circular (version 0.5-2)

Cardioid: Cardioid Density Function

Description

Density and random generation for the Cardioid circular distribution.

Usage

dcardioid(x, mu = circular(0), rho = 0)
rcardioid(n, mu = circular(0), rho = 0, control.circular=list())

Value

dcardioid gives the density and rcardioid generates random deviates.

Arguments

x

a vector. The object is coerced to class circular.

n

number of observations.

mu

mean direction of the distribution. The object is coerced to class circular.

rho

concentration parameter of the distribution. Absolute value of rho must be less than 0.5.

control.circular

the coordinate system used in the output of rcardioid. See circular for details.

Author

Claudio Agostinelli and Ulric Lund

Details

Random generation is done by rejection sampling. Prior versions (<0.5-1) had a bug in the simulation with negative rho's.

See alternative and other cardioid-related functions at Pewsey (2025).

References

Jammalamadaka, S. Rao and SenGupta, A. (2001). Topics in Circular Statistics, Section 2.2.2, World Scientific Press, Singapore. Pewsey, A. (2025). On Jeffreys’s cardioid distribution. Computational Statistics and Data Analysis.

Examples

  set.seed(1234) 
  resrad <- rcardioid(n=10)
  set.seed(1234)
  resdeg <- rcardioid(n=10, control.circular=list(units="radians", zero=pi))  
  max(abs(resrad - conversion.circular(resdeg, zero=0)))