Ho to perform Monte Carlo Simulation with a factor and a vector.

Hey everybody, I'm trying to perform a Monte Carlo Simulation by randomly choosing 10 numbers of the factor and its standard deviaton 0.5859+-0.2321. Then these factors has to be multiplied with the vector TSS which has 353665 values. I found two possible ways of doing it, but non of them works.

The first:

clc
clear all
%% Read Data

data_TSS=readtable('turb_danuube_15min.csv'); % data TSS & time
TSS=data_TSS{1:1:353665,2};
time=data_TSS{1:1:353665,1};

%% TSS-PAH-Factor
data_Corr2=readtable('Factor_York.xlsx'); % data corr. factor TSS - PAH
factor=data_Corr2{:,3};
fac=mean(factor); %mean of the different factors of York River = 0.5859
S=std(factor); %standard deviation = 0.2321

%% Calculate PAH with Monte Carlo
TSS=data_TSS{1:1:353665,2};

nsamples = 10;

MCfactor= 0.3538+0.4642*rand(nsamples,1); %(Mean-Std)+2*Std, always (10 times) choose one random Number in between 0.3538 and 0.8180
PAH=TSS.*MCfactor;

this is my error:

Arrays have incompatible sizes for this operation.

Error in Monte_Carlo_Var2 (line 21)

PAH=TSS.*MCfactor;

The second:

%% Read Data

data_TSS=readtable('turb_danuube_15min.csv'); % data TSS & time
TSS=data_TSS{1:1:353665,2};
time=data_TSS{1:1:353665,1};

%% TSS-PAH-Factor
data_Corr2=readtable('Factor_York.xlsx'); % data corr. factor TSS - PAH
factor=data_Corr2{:,3};
fac=mean(factor); %mean of the different factors of York River = 0.5859
S=std(factor); %standard deviation = 0.2321

%% Calculate PAH with Monte Carlo
TSS=data_TSS{1:1:353665,2};

nsamples = 10;
for i=1:nsamples
    MCfactor= 0.3538+0.4642*rand(1); %(Mean-Std)+2*Std, always choose one random Number in between 0.3538 and 0.8180
    PAH(i)=MCfactor.*TSS;
end

this is my error:

Unable to perform assignment because the indices on the left side are not compatible with the size of the right side.

Error in Monte_Carlo_Var1 (line 20)

PAH(i)=MCfactor.*TSS;

If anybody has an idea how to solve this problem I would be very happy. Thanks in advance.

Greetings Jonas

[Torsten]

Then these factors has to be multiplied with the vector TSS which has 353665 values.

... to get what ? A matrix of size 10 x 353665 ?

[Jonas Reibenspies]

Hello Torsten, thanks for your answer. I want to get a matrix of the size 353665x10 with these 10 random picked factors as columns and every factor multiplied with every single value of TSS in the lines.

In the secon version in the end the factor is multiplied with TSS but it doesnt work properly.

I also tried adding something like:

TSS=data_TSS{1:1:353665,2};



nsamples = 10;
A=nan(length(TSS),nsamples);
%% 

for i=1:nsamples
    MCfactor= 0.3538+0.4642*rand(1); %(Mean-Std)+2*Std, always choose one random Number in between 0.3538 and 0.8180
    MCPAH=MCfactor.*TSS;
end

A(:,i)=MCPAH(i);

but it still doesnt work.

Answer 1

[Torsten]

data_TSS=readtable('turb_danuube_15min.csv'); % data TSS & time
TSS=data_TSS(1:1:353665,2);
time=data_TSS(1:1:353665,1);
%% TSS-PAH-Factor
data_Corr2=readtable('Factor_York.xlsx'); % data corr. factor TSS - PAH
factor=data_Corr2(:,3);
fac=mean(factor); %mean of the different factors of York River = 0.5859
S=std(factor); %standard deviation = 0.2321
%% Calculate PAH with Monte Carlo
nsamples = 10;
MCfactor= 0.3538+0.4642*rand(nsamples,1); %(Mean-Std)+2*Std, always (10 times) choose one random Number in between 0.3538 and 0.8180
TSS_rand = [TSS*MCfactor(1),TSS*MCfactor(2),TSS*MCfactor(3),TSS*MCfactor(4),...
            TSS*MCfactor(5),TSS*MCfactor(6),TSS*MCfactor(7),TSS*MCfactor(8),...
            TSS*MCfactor(9),TSS*MCfactor(10)];

[Jonas Reibenspies]

Thanks again for answering this quick. It works fine! Thanks a lot.

I just have one following question.

the value of nsamples=10 is just to get to the code. Later there should be nsamples of values around 1000 or more. Do you know a way to then get the matrix for TSS_rand without having to type TSS*MCfactor(every number)?

[Torsten]

TSS_rand = repmat(TSS,1,nsamples)*diag(MCfactor)

[Jonas Reibenspies]

Thanks a lot!!