This is not a question about MATLAB. But you have done something.
You do not have a PDF. You have an approximation to a PDF, sampled over a finite range, at a finite set of steps.
If you wish to compute the mean of a random variable with known distribution parameters, you would be best advised to use resources like wikipedia. Here, for example:
Note that it is stated on that page (look on the right side) the mean and variance of a Lognormal distribution, given the usual distribution parameters.
As well, since you are using fitdist, you already have the stats toolbox. So you have access to tools like lognstat (or the corresponding tool for whatever distribution you are using). Use the available tools. Do NOT try to cobble up code to do what you do not really understand. Writing code to do what already exists for you to use is just a bad idea when you have no clue as to what you are doing. (What evidence do I have that you have no clue about these things? It is that you don't know how to compute the mean of a continuous random variable. At worst, something immediately found online.)
Can you compute the mean of a distribution where the PDF is approximated at a finite set of points? Well, yes. You might want to read about the mean of a continuous distribution.
In there, you will find that the mean of a random variable is given as
distibutionmean = int(x*pdf(x),-inf,inf)
So you want to compute the integral of x times the pdf(x), integrating from -inf to inf. In the case of a distribution like the lognormal, the pdf only lives on [0,inf) so that would be the bounds of interest.
Now, if I compute the actual mean and variance of a standard lognormal PDF, thus with distribution parameters of [0,1], I will find that the mean is exp(1/2).
exp(0 + 1^2/2)
ans =
1.64872127070013
[m,v] = lognstat(0,1)
m =
1.64872127070013
v =
4.67077427047161
As you see, lognstat agrees with my estimate of the mean.
Now, lets try it for a lognormal, approximated as you did.
x = 0:.01:10;
trapz(x,x.*lognpdf(x))
ans =
1.4898533607038
As you can see, trapz did not do very well here, off by roughly 10%. The problem was not that I did not sample the PDF finely enough either, or the integration error of trapz.
The problem is that this does not sample the lognormal PDF sufficiently far into the tails. The lognormal distribution has a heavy right tail.
logncdf(10)
ans =
0.9893489006583
Even trapz agrees with that measure.
trapz(x,lognpdf(x))
ans =
0.989348905931384
So, CAN you compute the means of those approximate PDFs? Well, yes, you can use trapz to do so, as I showed. Should you? Sigh.
