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Generating Random Numbers
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Mean, Variance, Standard Deviation
Mean:mean(x)Variance:mean((x-mean(x).*(x-mean(x)))Standard
Deviationstd(x)
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Correlation Coefficient
Correlation coefficient
function r = corco(x,y)
mx = mean(x);
my = mean(y);
covxy = mean((x-mx).*(y-my));
r = covxy/(std(x)*std(y));
Or use Matlab functioncorrcoef
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Random Numbers
rand(M,N):MxN matrix of uniformly distributed random numbers on
(0,1)randn(M,N)MxN matrix of normally distributed random numbers
(=0, 2=1)normrnd(m,s,M,N)MxN matrix of normally distributed random
numbers (=m, =s)
x=randn(1,10000);
mean((x
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Correlation Coefficient
x=normrnd(0,1,1,100);
y=2*x+1;
r=corrcoef(x.',y.')
plot(x,y,'+')
n=normrnd(0,1,1,100);
y=2*x+1+n;
r=corrcoef(x.',y.')
plot(x,y,'+')
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Joint Gaussian
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Joint Gaussian
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Joint Gaussian
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Joint Gaussian
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Generating Random Numbers
Generate
Return
Uniform
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Uniform
function genuni(N,a,b)
u=rand(1,N);
x=a+(b-a).*u;
minx=min(x);
maxx=max(x);
NumBins=51;
h=hist(x,NumBins);
for k=1:NumBins,
bincenters(k)=minx+((maxx-minx)/NumBins)*(k-1/2);
end
h=h/sum(h);
bar(bincenters,h)
Or use Matlab function unifrnd(a,b,M,N)
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Generating Random Numbers
Generate
Return
Exponential
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Exponential
function genexp(N,lambda)
u=rand(1,N);
x=-1/lambda.*log(1-u);
Or use Matlab function exprnd(lambda,M,N)
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Generating Random Numbers
Generate
Set
Generate
Return
Normal
Rayleigh
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Normal
function gennormal(N,mu,sigma)
for i=1:N
u=rand; z=sigma*(sqrt(2*log(1/(1-u))));
u=rand;
x1(i)=mu+z*cos(2*pi*u);
x2(i)=mu+z*sin(2*pi*u);
end
Or use Matlab function normrnd(mu,sigma,M,N)
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Generating Random Numbers
Generate IID Bernoulli(p) random numbers
Return
Binomial
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Binomial
function genbino(N,n,p)
for i=1:N,
u=rand(1,n);
y=(u
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Generating Random Numbers
Generate
Return
Geometric
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Geometric
function gengeo(N,p)
u=rand(1,N);
x=ceil(log(1-u)/log(1-p));
Or use Matlab function geornd(p,M,N)
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Generating Random Numbers
Set
Generate and replace by
If accept else increase by one and return to step 2
Poisson
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Poisson
function genpois(N,lambda)
for i=1:N,
k=0;p=1;
u=rand;
p=p*u;
while p>=exp(-lambda)
u=rand;
p=p*u;
k=k+1;
end
x(i)=k;
end
Or use Matlab function poissrnd(lambda,M,N)
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