As a commonly used distribution, we covered the gamma distribution in detail in Section 12.10. This chapter describes the range of possible modifications.

The *inverse gamma distribution* is also known as the *Pearson‐V distribution* and was covered in Section 27.5.

There are at least five distributions that are described as the *log‐gamma distribution*. In no particular order, the PDF of the first is

(31.1)

Raw moments are given by

(31.2)

This leads to

(31.3)

(31.4)

By replacing *δ*_{2} with 1/*δ*_{2}, we obtain the same distribution that might, at first glance, appear different

Figure 31.1 plots Equation (31.5) and shows, with *α* fixed at zero, the effect of varying *δ*_{1} and *δ*_{2}.

Raw moments are given by

(31.6)

This leads to

(31.7)

(31.8)

Fitting to the C_{4} in propane data, with ...

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