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 April 16th, 2018, 10:39 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, 01:25 PM #2 Global Moderator   Joined: May 2007 Posts: 6,704 Thanks: 669 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, 01:15 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) * (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 April 17th, 2018, 12:56 PM   #4
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 Originally Posted by consuli 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. April 18th, 2018, 05:31 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, 04:03 PM   #6
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 Originally Posted by consuli 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. $m_n=\int_{-\infty}^{\infty}x^ndF(x)$. Tags calculate, moments, pdf Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post Tangeton Applied Math 3 May 14th, 2016 02:38 PM karoon Economics 0 January 8th, 2013 01:30 AM karoon Linear Algebra 0 January 8th, 2013 01:09 AM jackmorgan3 Advanced Statistics 1 August 11th, 2012 07:28 PM thapchi Advanced Statistics 0 March 19th, 2010 09:39 PM

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