The data of this exercise were gathered as part of a study t

The data of this exercise were gathered as part of a study to estimate the population
size of the bowhead whale (Raftery and Zeh 1993). The statistical procedures
for estimating the population size along with an assessment of the variability of
the estimate were quite involved, and this problem deals with only one aspect
of the problem—a study of the distribution of whale swimming speeds. Pairs
of sightings and corresponding locations that could be reliably attributed to the
same whale were collected, thus providing an estimate of velocity for each whale.
The velocities, v1, v2, . . . , v210 (km/h), were converted into times t1, t2, . . . , t210
to swim 1 km—ti = 1/vi . The distribution of the ti was then fit by a gamma
distribution. The times are contained in the file whales.
a. Make a histogram of the 210 values of ti . Does it appear that a gamma distribution
would be a plausible model to fit?
b. Fit the parameters of the gamma distribution by the method of moments.
c. Fit the parameters of the gamma distribution by maximum likelihood. How
do these values compare to those found before?
d. Plot the two gamma densities on top of the histogram. Do the fits look reasonable?
e. Estimate the sampling distributions and the standard errors of the parameters
fit by the method of moments by using the bootstrap.
f. Estimate the sampling distributions and the standard errors of the parameters
fit by maximum likelihood by using the bootstrap. How do they compare to
the results found previously?

Solution