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Simulation: 2018 Tutorial 2 question 4(a)

0 votes
asked Mar 24 in STA 2004F - Statistical Theory and Inference by Ireneus (540 points)
What does the following question trying to say? 

Given a random variable X with the following density
                                        f(x)=5/x^6 for x greater than or equal to 1
a) Explain how you would simulate realisations from from X when supplied with uniform random numbers.

2 Answers

+1 vote
answered Mar 25 by Pandy (2,530 points)

My understanding is that they're asking you to simulate the random variable with the given PDF \(f(x)\), but making use of the Uniform distribution instead.

This is generally done when one can't simulate realizations of a random variable directly.

I imagine they're wanting you to use the Probability Integral Transform.

0 votes
answered Apr 2 by PaulBotes (430 points)

Find the CDF, \(F_x(x)\) of the distribution and then find its inverse \(F^{-1}_x(x)\).  \(F^{-1}_x(U)\) where \(U \sim U(0,1)\) will then admit realisations from the random variable.