Creating a custom PDF to find the parameters

Hello,

I have 4 known discharge values as well as their probabilities. I am trying to write my own matlab code to give me the 3 parameters associated with these known values. The log-pearson type 3 distribution isn't built into matlab, so this requires me to write a custom pdf function for it. This is where I am getting my errors. I have tried:

custpdf=@(Q,a) (1/(Q*abs(a(1))*gamma(a(2))))*((ln(Q)-a(3))/a... )^(a(2)-1)*exp(-(ln(Q)-a(3))/a(1));

as well as:

custpdf=@(Q,a,b,c) (1/(Q*abs(a)*gamma(b)))*((ln(Q)-c)/a... )^(b-1)*exp(-(ln(Q)-c)/a);

I am getting a not enough input arguments for both cases. Next the code I am trying to use is to estimate the parameters via minimizing the R^2 value:

Flogp3pdf = @(a,b,c) sum((Po - custpdf(Q,a,b,c)).^2);

Where Po are my known probabilities associated with my known discharge values, Q.

[a,b,c] = fminsearch(Flogp3pdf,[1,1,1]);

[a,b,c,fval]=fminsearch(custpdf,[1,1,1]);

I figured this would work because a friend had a similar code to estimate the parameters for the lognormal distribution. I got that code and modified it to work for the Log-pearson3. However, it's not that simple and I am having trouble.

some errors I am getting are:

Error in fminsearch (line 190) fv(:,1) = funfcn(x,varargin{:});

Error in pearson_fit (line 17) [a,b,c,fval]=fminsearch(custpdf,[1,1,1]);

Any help whatsoever would be welcome. I am a somewhat novice coder and I have tried reading through the MLE as well as fminsearch help pages and I can't seem to figure this out.

Thank you in advance!!

PS: the code that I am trying to model it after is only 2 lines:

% begin - fit lognormal parameters by minimizing the sum of squares error

Flogcdf = @(c) sum((Pf - logncdf(Sa,c(1),c(2))).^2); [c] = fminsearch(Flogcdf,[1,1]);

% end - fit lognormal parameters by minimizing the sum of squares error

-David