Rockwell-automation Arena Basic Edition Users Guide Bedienungsanleitung PDF herunterladen (Seite 67)

A • STATISTICAL DISTRIBUTIONS

• • • • •

A • Statistical Distributions

Beta(

)BETA(Beta, Alpha)

Shape parameters Beta (β) and Alpha (α) specified as positive real numbers.

[0, 1] (Can also be transformed to [a,b] as described below)

Because of its ability to take on a wide variety of shapes, this distribution is often used as

a rough model in the absence of data. Also, because the range of the beta distribution is

from 0 to 1, the sample X can be transformed to the scaled beta sample Y with the range

from a to b by using the equation Y = a + (b-a)X. The beta is often used to represent

random proportions, such as the proportion of defective items in a lot.

Probabilit

Densit

Function

β 1–

1 x–()

α 1–

B βα(,)

---------------------------------------

0 otherwise

where

is the complete beta

function given by

B βα,() t

β 1–

1 t–()

α 1–

∫

f(x) =

for 0 < x < 1

Parameters

Range

Mean

βα+

-------------

Variance

βa

β a+()

β a 1++()

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Applications

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Rockwell-automation Arena Basic Edition Users Guide Bedienungsanleitung Seite 67