In this problem you are to extend the rejection method so that a random variable having infinite support can be generated. The target pdf describes the generalized Gaussian random variable, which is defined by
Where m is the mean, v is the mode σ is a parameter, and Γ(·) denotes the gamma function. Note that for v = 2, fX(x) is Gaussian.
(a) Plot the generalized Gaussian pdf for m = 0 and v = 1, 1.5, 2, and 2.5.
(b) Develop, using a rejection method, an algorithm for generating X with v = 1.5 and m = 0. Select a bounding function and plot both the bounding function and fX(x).
(c) Using the algorithm with v = 1.5 and m = 0, generate 10,000 values of X. Plot the resulting histogram and compare with the theoretical pdf.