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Statistics[Distributions][Erlang] - Erlang distribution

Calling Sequence

Erlang(b, c)

ErlangDistribution(b, c)

Parameters

b

-

scale parameter

c

-

shape parameter

Description

• 

The Erlang distribution is a continuous probability distribution with probability density function given by:

ft=0t<0tbc1&ExponentialE;tbbΓcotherwise

  

subject to the following conditions:

0<b&comma;c::posint

• 

The Erlang distribution is equivalent to the Gamma distribution except for the imposed condition that c is a positive integer.

• 

Note that the Erlang command is inert and should be used in combination with the RandomVariable command.

Examples

withStatistics&colon;

X:=RandomVariableErlangb&comma;c&colon;

PDFX&comma;u

&lcub;0u<0ubc1&ExponentialE;ubb&Gamma;cotherwise

(1)

PDFX&comma;0.5

0.5bc1.&ExponentialE;0.5bb&Gamma;c

(2)

MeanX

bc

(3)

See Also

Statistics, Statistics[Distributions], Statistics[RandomVariable]

References

  

Evans, Merran; Hastings, Nicholas; and Peacock, Brian. Statistical Distributions. 3rd ed. Hoboken: Wiley, 2000.

  

Johnson, Norman L.; Kotz, Samuel; and Balakrishnan, N. Continuous Univariate Distributions. 2nd ed. 2 vols. Hoboken: Wiley, 1995.

  

Stuart, Alan, and Ord, Keith. Kendall's Advanced Theory of Statistics. 6th ed. London: Edward Arnold, 1998. Vol. 1: Distribution Theory.


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