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

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Jardine Shi 2020-11-19

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https://ww2.mathworks.cn/matlabcentral/answers/653318-how-to-do-looping-with-over-many-variables-monte-carlo

评论： KSSV 2020-11-19

采纳的回答： KSSV

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

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Answer 1

KSSV 2020-11-19

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https://ww2.mathworks.cn/matlabcentral/answers/653318-how-to-do-looping-with-over-many-variables-monte-carlo#answer_549588

在 MATLAB Online 中打开

for n = 3:100
n
end

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Jardine Shi 2020-11-19

在 MATLAB Online 中打开

%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 2020-11-19

在 MATLAB Online 中打开

%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