Statistics[Distributions] - Maple Programming Help

Online Help

All Products    Maple    MapleSim


Home : Support : Online Help : Statistics and Data Analysis : Statistics Package : Distributions : Statistics/Distributions/Gamma

Statistics[Distributions]

  

Gamma

  

gamma distribution

 

Calling Sequence

Parameters

Description

Examples

References

Calling Sequence

Gamma(b, c)

GammaDistribution(b, c)

Parameters

b

-

scale parameter

c

-

shape parameter

Description

• 

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

ft=0t<0tbc1&ExponentialE;tbbΓcotherwise

  

for 0<b&comma;0<c where Γc is the Gamma function.

• 

The gamma variate with scale parameter b and shape parameter 1 is equivalent to the Exponential variate with scale parameter b.

• 

The gamma variate with scale parameter 1 and shape parameter c is equivalent to the Erlang variate with shape parameter c.

• 

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

Examples

withStatistics&colon;

XRandomVariableGammaDistributionb&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)

VarianceX

b2c

(4)

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]

 


Download Help Document

Was this information helpful?



Please add your Comment (Optional)
E-mail Address (Optional)
What is ? This question helps us to combat spam