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Statistics[Distributions]

  

VonMises

  

von Mises distribution

 

Calling Sequence

Parameters

Description

Examples

References

Calling Sequence

VonMises(b, a)

VonMisesDistribution(b, a)

Parameters

b

-

shape parameter

a

-

distribution mode

Description

• 

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

ft=0t<aπ&ExponentialE;bcosta2πBesselI0&comma;bta+π0otherwise

  

subject to the following conditions:

0<b,a::real

• 

The von Mises variate with location parameter a and scale parameter b tending to 0 from the right, tends to the Uniform variate Uniform(a - Pi, a + Pi).

• 

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

Examples

withStatistics&colon;

XRandomVariableVonMisesb&comma;a&colon;

PDFX&comma;u

0u<aπ&ExponentialE;bcosau2πBesselI0&comma;bua+π0otherwise

(1)

PDFX&comma;Pi2assumingPi2<a&comma;a<3Pi2

&ExponentialE;bsina2πBesselI0&comma;b

(2)

ModeX

a

(3)

MeanX

a

(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]