VonMises - Maple Help
For the best experience, we recommend viewing online help using Google Chrome or Microsoft Edge.
Our website is currently undergoing maintenance, which may result in occasional errors while browsing. We apologize for any inconvenience this may cause and are working swiftly to restore full functionality. Thank you for your patience.

Online Help

All Products    Maple    MapleSim


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;π2assumingπ2<a,a<3π2

&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]