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Statistics for Process Control Engineers by Myke King

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21Burr Distribution

There are 12 Burr distributions.[11] In many cases there are no published formulae for mean, variance, skewness or kurtosis. Although these might be developed, the majority of the distributions would offer a poor fit to process data that would almost certainly be bettered by other distributions for which the formulae exist. Indeed, they are largely neglected in the literature. The exception is Type XII, which we will show gives one of the best fits to the C4 in propane data.

21.1 Type I

The Burr‐I distribution is more commonly known as the uniform distribution, as described in Section 5.1.

21.2 Type II

The Burr‐II distribution is also known as the generalised logistic distribution, as described in the next chapter.

21.3 Type III

The Burr‐III distribution is described by the PDF

(21.1)images

Figure 21.1 shows the effect of varying δ1 and δ2 with α fixed at 0 and β at 1. The CDF is

(21.2)images

Fitting to the C4 in propane data gives α as −4.35, β as 3.84, δ1 as 4.86 and δ2 as 35.3. RSS is 0.0399.

x vs. f(x) displaying 3 right-skewed curves for δ1 = 2 and δ2 = 4, δ1 = 2 and δ2 = 2, and δ1 = 1 and δ2 = 2, illustrating the effect of varying δ1 and δ2 with α fixed at 0 and ϐ at 1.

Figure 21.1 Burr‐III: Effect of δ1 and δ2 on shape

The CDF can be inverted to give the QF.

(21.3)

21.4 Type IV

The Burr‐IV distribution is described by the PDF

(21.4) ...

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