In this project, we are going to implement parameter estimation by method of moments and then maximum likelihood in R. We are using R as it allows for easy random sampling and quick calculation.
The problem statement is taken from Chapter 8 (Estimation of Parameters and Fitting of Probability Distributions) Question no. 43 of "Mathematical Statistics and Data Analysis" by John A. Rice (University of California, Berkeley).
The question contains a lot of parts, but we have consolidated some of these parts together in order to re-use code and answer as much as possible together.
The data set gamma-arrivals consists of data collected from the Compton Gamma Ray Observatory, a satellite launched by NASA in 1991. This dataset contains the interarrival times, the times between arrivals, of 3935 photons measured in seconds.
It is written in the code as comments.