Dear Dr. Abedini, As far as I understand there are two different definitions of the variogram around:
2\gamma(x,x)=Var(Y(x)-Y(x'))=VAR[Y(x)-m(x)-Y(x')+m(x')] and 2\gamma(x,x)=E[(Y(x)-Y(x'))^2]=VAR[Y(x)-m(x)-Y(x')+m(x')]+ (m(x')-m(x))^2 and furthermore the second definition is often applied to Y(x)=Z(x)-m(x) which is than again numerically equal to the first definition (in any case). All these definitions are equal as long as the field is intrinsically stationary. And as most Textbooks are discussing the stationary case, both definitions are used without contradiction. However in the instationary case you get the difference you observed. Cressie insisted in some publications (e.g. in his 1993 book) that the second definition is the correct definition for several reasons. Best regards, Gerald Am Samstag, 5. Mai 2007 10:20 schrieb M.J. Abedini: > Dear Colleagues > > I would greatly appreciate it if someone could shed some light on the > following issue: > > For a nonstationary random function, variogram is defined as: > > 2*\gamma(x,x')=VAR[Y(x)-m(x)-Y(x')+m(x')] > > If one simplifies the right hand side, the whole equation becomes: > > 2*\gamma(x,x')=R(x,x)+R(x',x')-2*R(x,x') > > In a number of textbook, relation between covariance and variogram is > written as: > > 2*\gamma(x,x')=R(x,x)+R(x',x')-2*R(x,x')+[m(x)-m(x')]^2 > > Am I missing something from this mathematical manipulation? > > Thanks > Abedini > + > + To post a message to the list, send it to [email protected] > + To unsubscribe, send email to majordomo@ jrc.it with no subject and > "unsubscribe ai-geostats" in the message body. DO NOT SEND > Subscribe/Unsubscribe requests to the list + As a general service to list > users, please remember to post a summary of any useful responses to your > questions. + Support to the forum can be found at > http://www.ai-geostats.org/ -- ------------------------------------------------- Prof. Dr. K. Gerald v.d. Boogaart Professor als Juniorprofessor fuer Statistik http://www.math-inf.uni-greifswald.de/statistik/ B�ro: Franz-Mehring-Str. 48, 1.Etage rechts e-mail: [EMAIL PROTECTED] phone: 00+49 (0)3834/86-4621 fax: 00+49 (0)3834/86-4615 (Institut) paper-mail: Ernst-Moritz-Arndt-Universitaet Greifswald Institut f�r Mathematik und Informatik Jahnstr. 15a 17487 Greifswald Germany -------------------------------------------------- + + To post a message to the list, send it to [email protected] + To unsubscribe, send email to majordomo@ jrc.it with no subject and "unsubscribe ai-geostats" in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list + As a general service to list users, please remember to post a summary of any useful responses to your questions. + Support to the forum can be found at http://www.ai-geostats.org/
