cusp (version 2.3.6)

dcusp: Cobb's Cusp Distribution

Description

Functions for the cusp distribution.

Usage

dcusp(y, alpha, beta)
pcusp(y, alpha, beta, subdivisions = 100, rel.tol = .Machine$double.eps^0.25, 
            abs.tol = rel.tol, stop.on.error = TRUE, aux = NULL, keep.order = TRUE)
qcusp(p, alpha, beta)
rcusp(n, alpha, beta)

Value

dcusp gives the density function, pcusp gives the distribution function, qcusp gives the quantile function, and rcusp generates observations.

Arguments

y

vector of quantiles

p

vector of probabilities

n

number of observations.

alpha

normal/asymmetry factor value of cusp density

beta

bifurcation/splitting factor value of cusp density

subdivisions

See cusp-package.

rel.tol

See cusp-package.

abs.tol

See cusp-package.

stop.on.error

See cusp-package.

aux

See cusp-package.

keep.order

logical. If true the order of the output values is the same as those of the input values y

Author

Raoul Grasman

Details

The cusp distribution is defined by $$ f(y) = \Psi \exp(\alpha y + \beta y^2/2 - y^4/4), $$ where \(\Psi\) is the normalizing constant.

rcusp uses rejection sampling to generate samples.

qcusp implements binary search and is rather slow.

References

See cusp-package, integrate

See Also

cusp-package

Examples

    # evaluate density and distribution
    dcusp(0,2,3)
    pcusp(0,2,3)
    pcusp(qcusp(0.125,2,3),2,3) # = 0.125
    
    # generate cusp variates
    rcusp(100, 2, 3) 
    
    # generate cusp variates for random normal and splitting factor values
    alpha = runif(20, -3, 3)
    beta =  runif(20, -3, 3)
    Vectorize(rcusp)(1, alpha, beta)