enter parameters in box as below for Excel

enter variable to be fitted in upper left box

enter equation Y*(1-(1-q)*binlogged/k)**(1/(1-q))

where binlogged (x, whatever) is the name of the binsize variable to which your data are keyed

Minimize sum of squares (can be sum of sums)

the Ss are a row of squared differences

they refer to two different rows:

the raw data

the fitted data, from three parameters:

Y

k

q

Those values are initialized

Instruct solver to change those values

Add constraints to the parameters

Y>10

k>5

q>0

enter parameters in box as below for Excel

t0>10

k>5

c>0

enter variable to be fitted in upper left box

enter equation N0/(t0-year)**c

where year is the name of the actual variable for the year to which your data are keyed

popgrowth.pdf

Ignore the following

From tsallis@santafe.edu Thu Aug 3 15:44:14 2006 Date: Sun, 08 May 2005 07:17:26 -0600 From: Constantino TsallisTo: Douglas R. White Subject: Re: monolog plot question A tutorial on fitting q The fitting of q-laws as replacement for power-law fit: A social science tutorial, Douglas R. White Doug, yes, you can. Start with the data series which is the UPPER one among those that you sent me in the Excel a few days ago. That one might be the easiest case to start with. Do like this: 1) Let us call y(x) your data. Estimate with your eye the EXTRAPOLATED value y(0) in the log-log plot that you sent me. 2) Calculate, for all x, y(x) / y(0) 3) Then calculate, for all x, z(x) = {[y(x) / y(0)]^(1-q) - 1} / (1-q) 4) Then plot in a linear-linear scale z(x) versus x for various values of q (say q=1.3, 1.4, 1.5, 1.6, 1.7, etc...). The q that produces the "best straight" line provides you the estimate of q that you are looking for. 5) The SLOPE of the linear-linear plot z versus x directly provides you (- kappa). Then your data have been so fitted with y(x) = y(0) exp_q (- x / kappa) Comment (i): The "best straight line" can be found either by eye, or, more systematically, by making a linear regression, and choosing that value of q that gives the "linear correlation coefficient r" closest to unity. Comment (ii): Once you have a quite good set [y(0), q], you can slightly improve them. To do this you go back to your log-log representation that you sent me in the Excel, and change slightly around your pair [y(0), q] until you are satisfied the most. Comment (iii) Stefan Thurner / Vienna and I are just now writing a paper where we essentially follow the procedure that I described to you. I am attaching the figure we get, so that you will have an illustration in front of your eyes. The inset precisely shows the linear correlation coefficient r versus q, which allows a quite precise determination of q for our problem. Cheers and good luck! Constantino -------------------------- At 00:42 8/5/2005 -0700, you wrote: >I note from the Malacrne and Mendes paper 2nd page right that using their >generalized monolog plot that q can be estimated directly, independent of >the other parameters. > >Constantino, given the error bars, would you advising using that method to >estimate the q values in our city data? > >Doug