how can i fit a probability density function without knowing the specific distribution family

hi all, i have some data, taken from a Drift Diffusion Model. I wish to fit a pdf to that data, but can't seem to find a specific family that matches out of the pdf available inputs:

y=pdf(name,X);

how can i fit an optimum function? actually - how can i fit general data with a probability density function? I am adding a picture of the distribution just to give a sense of its looks.

[Brendan Hamm]

It appears that this data is originating from a Geometric Brownian Motion which would have implications that the data is log-normally distributed. I may be wrong on this front, but I would imagine you have some intuition on the stochastic process which the data is coming from.

If on the other hand you are not able to make an apriori assumption about the distribution, a non-parametric distribution might be your best options.

kFit = fitdist('Kernel',x);

Another option, which statisticians would generally not recommend but I see done often in practice is to compare many different fits. Consider the AIC or BIC of the models to select an appropriate choice.