Erlang - Maple Help
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Statistics[Distributions]

  

Erlang

  

Erlang distribution

 

Calling Sequence

Parameters

Description

Examples

References

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,c::+

• 

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;

XRandomVariableErlangb&comma;c&colon;

PDFX&comma;u

0u<0ubc1&ExponentialE;ubbΓcotherwise

(1)

PDFX&comma;0.5

0.5bc1.&ExponentialE;0.5bbΓc

(2)

MeanX

bc

(3)

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.

See Also

Statistics

Statistics[Distributions]

Statistics[RandomVariable]