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Statistics for Process Control Engineers by Myke King

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31Gamma Distribution

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

31.1 Inverse Gamma

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

31.2 Log‐Gamma

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)images

Raw moments are given by

(31.2)images

This leads to

(31.3)images
(31.4)images

By replacing δ2 with 1/δ2, 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 δ1 and δ2.

Log-gamma (1): Effect of δ1 and δ2 on shape, with α fixed at zero, displaying 2 ascending, descending curves for δ1 = 2, δ2 = 2 and δ1 = 2, δ2 = 1; and descending curve for δ1 = 1, δ2 = 0.5.

Figure 31.1 Log‐gamma (1): Effect of δ1 and δ2 on shape

Raw moments are given by

(31.6)

This leads to

(31.7)
(31.8)

Fitting to the C4 in propane data, with ...

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