function [w,bins] = scott(c,normal,factor); % function [w,bins] = scott(c,normal,factor); % Calculate bins width and bins vector using the Scott's rule applied to vector c % normal = 1 : Use Normal rule % normal = 0 : Use Correct normal rule with skewness factor % factor : Multiply calculated width by factor % Copyright (c) 2004-2006 Alessio Botta, Alberto Dainotti, Antonio Pescapè % Email: {a.botta , alberto , pescape }@unina.it % DIS - Dipartimento di Informatica e Sistemistica % University of Napoli Federico II, ITALY % All rights reserved. % % Redistribution and use in source and binary forms, with or without % modification, are permitted provided that the following conditions % are met: % 1. Redistributions of source code must retain the above copyright % notice, this list of conditions and the following disclaimer. % 2. Redistributions in binary form must reproduce the above copyright % notice, this list of conditions and the following disclaimer in the % documentation and/or other materials provided with the distribution. % 3. Redistributions of source code or in binary form must clearly reproduce % the reference to the web site from which they were downloaded. % % THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND % ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE % IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE % ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE % FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL % DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS % OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) % HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT % LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY % OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF % SUCH DAMAGE. if nargin < 3 factor = 1; end if nargin < 2 normal = 1; end % Compute bins width by Scott's rule w = 3.49 * std(c) * length(c)^(-1/3); if normal ~= 1 % Distribution in lognormal-like s = std(log10(c)); skew = (2^(1/3) * s) / ( exp(5/4*s^2) * (s^2 + 2)^(1/3) * (exp(s^2)-1)^(1/2) ); clear s; fprintf('Skewness factor: %d (inverse: %d)\n', skew, 1/skew); w = w * skew; end w = w * factor; % Establish bins vector bins = (min(c)+w/2):w:max(c);