MATLAB Examples

Contents

Generate N Standard Normally Distributed Random Variable

N = 1000000;
X = randn(N,1);

Points for which CDF and PDF are to be evaluated

x = linspace(-10,10,1000);

Estimate PDF and CDF

[f,F] = EstimateDistribution(X,x);

Plot Results

figure(1);
plot(x,f,x,F);
xlabel('x');
ylabel('Simulated PDF & CDF');
str1 = strcat('PDF;','Area = ',num2str(trapz(x,f)));
legend(str1,'CDF','Location','northwest');

Generate N Gaussianly Distributed Random Variable with specific mean and

Standard Deviation

N = 1000000;
mu = -1;
sigma = 5;
X = mu + sigma*randn(N,1);

Points for which CDF and PDF are to be evaluated

x = linspace(-10,10,1000);

Theoretical PDF and CDF

fx = (1/sqrt((2*pi*sigma*sigma)))*exp(-(((x - mu).^2)/(2*sigma*sigma)));
Fx = 0.5*(1 + erf((x - mu)/(sqrt(2*sigma*sigma))));

Estimate PDF and CDF

[f,F] = EstimateDistribution(X,x);

Plot Results

figure(2);
plot(x,f,x,fx,x,F,x,Fx);
xlabel('x');
ylabel('PDF & CDF');
str1 = strcat('Simulated PDF;','Area = ',num2str(trapz(x,f)));
str2 = strcat('Theoretical PDF;','Area = ',num2str(trapz(x,fx)));
legend(str1,str2,'Simulated CDF','Theoretical CDF','Location','northwest');

Generate N Uniformaly Distributed Random Variable

N = 1000000;
X = rand(N,1);

Points for which CDF and PDF are to be evaluated

x = linspace(-10,10,1000);

Estimate PDF and CDF

[f,F] = EstimateDistribution(X,x);

Plot Results

figure(3);
plot(x,f,x,F);
xlabel('x');
ylabel('Simulated PDF & CDF');
str1 = strcat('PDF;','Area = ',num2str(trapz(x,f)));
legend(str1,'CDF','Location','northwest');