The analysis of functional data following a distributional model with time-dependent parameters is getting more common in recent studies. This allows to estimate any time-dependent characteristic, in addition to merely estimating a time-dependent mean. The most standard approach is to fit local exponential family one-parameter models by spline smoothing. In this work, we present an alternative non-parametric smoothing procedure based on local constant likelihood approach which is valid for distributions not in the exponential family, or having more than one parameter depending on time. We apply our proposals to model continuous monitoring glucose curves. First, glucose values are re-scaled to the interval [0, 1], considering the historical minimum and maximum observed values. Then Beta distributions with parameters smoothly depending on t are estimated.