probability density function) of a new distribution.

I want to calculate their moments (mean, sd, skewness, kurtosis).

How can I do this?

Consuli

 mathman April 16th, 2018 01:25 PM

There are standard formulas for the moments: $m_n=\int_{-\infty}^{\infty} x^n f(x)dx$, where f(x) is the probability density function.

 consuli April 17th, 2018 01:15 AM

Thanks.

Meanwhile I have found the following integrals to calculate the moments:

E(x) = Integral f(x) * x dx

Var(x) = Integral f(x) * (x-E(x))^2 dx

s= Var(x)^0.5

M3= Integral f(x) * ((x-E(x))/s)^3 dx

M4= Integral f(x) * ((x-E(x))/s)^4 dx

Where fx) refers to the pdf of the distribution.

Are these equivalent to your formula?

Consuli

 mathman April 17th, 2018 12:56 PM

Quote:
 Originally Posted by consuli (Post 592621) Thanks. Meanwhile I have found the following integrals to calculate the moments: E(x) = Integral f(x) * x dx Var(x) = Integral f(x) * (x-E(x))^2 dx s= Var(x)^0.5 M3= Integral f(x) * ((x-E(x))/s)^3 dx M4= Integral f(x) * ((x-E(x))/s)^4 dx Where fx) refers to the pdf of the distribution. Are these equivalent to your formula? Consuli
These are similar. Your formulas for M3 and M4 are centralized and normalized to correspond to a scale change to zero mean and unit deviation.

 consuli April 18th, 2018 05:31 AM

To get this on to point.

My formulas would work out for any distribution, but yours only for standardized distribution, like the standard normal distribution?

Sorry for the little inconvenience, but I need to know in detail, simply.

Consuli

 mathman April 18th, 2018 04:03 PM

Quote:
 Originally Posted by consuli (Post 592720) To get this on to point. My formulas would work out for any distribution, but yours only for standardized distribution, like the standard normal distribution? Sorry for the little inconvenience, but I need to know in detail, simply. Consuli
My formula is for any distribution defined by a density function f(x). If there is no density function and you have only a distribution function F(x) then you must use a Stieltjes integral. $m_n=\int_{-\infty}^{\infty}x^ndF(x)$.

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