Problem 1.4 1. Open and run the script file powerspot.asc to create the numeric vector PSPOT. The entries of this vector represent the daily Palo Verde (firm on peak) spot prices of electricity between January 4, 1999 and August 19, 2002.

2. Use exploratory data analysis tools to argue that the tails of the distribution are heavy, fit a GPD to the data, and provide estimates of the shape parameters.

Problem 1.5 The goal of this problem is to design and use a home-grown random number generator for the exponential distribution.

1. Compute the cdf Fλ(x) = P{X ≤ x} of a random variable X with an exponential distribution with parameter λ > 0.

2. Compute its inverse F

−1

λ and write an S-Plus function myrexp which takes the parameters N, and LAMBDA, and which returns a numeric vector of length N containing N samples of random variates from the exponential distribution with parameter LAMBDA.

3. Use your function myrexp to generate a sample of size N = 1024 from the exponential distribution with mean 1.5, use the function rexp from the S-Plus distribution to generate a sample of the same size from the same distribution, and produce a Q-Q plot of the two samples.

Are you satisfied with the performance of your simulation function myrexp? Explain.