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Statistics for Process Control Engineers
book

Statistics for Process Control Engineers

by Myke King
October 2017
Intermediate to advanced content levelIntermediate to advanced
624 pages
17h 24m
English
Wiley
Content preview from Statistics for Process Control Engineers

25Beta Distribution

As one of the more commonly used distributions, the classic beta distribution was described in Section 12.3. Here we cover special cases and enhancements.

25.1 Arcsine

Setting, in Equation (12.13), both δ1 and δ2 to 0.5 gives the special case known as the arcsine distribution

(25.1)images

It is the CDF that gives the distribution its name

(25.2)images

Inverting give the QF

(25.3)images

Statistical parameters are

(25.4)images
(25.5)images
(25.6)images
(25.7)images

There is also the second kind of the arc‐sine distribution; its PDF is

(25.8)images

Figure 25.1 shows both kinds. Without a shape factor they cannot be fitted to data but, in any case, it is difficult to see what application either of the anti‐modal distributions ...

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Publisher Resources

ISBN: 9781119383505