Hallo Ivan Thanks. Yes, this approach seems to be viable. I did not consider using dnorm in fitting procedure. But as you pointed
> (Some nonlinear least squares problems will be much harder to solve > though.) This simple example is quite easy. The more messy are data and the more distributions are mixed in them the more problematic could be the correct starting values selection. Errors could be quite common. x <- (0:200)/100 y1 <- dnorm(x, mean=.3, sd=.1) y2 <- dnorm(x, mean=.7, sd=.2) y3 <- dnorm(x, mean=.5, sd=.1) ymix <- ((y1+2*y2+y3)/max(y1+2*y2+y3))+rnorm(201, sd=.001) plot(x, ymix) With just sd1 and sd2 slightly higher, the fit results to error. > fit <- minpack.lm::nlsLM( + ymix ~ a1 * dnorm(x, mu1, sd1) + a2 * dnorm(x, mu2, sd2)+ + a3 * dnorm(x, mu3, sd3), + start = c(a1 = 1, mu1 = .3, sd1=.3, a2 = 2, mu2 = .7, sd2 =.3, + a3 = 1, mu3 = .5, sd3 = .1), + lower = rep(0, 9) # help minpack avoid NaNs + ) Error in nlsModel(formula, mf, start, wts) : singular gradient matrix at initial parameter estimates If sd1 and sd2 are set to lower value, the function is no longer singular and arrives with result. Well, it seems that the only way how to procced is to code such function by myself and take care of suitable starting values. Best regards. Petr > -----Original Message----- > From: Ivan Krylov <krylov.r...@gmail.com> > Sent: Friday, December 31, 2021 9:26 AM > To: PIKAL Petr <petr.pi...@precheza.cz> > Cc: r-help mailing list <r-help@r-project.org> > Subject: Re: [R] mixture univariate distributions fit > > On Fri, 31 Dec 2021 07:59:11 +0000 > PIKAL Petr <petr.pi...@precheza.cz> wrote: > > > x <- (0:100)/100 > > y1 <- dnorm((x, mean=.3, sd=.1) > > y2 <- dnorm((x, mean=.7, sd=.1) > > ymix <- ((y1+2*y2)/max(y1+2*y2)) > > > My question is if there is some package or function which could get > > those values ***directly from x and ymix values***, which is > > basically what is measured in my case. > > Apologies if I'm missing something, but, this being a peak fitting > problem, shouldn't nls() (or something from the minpack.lm or nlsr > packages) work for you here? > > minpack.lm::nlsLM( > ymix ~ a1 * dnorm(x, mu1, sigma1) + a2 * dnorm(x, mu2, sigma2), > start = c(a1 = 1, mu1 = 0, sigma1 = 1, a2 = 1, mu2 = 1, sigma2 = 1), > lower = rep(0, 6) # help minpack avoid NaNs > ) > # Nonlinear regression model > # model: ymix ~ a1 * dnorm(x, mu1, sigma1) + a2 * dnorm(x, mu2, sigma2) > # data: parent.frame() > # a1 mu1 sigma1 a2 mu2 sigma2 > # 0.1253 0.3000 0.1000 0.2506 0.7000 0.1000 > # residual sum-of-squares: 1.289e-31 > # > # Number of iterations to convergence: 23 > # Achieved convergence tolerance: 1.49e-08 > > (Some nonlinear least squares problems will be much harder to solve > though.) > > -- > Best regards, > Ivan
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