Chapter 4 Exercises

Exercise 4.1

Generate some data from the Wald distribution with known parameter values \(m=2\), \(a=2.5\), \(T=0.5\), and fit the Wald back to the generated data using maximum likelihood estimation. For large \(N\), you should find a close agreement between the ML parameter estimates and the true values.

To generate data from the Wald distribution, note that the Wald distribution is directly related to the inverse Gaussian distribution. Specifically, data from the Wald with parameters \(m\) (drift) and \(a\) (boundary) are distributed as \(IG(a/m,a^2)\). A number of packages are provided on CRAN to simulate from the inverse gaussian; we used the rinvgauss function in the library statmod.