From mboxrd@z Thu Jan 1 00:00:00 1970 Return-Path: Received: (qmail 18993 invoked by alias); 20 Mar 2007 12:00:26 -0000 Received: (qmail 18984 invoked by uid 22791); 20 Mar 2007 12:00:25 -0000 X-Spam-Check-By: sourceware.org Received: from network-theory.com (HELO mail.network-theory.co.uk) (66.199.228.187) by sourceware.org (qpsmtpd/0.31) with ESMTP; Tue, 20 Mar 2007 12:00:22 +0000 Date: Tue, 20 Mar 2007 12:00:00 -0000 Message-ID: <87odmof7l9.wl%bjg@network-theory.co.uk> From: Brian Gough To: Ben Klemens Cc: gsl-discuss@sourceware.org Subject: Re: Sample skew and kurtosis In-Reply-To: <20070315233956.GF1287@thebes.hss.caltech.edu> References: <20070315233956.GF1287@thebes.hss.caltech.edu> User-Agent: Wanderlust/2.14.0 (Africa) Emacs/21.3 Mule/5.0 (SAKAKI) MIME-Version: 1.0 (generated by SEMI 1.14.6 - "Maruoka") Content-Type: text/plain; charset=US-ASCII X-Message-Mac: d00d2cf4a2f325c123cc927626eb5995 Mailing-List: contact gsl-discuss-help@sourceware.org; run by ezmlm Precedence: bulk List-Id: List-Subscribe: List-Archive: List-Post: List-Help: , Sender: gsl-discuss-owner@sourceware.org X-SW-Source: 2007-q1/txt/msg00054.txt.bz2 At Thu, 15 Mar 2007 15:39:56 -0800, Ben Klemens wrote: > The same holds for the kurtosis and skew: if you have a sample and not a > population, then the unbiased estimate is of the form \sum(...)/(n-1). But > the above starts with 1/n, meaning we have population kurtosis normalized > by sample variance squared. > > If we have to choose only one kurtosis and skew function, it should > probably be the sample and not the population version. The fix is trivial: > just return kurtosis * n/(n+1.0) at the end of kurtosis_m_sd, and > similarly for skew. Hello, I originally looked at the formulas for unbiased estimators of skewness and kurtosis and they were pretty complicated, so I went with the simple definition used by Octave & Matlab. -- Brian Gough