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Student[Statistics]

  

GammaRandomVariable

  

gamma random variable

 

Calling Sequence

Parameters

Description

Examples

References

Compatibility

Calling Sequence

GammaRandomVariable(b, c)

Parameters

b

-

scale parameter

c

-

shape parameter

Description

• 

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

ft=0t<0tbc1&ExponentialE;tbbΓcotherwise

  

subject to the following conditions:

0<b&comma;0<c

• 

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.

Examples

withStudent&lsqb;Statistics&rsqb;&colon;

XGammaRandomVariableb&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)

YGammaRandomVariable2&comma;3&colon;

PDFY&comma;x&comma;output&equals;plot

CDFY&comma;x

&lcub;0x018x2&ExponentialE;12x12&ExponentialE;12xx&ExponentialE;12x&plus;10<x

(5)

CDFY&comma;6&comma;output&equals;plot

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.

Compatibility

• 

The Student[Statistics][GammaRandomVariable] command was introduced in Maple 18.

• 

For more information on Maple 18 changes, see Updates in Maple 18.

See Also

Statistics[Distributions][Gamma]

Student

Student[Statistics]

Student[Statistics][RandomVariable]

 


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