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I guess a moving average and likewise, a moving variance and moving skewness, will give a similar function of $x$. But I would like to make use of GAMLSS's optimisation (e.g. ML, GAIC or GCV) including some penalisation for overfitting. If this exists. If that even makes sense without defining a distribution first.

I guess a moving average and likewise, a moving variance and moving skewness, will give a similar function of $x$. But I would like to make use of GAMLSS's optimisation (e.g. ML, GAIC or GCV) including some penalisation for overfitting. If this exists. If it even makes sense without specifying a distribution first.

Let's generate two B-splines. These serve as the input parameters for a LogNormal distribution. We now sample $y$'s for various $x$'s following this skewed distribution.

Let's generate two B-splines.

These serve as the input parameters for a LogNormal distribution. We now sample $y$'s for various $x$'s following this skewed distribution.

xs <- ceiling(runif(datan, 0, xlim))
ys <- sapply(xs, function(x){rlnorm(1, meanlog = mu[x], sdlog = sigma[x])})