problem-9.20

problem-9.20  A plot of both the empirical density and the theoretical density of the gamma distribution with parameters chosen by fitdistr() can be produced as follows:
> library(MASS)
> fitdistr(rivers,"gamma")
     shape       rate
  2.5783541   0.0043609
 (0.2489438) (0.0004386)
... skip warnings ...
> plot(density(rivers))
> x = 0:4000
> lines(x, dgamma(x,shape=2.578, rate= 0.00436), lty=2)
    
The gamma shape matches the data, but the tail behavior does not seem that similar. A quantile-quantile plot will show this:
> qqplot(rivers, rgamma(100,shape=2.578, rate= 0.00436))