Statistics[Distributions]
VonMises
von Mises distribution
Calling Sequence
Parameters
Description
Examples
References
VonMises(b, a)
VonMisesDistribution(b, a)
b
-
shape parameter
a
distribution mode
The von Mises distribution is a continuous probability distribution with probability density function given by:
ft=0t<a−πⅇbcost−a2πBesselI0,bt≤a+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.
withStatistics:
X≔RandomVariableVonMisesb,a:
PDFX,u
0u<a−πⅇbcosa−u2πBesselI0,bu≤a+π0otherwise
PDFX,π2assuming−π2<a,a<3π2
ⅇbsina2πBesselI0,b
ModeX
MeanX
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[RandomVariable]
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