How to draw a random number from Cauchy Distribution with a particular mean and standard deviation?

We can generate a random number from the normal distribution with mean parameter mu and standard deviation parameter sigma using normrnd(mu,sigma). However, how can we generate a random number from the Cauchy distribution using specific mu and sigma;, e.g., mu=0.5 and sigma=0.1?

Answer 1

[Chunru]

Using the fact that Cauchy distribution is the Student's t distribution with dof=1.

mu =4e5; sigma = 20;
r = mu+sigma*trnd(1, 100000, 1);    % mu, signam: location and scale parameters (not mean and std)
hist(r, 1000); 

[Md. Asadujjaman]

Thanks for your reply. However, I need to generate a random number from the Cauchy distribution using a specific mu and sigma; e.g., mu=0.5 and sigma=0.1.

[Chunru]

We are generating Caucht distributed random numbers above with mu and sigma!!! You can change mu and sigma to any value you like.

mu =0.5; sigma = 0.1;
r = mu+sigma*trnd(1, 10, 1)

r = 10×1

0.2176 0.2956 0.7131 0.3013 0.1826 0.1251 0.5845 0.6408 0.4869 0.7205

[Md. Asadujjaman]

Thanks.

Answer 2

[Image Analyst]

From the link on the right:

https://www.mathworks.com/help/stats/generate-standard-cauchy-random-numbers-using-students-t-distribution.html?s_tid=answers_rc2-2_p5_MLT

[Md. Asadujjaman]

Thnaks for your reply. However, here mu = 0 and sigma = 1 is fixed. If we want to change the mu and sigma, e.g mu = 0.5 and sigma = 0.1, then what should to do?

[Image Analyst]

https://www.mathworks.com/help/stats/work-with-the-cauchy-distribution-using-the-t-location-scale-distribution.html

[Md. Asadujjaman]

Thank you.