Creating Distribution by Specifying Densities

Hi,

I would like to fit a distribution to a vector that contains the probability mass/densities of the desired distribution.

For example, assume my vector of probability masses is [0.02 0.1 0.015] with the corresponding x-coordinates being [-1 0 1.2].

(So I have a probability mass of 0.02 at x = -1, a probability mass of 0.1 at x = 0 and so on).

Is there any function in MATLAB that would allow me to fit say, a normal distribution to a distribution with the probability masses at the specified coordinates? I understand that options such as fitdist are available if I am dealing with a histogram/dataset but here I would like to fit a distribution given the probability masses/densities at certain points.

Any help would be much appreciated and thank you in advance.

Answer 1

[Torsten]

If the masses add to 1, your x-coordinates together with the probability masses already define the distribution. There is no reason for fitting here.

If the masses don't add to 1, you can arbitrarily distribute (1-sum of masses) on the x-axis. So there is not senseful way of fitting and obtaining a distribution in this case.

[Chun Hei Chan]

Hi Torsten,

Thanks for your answer. Indeed I have a very long row vector whose entries sum up to 1 so I do know the exact quantities of the distribution of interest. The reason I am asking this question is because I want to know how well this distribution can be approximated by common distributions (e.g Normal). I want to know if there is any way of fitting a distribution as I have specified in my answer as to achieve this.

Thanks again for your help.

[Torsten]

Then I suggest you generate samples from your discrete distribution and use fitdist to fit another distribution (e.g. a normal distribution) to this sample vector.