Histogram Fitting with Fixed Interval of the x Axis

So I have a data distribution represented as a histogram. The data itself is generated based on rand function, so that each time I run my code containing this data distribution I will get different set of data, however the distribution profile only changes very slightly, as it should. I want to fit this distribution to a curve of 'fixed interval'. What I meant with fixed interval is that each time I run the code I will get the fitted curve with the same interval of its x axis, even though the histogram actually still changes slightly. Is it possible to do this?

There are some built-in functions for histogram fitting such as histfit, but instead of giving fixed interval, it gives fixed point which is 100 every time I use this function.

If that's not easy to implement then what if making curve fitting with fixed points? My goal is actually to increase the points so that the fitting gets smoother.