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%nakedsoftware.org opensource license, copyright 2010 stephane.poirier@oifii.org % %developed by Stephane Poirier, M.Sc. Optical Physics, Remote Sensing Application Software Developer (1991-2010) % %this function is part of oifii.org's ar\sp\ Microwave- derived 30-year Canada-Alaska Daily Temperature and Snowcover Databases library % %this function is part of oifii.org's ar\sp\'this folder' application (lauched with ar\sp\'this file'.m) %oifii.org's ar\sp\affiche_carte application is part of the oifii.org's ar\sp set of applications which %may also contain similar variant versions of this function with identical filename. % %A geophysical research paper about this work has been submitted in June 2009 for publication in JGR-Atmosphere %Royer, A. and Poirier S., Surface temperature spatial and temporal variations in North America from homogenized %satellite SMMR-SSM/I microwave measurements and reanalysis for 1979-2008, Journal of Geophysical Research - Atmosphere, %Submitted June 2009, http://www.oifii.org/tsatdb/Royer- Poirier_Microwave-derived-daily-surface- temperature_JGR2009JD012760_R2.pdf % %This study's database can be downloaded from the author web site at: %http://www.oifii.org/tsatdb/Royer-Poirier_Microwave-derived- daily-surface-temperature-db_1979-2008.zip % %this function is used to display the raw microwave raster data (NSIDC's SMMR and SSMI satellite, ref. nsidc.org) % %usage: % 20yymmmdd % %version 0.0, 20yymmmdd, spi, initial function draft % %nakedsoftware.org opensource license, copyright 2010 stephane.poirier@oifii.org

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function [a,delta_a,b,delta_b,syx,r] = stat(x,y,ordre,t); % INPUT % ordre : degre du polynome % t : coef de student clc [p,s]=polyfit(x,y,ordre) ; % coef des polynome if length(p)==2 n = length(x) ; % degre de liberte dl = length(x)-2 ; % y = ax + b a = p(1,1) ; b = p(1,2) ; % coefficient de correlation r = corrcoef(x,y) ; r = r(1,2) ; % ecart type residuel syx = sum(y.*y) - (sum(y)*sum(y)/n) ; syx = syx - a*a*(sum(x.*x)-(sum(x)*sum(x)/n)) ; syx = sqrt(syx/dl) ; % ecart type de y sy=syx/sqrt(1-r*r) ; % estimateur de ecart type % de la pente Sa = a * sqrt((1-r*r)/(r*r*(dl))) ; % ou encore : Sa = syx / sqrt(sum((x - mean(x)).^2) ) % del'ordonnee a origine s = 0 ; e = sum(x.* x) / n ; Sb = Sa * sqrt(e) ; clear e ; delta_a = t * abs(Sa / sqrt(dl)) ; delta_b = t * abs(Sb / sqrt(dl)) ; %-----------------------------% % TEST de CONFIANCE % %-----------------------------% % sur le coef de correlation tr = r * sqrt(dl/(1-r*r)) ; % autre hypothese r ~= 0 r0 = 0.95 ; z = 1.1513.*log10((1+r)/(1-r)) ; uz = 1.1513.*log10((1+r0)/(1-r0)) ; oz = 1/sqrt(n-3) ; zz = (z-uz) * sqrt(n-3) ; disp (['hypo : coef de correlation : r0 = ',num2str(r0)]) ; disp ([' hypo rejetee si : ', num2str(zz),' > t de student']) ; % sur la pente (si on veut comparer par rapport au coef beta0) % hypo0 : pente = 0 % hypo1 : pente ~= 0 (=& par exemple) pente0 = 0 ; t_pente = (a-pente0) / Sa ; %---------------------------% % INTERVALLE DE CONFIANCE % %---------------------------% % sur la droite de régression disp(' ') ; disp('%-------------% ' ); disp('coef directeur') disp(['a : ',num2str(a),' +/- ',num2str(delta_a)]) ; x1 = x(1) ; x2 = x(length(x)) ; arel = (a * (x2-x1)) / mean(y) ; amax = a + abs(delta_a) ; amax = (amax * (x2-x1)) / mean(y) ; amin = a -abs(delta_a) ; amin= (amin * (x2-x1)) / mean(y) ; disp(['variation relative : ',num2str(amin),' < ',... num2str(arel),' < ',num2str(amax)]); disp(' '); disp(['hypothese de la pente : pente = ',num2str(pente0)]); disp(['hypothese rejetee si : ',num2str(t_pente),... ' > t de student ']); disp(' ') ; disp(['ordonnée à l''origine']) ; disp(['b : ',num2str(b),' +/- ',num2str(delta_b)]) ; % a 95 % lim1 = z - 1.96*oz ; lim2 = z + 1.96*oz ; lim1 = 10^(lim1/1.1513) ; lim2 = 10^(lim2/1.1513) ; lim1 = (lim1-1)/(lim1+1) ; lim2 = (lim2-1)/(lim2+1) ; disp(' '); disp('%---------------%') ; disp([' coeff de correlation : ']); disp([num2str(lim1),' < ',num2str(r),' (r² : ',num2str(r*r),') < ',num2str(lim2)] ) ; disp(' '); disp('Signification statistique') ; disp('Hypo coef de correlation = 0 (pas de correlation)'); disp(['si : ',num2str(tr),' > t de student'] ); end

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