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Statistics for Process Control Engineers by Myke King

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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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