Chapter 4 Univariate random variables

This chapter will deal with algorithms for simulating observations from a distribution on \(\mathbb{R}\) or any subset thereof. There can be several purposes of doing so, for instance:

  • We want to investigate properties of the distribution.
  • We want to simulate independent realizations of univariate random variables to investigate the distribution of a transformation.
  • We want to use Monte Carlo integration to compute numerically an integral (which could be a probability).

In this chapter the focus is on the simulation of a single random variable or an i.i.d. sequence of random variables primarily via various transformations of pseudorandom numbers. The pseudo random numbers themselves being approximate simulations of i.i.d. random variables uniformly distributed on \((0, 1)\).