Rockwell-automation Arena Basic Edition Users Guide Manual do Utilizador descarregar pdf (Página 71)

A • STATISTICAL DISTRIBUTIONS

• • • • •

A • Statistical Distributions

Erlang(

)ERLANG(ExpMean,

) or ERLA(ExpMean,

)

If X1, X2, . . . , Xk are independent, identically distributed exponential random variables,

then the sum of these k samples has an Erlang-k distribution. The mean (

) of each of the

component exponential distributions and the number of exponential random variables (k)

are the parameters of the distribution. The exponential mean is specified as a positive real

number, and k is specified as a positive integer.

[0, +

The Erlang distribution is used in situations in which an activity occurs in successive

phases and each phase has an exponential distribution. For large k, the Erlang approaches

the normal distribution. The Erlang distribution is often used to represent the time

required to complete a task. The Erlang distribution is a special case of the gamma distri-

bution in which the shape parameter, α, is an integer (k).

Probability

Density

Function

f(x) =

k–

k 1–

x β⁄–

k 1–()!

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

f(x) =

for x > 0

0otherwise

Parameters

Range

∞)

Mean

Variance

Applications

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Rockwell-automation Arena Basic Edition Users Guide Manual do Utilizador Página 71