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Generalized Error Distribution Ged

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Skewed Generalized Error Distribution

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Sged Distribution

Error Distribution? Generalized error distributions (sometimes called generalized normal distributions) are a symmetric family of distributions used in mathematical modeling, usually when errors (the difference between the expected value and the observed values) aren't normally distributed. Special cases of this distribution are identical to the normal distribution and the Laplace distribution. The Generalized error distribution is useful when the errors around the mean or in

Generalized Normal Distribution R

the tails are of special interest. If other deviations from the normal distribution are being studied, other families of distributions can be used. For example, the t-distribution is used if the tails are of interest; the t-distribution approximates the normal distribution as degrees of freedom in the distribution approach infinity. Three parameters define the distribution: The mean, μ, which determines the mode (the peak) of the distribution. Like the standard normal distribution, the median and mode are equal to μ. The standard deviation, σ, which determines the dispersion. A shape parameter, Β. Some authors refer to this as kurtosis, as kurtosis determines how peaked or how flat the distribution is. A generalized normal distribution with Β = 1/2 is equal to the normal distribution; if Β = 1 it is equal to the Double Exponential or Laplace distribution. For values of Β that tend toward zero, the distribution starts to look like a uniform distribution. Several different effects of the shape paramter, Β on the generalized normal distribution. Image: Skbkekas|Wikimedia Commons. Classes of the Generalized Error Distribution The two classes of the Generalized Error Distribution have heavy tails or highly skewed tails. Statisticians R.

[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index] Re: Re: st: exponential power distribution Generalized Error Distribution (GED) in Stata From Stas Kolenikov

Generalized Error Distribution R

To statalist@hsphsun2.harvard.edu Subject Re: Re: st: Generalized Error Distribution (GED) in Stata Date power normal distribution Mon, 1 Nov 2010 12:15:09 -0400 On Mon, Nov 1, 2010 at 10:51 AM, Christopher Baum wrote: > This distribution is well known in http://www.statisticshowto.com/generalized-error-distribution-generalized-normal/ the time series econometrics literature, and implemented by most programs that > estimate ARCH/GARCH models -- including Stata. See [TS] arch and its distribution(ged) option. Stata's documentation > cites > > Nelson, D. B. 1991. Conditional heteroskedasticity in asset returns: A new approach. Econometrica 59: 347–370. > > as using this http://www.stata.com/statalist/archive/2010-11/msg00033.html distribution.  He in turn cites works by Harvey (1981), Box and Tiao (1973). In the Econometrica article, Nelson gives the GED density function, which involves the gamma function and the incomplete gamma function. > > Wikipedia's article(http://en.wikipedia.org/wiki/Generalized_normal_distribution) suggests that it is known as the Generalized normal distribution, the Exponential power distribution, etc. I see -- in my blissful ignorance, I know this under the nickname of the exponential power distribution. Having several names for the same object is a sure way to confusion (what happens if you pass a matrix to a Mata function both as a parameter by reference and as an -external- declaration?). -gammap()-, -invgammap()- and -lngamma()- functions should do the job, then. Looking into -viewsource arch.ado- might help, too. -- Stas Kolenikov, also found at http://stas.kolenikov.name Small print: I use this email account for mailing lists only. * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://

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Phone: +1 (888) 427-9486+1 (312) 257-3777 Contact Us Home >> Support >> Documentation >> NumXL >> Reference Manual >> Descriptive Stats >> GED_XKURT (Pro.) GED_XKURT (Pro.) AttachmentSize GED_XKURT.xlsx Calculates the excess kurtosis of the generalized error distribution (GEDi). Syntax GED_XKURTi(V) V is the shape parameter (or degrees of freedom) of the distribution (V > 1). Remarks The generalized error distribution is also known as the exponential error distribution power distribution. The probability density function of the GED is defined as: Where: is the shape parameter (or degrees of freedom). The excess-kurtosis for GED(v) is defined as: Where: is the gamma function. is the shape parameter. IMPORTANTThe GED excess kurtosis is only defined for shape parameters (degrees of freedom) greater than one. Special Cases:

GED becomes a normal distribution.

GED approaches uniform distribution.

GED exhibits generalized error distribution the highest excess-kurtosis (3). Examples GED_XKURT Plot Example 1: A B 1 Formula Description (Result) 2 =GED_XKURT(2) GED(2) is Normal distribution (0.000) 3 =GED_XKURT(1.0001) Maximum excess kurtosis of a GED is 3.0 (3.000) 4 =GED_XKURT(100) GED approaches uniform distribution for v >> 1 (-1.199) Files Examples Related Links Financial Dictionary - Excess kurtosis Wikipedia - Excess kurtosis Wikipedia - Exponential power distribution GILLER, G.L, Generalized Error Distribution, working paper AttachmentSize GED_XKURT.xlsx13.52 KB ‹ ACFCI (Pro.)upPACF › Reference TDIST_XKURT (Pro.) Download Sites - NumXL Try our full-featured product free for 14 days

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