The file gamma-arrivals contains another set of gamma-ray data, this one consisting of the times between arrivals (interarrival times) of 3,935 photons (units are seconds).
a. Make a histogram of the interarrival times. Does it appear that a gamma distribution would be a plausible model?
b. Fit the parameters by the method of moments and by maximum likelihood. How do the estimates compare?
c. Plot the two fitted gamma densities on top of the histogram. Do the fits look reasonable?
d. For both maximum likelihood and the method of moments, use the bootstrap to estimate the standard errors of the parameter estimates. How do the estimated standard errors of the two methods compare?
e. For both maximum likelihood and the method of moments, use the bootstrap to form approximate confidence intervals for the parameters. How do the confidence intervals for the two methods compare?
f. Is the interarrival time distribution consistent with a Poisson process model for the arrival times?
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