Jump to content

How to calculate the Moments of a new PDF


consuli

Recommended Posts

No, I dont. I am just an applied statistician, not a methematical statistician. Thus, the easierst (and maybe mathematical inelegant) solution is asked for. ;-)

The pdf has 4 parameters: construction offset, construction sd, kurtosis and skewness parameter.

Consuli

Edited by consuli
Link to comment
Share on other sites

By develop the pdf do you mean you have developed a closed form for it? If so, calculating the moment generating function would be the best (most precise) way. It's not too hard to calculate assuming the pdf isn't some beast of a function - it's an integral of the pdf exponentiated. Post it here, i'm sure a few people would have a go.

If you have an empirical distribution rather than the closed form there are estimators for skew/kurtosis - something like R should have a function, or at least a package, to do this.

If you have a closed form and really don't fancy the integral you could build an empirical distribution by taking samples from your distribution and then use an estimator for skew/kurtosis. Should converge to the true values for a sufficient number of samples, assuming the estimators aren't biased.

 

Link to comment
Share on other sites

I have heard, one could more easily calculate the 4 moments of a new distribution by solving the following integrals:

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.

Is that true?

Consuli

 

Edited by consuli
Link to comment
Share on other sites

You can find moment generating functions in just about any book on fundamental statistics, something like A First Course in Probability by Sheldon Ross. I'm not sure of a specific book with the specific equations you want. There are plenty of books on google you can check - they'de be under moment generating functions or MGFs section (or maybe under a thorough chapter on expectation).

Link to comment
Share on other sites

Because the direct google search for one or more of the formalas is not aim leading, as google - due to different typo of mathematical formulas - is currently not really able to handle them correctly ?

Consuli

Edited by consuli
Link to comment
Share on other sites

Create an account or sign in to comment

You need to be a member in order to leave a comment

Create an account

Sign up for a new account in our community. It's easy!

Register a new account

Sign in

Already have an account? Sign in here.

Sign In Now
×
×
  • Create New...

Important Information

We have placed cookies on your device to help make this website better. You can adjust your cookie settings, otherwise we'll assume you're okay to continue.