Hoaglin (1980) suggested a “Poissoness plot”-a simple visual method for assessing goodness of fit. The expected frequencies for a sample of size n from a Poisson distribution are

Thus, a plot of log(0k) log k! versus k should yield nearly a straight line with a slope of log  and an intercept of log n – . Construct such plots for the data of Problems 1, 2, and 3 of chapter 8. Comment on how straight they are A random variable X is said to follow a lognormal distribution if Y = log(X) follows a normal distribution. The lognormal is sometimes used as a model for heavy-tailed skewed distributions.

a Calculate the density function of the lognormal distribution.

b Examine whether the lognormal roughly fits the following data (Robson 1929), which are the dorsal lengths in millimeters of taxonomically distinct octopods.

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