# How to fit a multi modal distribution using a weighted sum of PDFs?

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I am new to matlab and I know my question is rudimentary. I really appreciated if you help me. I have a data-set (attached) shows multi modal distributions and I want to make a fit using a weighted sum of PDFs. How may I do that?

I have applied the Kernel distribution but I am not sure is right.

clc;

clear all;

close all;

%.....................................................................

data=xlsread('A');

rr=data(:,1);%gr/cm3

[x11,y11]=hist(rr,36);

hist(rr,36);

hold on

[f,x11] = ksdensity(rr,'Bandwidth',0.0028);

plot(x11,f,'-r','LineWidth',2)

### Accepted Answer

Bjorn Gustavsson
on 2 Mar 2021

Edited: Bjorn Gustavsson
on 2 Mar 2021

You don't have enough samples to confidently claim you have a multimodal distribution. If you simply try this with fitting exponential distributions to your data you'll see that they work reasonably OK:

PARHAT = expfit(abs(rr));

PARHATp = expfit(rr(rr>=0));

PARHATm = expfit(-rr(rr<=0));

hist(NUM,40)

hold on

x = linspace(-0.1,0.1,1001);

plot(x,30*exp(-abs(x)/PARHAT),'c')

plot(x,30*exp(-abs(x)/PARHATp),'r')

plot(x,30*exp(-abs(x)/PARHATm),'m')

There are indications that there might be a multimodal distribution, but if you do fit for a multimodal distribution you will probably find that the parameter uncertainty will be very large. First you need to gather more observations (hopefully this will be possible without too large costs in time and resources).

HTH

### More Answers (1)

Tom Lane
on 2 Mar 2021

I'm glad Bjorn provided an answer that works for you. For future reference, there is a function for fitting mixtures of normal distributions:

Also, there is an example that fits a mixture of two normals, but it can be adapted to fix mixtures of any distributions:

##### 3 Comments

Tom Lane
on 3 Mar 2021

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