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April 16th, 2018, 11:39 AM  #1 
Newbie Joined: Apr 2018 From: Germany Posts: 3 Thanks: 0  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 
April 16th, 2018, 02:25 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,641 Thanks: 625 
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.

April 17th, 2018, 02:15 AM  #3 
Newbie Joined: Apr 2018 From: Germany Posts: 3 Thanks: 0 
Thanks. Meanwhile I have found the following integrals to calculate the moments: E(x) = Integral f(x) * x dx Var(x) = Integral f(x) * (xE(x))^2 dx s= Var(x)^0.5 M3= Integral f(x) * ((xE(x))/s)^3 dx M4= Integral f(x) * ((xE(x))/s)^4 dx Where fx) refers to the pdf of the distribution. Are these equivalent to your formula? Consuli 
April 17th, 2018, 01:56 PM  #4  
Global Moderator Joined: May 2007 Posts: 6,641 Thanks: 625  Quote:
 
April 18th, 2018, 06:31 AM  #5 
Newbie Joined: Apr 2018 From: Germany Posts: 3 Thanks: 0 
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 
April 18th, 2018, 05:03 PM  #6 
Global Moderator Joined: May 2007 Posts: 6,641 Thanks: 625  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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