Rockwell-automation Arena Basic Edition Users Guide Manual do Utilizador descarregar pdf (Página 75)

A • STATISTICAL DISTRIBUTIONS

• • • • •

A • Statistical Distributions

Lognormal(

)LOGNORMAL(LogMean, LogStd) or

LOGN(LogMean, LogStd)

Mean LogMean (

> 0) and standard deviation LogStd (

> 0) of the lognormal random

variable. Both LogMean and LogStd must be specified as strictly positive real numbers.

[0, +

LogMean =

(LogStd)

The lognormal distribution is used in situations in which the quantity is the product of a

large number of random quantities. It is also frequently used to represent task times that

have a distribution skewed to the right. This distribution is related to the normal

distribution as follows. If X has a lognormal (

) distribution, then ln(X) has a normal

(

) distribution. Note that

and

are not the mean and standard deviation of the

Probability

Density

Function

Denote the user-specified input parameters as

LogMean =

and LogStd =

Then let

the probability density function can then be

written as

)/ln(

222

lll

μσμ

and

[

]

(ln

lll

μμσσ

f(x) =

)2/())(ln(

σμ

πσ

−− x

for x > 0

0otherwise

Parameters

Range

∞)

Mean

μσ

2⁄+

Variance

μσ

1–()

Applications

1 2 ... 70 71 72 73 74 75 76 77 78 79 80 ... 89 90

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