generating a randn values to study the effect of an input parameter on output parameter

Hello all,

I have an input parameter alpha, and I want to study the variation effect of this parameter on an output parameter Output_par. What I did is the following, I tried to change the alpha using the randn function to generate a gaussian.

I have actually 2 questions :

   1-When am using the randn function in the following way       
     alpha=alfa(iii)+5*randn/100;
     am I changing the alpha value 5 percent? if not can someone  
     explain to me what it means using it this way ? 

   2-once I get  all the 10000 values of my output_par, do I have   
     to add the 5 percent  to the std of the gaussian or not ?

for iii=1:10000
                tic
                alpha=alfa(iii)+5*randn/100;
                S_f=(2*mr-5) * (alpha).^2
                Tu_f=S_f.*max_lid_beta_f_int;  
                B=S_f.*Gamma_f;
                % for i=1:bheem;
                EC_f=final_beta_fine.*B;
                [number_line,number_column]=size(EC_f);
                EC_f_integrated=[];
                transposee_EC_f=EC_f';
                for i=1:number_column
                    X=altitude;
                    Y(i,:)=transposee_EC_f(i,:);
                    Y=Y(i,:);
                    EC_f_int=trapz(X,Y);

                      EC_f_integrated=[EC_f_integrated EC_f_int];
                  end; 
                  Output_par=[Output_par EC_f_integrated];
                  toc
              end
thanking you in advance,

Answer 1

[LE FOU]

ok is there a way to do what I want ? I mean how to do it in matlab if I want to study an input parameter variation on an output parameter ?

[Fangjun Jiang]

What you did is right. Generate an input with known Mean and STD, calculate the output, and then probably calculate the Mean and STD of the output. I don't see that part yet. Only you know what's behind those parameters and calculations. You need to know what you try to achieve and ask specific MATLAB questions here.

[LE FOU]

after generating this I am plotting the histogram using the function hist, that gives me the gaussian shape, and of course I calculate the std and the mean of the ouptput_par.

do you think it's better to change the 5 percent and use something else ?

[Fangjun Jiang]

That depends. What is the typical input supposed to be? Is the input a pure random number, or you want to add some random noise to an exist input like alfa(iii) you have? Regarding 5 percent or something else, it also depends on the value of alfa(iii). Remember there is no boundary for the value of 5*randn/100. You might want to consider rand() which is guaranteed between 0 and 1 but it is uniformly distributed.

[LE FOU]

alpha can vary between 1 and 3, and I want to add some random noise to an exist input (which is alpha). I want to take the maximum and the minimum value of alpha and see how it affects my output parameters by adding noise to alpha.

[Fangjun Jiang]

In that case, I would think rand() is better because it's value is bounded. You can multiply it with a proper scale to make it the effect of a noise but not overwhelm the true signal. But again, you have to make the decision because you know your application.

[LE FOU]

ok thanks, I will keep the gaussian.

Answer 2

[Fangjun Jiang]

1. No, it's not. randn could vary from large negative to large positive although the possibility of a large number is small.

Y = randn returns a pseudorandom, scalar value drawn from a normal distribution with mean 0 and standard deviation 1.

2. You probably have to answer yourself. What is the purpose of the code?

Answer 3

[LE FOU]

Hello,

   1. if randn returns a pseudorandom, scalar value drawn from a  
      normal distribution with mean 0 and standard deviation 1, 
      multiplying it by 5 and dividing it by 100 should do the same 
      for the std, no ? and when I add the alpha as a sum, it means 
      my alpha value is the mean value, no ?

   2. the purpose of the code is to see how much the output 
      parameter varies or is affected by the input parameter alpha 
      variation.
 thanks

[Fangjun Jiang]

1. No and No. Please check a text book. Also, remember you have alfa(iii) involved.