how to do looping with over many variables ? (MONTE CARLO)

Hey, very new to matlab. What command should I use to loop over many variables ? e.g. n=3,4,5,.....100. Thanks.

Answer 1

[KSSV]

for n = 3:100
n
end

[Jardine Shi]

(its a typo should be 3,4,....100)

Here's the first part that I did, can you specify to repeat this using n=3,4,....100. where exactly should I put

n =3:100 ?

Trying it on the sample size will give me "Error using randn, size inputs must be scalar"

[KSSV]

What ever the code you have....make it into a function or run it nside the loop.

for n = 3:100
%% Do what you want
%% Copy your code here 
end

When you give n = 3:100 in a loop, the loop index is n, it keep changing by 1 from 3 to 100.

% check your self
for n = 3:100
    n   % see what is printed 
end

[Jardine Shi]

Oh, so I'd have to generate both rejt_n &rejN_n as functions of n ? How do I generate them into functions of n ?

[KSSV]

Copy paste your code here...image snippet will not help in any way.

[Jardine Shi]

%HERE YOU GO :)

%QUESTION 1
rng(480058999)

%A Monte Carlo Simulation with n = 2 and 10,000 repetitions
%=============================================================================================================================
%i)random sample size n by sampling from N(mu,sample variance)
%with mu = 0 and sample variance = 1

%sample size
n=2     

%independent draws given N(0,1)
X = randn(n,1);

%sample mean
Xbar = sum(X)/n

%sigma-hat squared
X2bar = sum(X.^2)/n;
sigmahat2 = X2bar-Xbar^2

%sample variance
S2= (n/(n-1))*sigmahat2

%continuation
%setting the number of repetitions
M=10000

%Creating the Mx1 vectors to save the realized sample stats
RealizedXbar=NaN(M,1);
realizedsigmahat2 = NaN(M,1);
RealizedS2 = NaN(M,1);

%looping the repetitions
for m= 1:M
    
    %generating the random sample
    X = randn(n,1);
    
    %computing the sample stats
    Xbar = sum(X)/n;
    X2bar = sum(X.^2)/n;
    sigmahat2 = X2bar-Xbar^2;
    S2 = (n/(n-1))*sigmahat2;
    
    %lastly, saving the sample stats
    RealizedXbar(m,1) = Xbar;
    Realizedsigmahat2(m,1) = sigmahat2;
    RealizedS2(m,1) = S2;
end


%=============================================================================================================================
%ii) t-stat for testing null hypothesis Ho:mu = 0

 tstat= RealizedXbar./sqrt(RealizedS2/n)

%=============================================================================================================================
%iii) Record whether the abs value of t-stat exceeds cn-1(0.05)
%recall n = 2, so n-1 = 1
alpha=0.05;
c=tinv(1-alpha/2,n-1);

%proportion
rejt_of_n=sum(tstat>c | tstat<-c, "all")/M


%=============================================================================================================================
%iv) Record whether the abs value of t-stat exceeds c(0.05)
c=norminv(0.975);

%proportion
rejN_of_n=sum(tstat>c | tstat<-c, "all")/M
%from the value given, 0.2904, it shows that it is not approximating well


%=============================================================================================================================
%B repeat part a using n=3,4.....100. Graph both rejt(n) & rejN(n)
%as functions of n. Set the vertical axis values in both graphs to range
%from 0-3

[KSSV]

%HERE YOU GO :)
%QUESTION 1
rng(480058999)
%A Monte Carlo Simulation with n = 2 and 10,000 repetitions
%=============================================================================================================================
%i)random sample size n by sampling from N(mu,sample variance)
%with mu = 0 and sample variance = 1
%sample size
for n = 2:100     
%independent draws given N(0,1)
X = randn(n,1);
%sample mean
Xbar = sum(X)/n
%sigma-hat squared
X2bar = sum(X.^2)/n;
sigmahat2 = X2bar-Xbar^2
%sample variance
S2= (n/(n-1))*sigmahat2
%continuation
%setting the number of repetitions
M=10000
%Creating the Mx1 vectors to save the realized sample stats
RealizedXbar=NaN(M,1);
realizedsigmahat2 = NaN(M,1);
RealizedS2 = NaN(M,1);
%looping the repetitions
for m= 1:M
    
    %generating the random sample
    X = randn(n,1);
    
    %computing the sample stats
    Xbar = sum(X)/n;
    X2bar = sum(X.^2)/n;
    sigmahat2 = X2bar-Xbar^2;
    S2 = (n/(n-1))*sigmahat2;
    
    %lastly, saving the sample stats
    RealizedXbar(m,1) = Xbar;
    Realizedsigmahat2(m,1) = sigmahat2;
    RealizedS2(m,1) = S2;
end
%=============================================================================================================================
%ii) t-stat for testing null hypothesis Ho:mu = 0
 tstat= RealizedXbar./sqrt(RealizedS2/n)
%=============================================================================================================================
%iii) Record whether the abs value of t-stat exceeds cn-1(0.05)
%recall n = 2, so n-1 = 1
alpha=0.05;
c=tinv(1-alpha/2,n-1);
%proportion
rejt_of_n=sum(tstat>c | tstat<-c, "all")/M
%=============================================================================================================================
%iv) Record whether the abs value of t-stat exceeds c(0.05)
c=norminv(0.975);
%proportion
rejN_of_n=sum(tstat>c | tstat<-c, "all")/M
%from the value given, 0.2904, it shows that it is not approximating well
%=============================================================================================================================
%B repeat part a using n=3,4.....100. Graph both rejt(n) & rejN(n)
%as functions of n. Set the vertical axis values in both graphs to range
%from 0-3
end

[Jardine Shi]

ahhh I see, that was rather surprising. I thought it would be something very difficult. Thanks for your help!

[Jardine Shi]

quick question here, how to set the range of a graph ? e.g. range for vertical & horizontal axis

[KSSV]

Read about axis.

[Jardine Shi]

yeap, I just found it. I just need to put xlim or ylim on the last line hahaha

[KSSV]

axis works for both the limits at once...._xlim_, ylim is to fix seperately.

And thanks is accepting/ voting the answer. :)