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Statistics for Process Control Engineers by Myke King

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Chapter 23Pareto Distribution

There are four types of Pareto distribution. Originally developed for exploring the distribution of wealth, they lead to Pareto analysis and to the Pareto principle, or ‘80/20 rule’, familiar to many engineers.

23.1 Pareto Type I

The Pareto‐I distribution is described by the PDF

(23.1)images

The shape parameter δ is sometimes described as the tail index; β is the minimum nonzero value that x can have. Figure 23.1 shows the effect of changing these parameters.

x vs. f(x) displaying 3 right-skewed curves for ϐ = 0.5 and δ = 0.6, ϐ = 0.3 and δ = 0.3, and ϐ = 0.1 and δ = 0.1.

Figure 23.1 Pareto‐I: Effect of β and δ on shape

The CDF is

(23.2)images

The QF is

(23.3)images

The moments are given by

(23.4)images

From this can be derived

(23.5)images

(23.6)images
(23.7)images
(23.8)

One application is to assess the ...

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