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I am trying to test if the q-Weibull distribution is better at describing the behavior of certain data than other distributions. Since I am from a biological sciences background, math and coding are not my stronger suits, and I have been struggling a little bit with implementing such analysis. I am basing my analysis on a paper on the subject of estimating the parameters of q-Weibull distributions. The paper states that to estimate the parameters I have to equate the following equations to zero and solve the resulting system: According to the paper, since the equations are nonlinear, a closed form cannot be found and optimizers need to be used to find the minimum

I have read the Matlab documentation, and I found the function fsolve to solve nonlinear equations. The problem is that there is a sum of multiple terms in those equations. Normally, I would use a for loop or a "sum" to solve those, but I have no idea how to make that within a fsolve function. Any insights on how to do it? Any advice would be greatly appreciated. Sincerely, Leo.

Leonardo Lopes
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You may not need to solve the nonlinear equations from first principles, MATLAB has a built-in Weibull fit function. Read https://www.mathworks.com/help/stats/weibull-distribution.html https://www.mathworks.com/help/stats/wblfit.html

aaquib
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  • The q-Weibull distribution is a generalization of the Weibull distribution. According to what I've read, the built-in Weibull function should not work in this case (unfortunately). The paper "q-exponential, Weibull, and q-Weibull distributions: an empirical analysis" by Picoli et al. has more information on the subject if you are interested. Any advice on how to implement those calculations in Matlab would be appreciated. I still haven't figured that out. – Leonardo Lopes Aug 08 '23 at 09:10