dcusp: Cobb's Cusp Distribution

In cusp: Cusp-Catastrophe Model Fitting Using Maximum Likelihood

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) 

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

Details

The cusp distribution is defined by

f(y) = Ψ \exp(α y + β y^2/2 - y^4/4),

where Ψ is the normalizing constant.

rcusp uses rejection sampling to generate samples.

qcusp implements binary search and is rather slow.

Value

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

Author(s)

Raoul Grasman

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)

Example output

[1] 0.002845046
[1] 0.002802908
[1] 0.125
  [1] 2.1138156 1.9084996 1.8499006 1.6034992 1.5848891 2.0834681 2.3916107
  [8] 1.0866281 1.7517574 1.6765625 2.2128962 1.5584022 1.6858524 2.0065576
 [15] 2.3930447 2.0962522 1.9312345 1.7188332 1.8070624 2.4178738 2.6019497
 [22] 1.1982729 2.3058361 1.8649085 1.4937600 2.0810587 2.2697907 2.0907782
 [29] 2.2422741 1.5142936 1.9870952 2.2982058 2.1015882 1.4886337 1.3218375
 [36] 2.2317231 1.7744893 2.1898212 2.2524980 1.8559179 1.8925744 2.2491147
 [43] 1.2760692 1.8087227 2.0390539 1.9257983 1.8861800 1.6982375 1.9365106
 [50] 0.9044911 2.1400074 1.8417989 1.9140590 1.5411629 1.6419498 1.8637986
 [57] 1.6510275 2.2721653 1.9993832 2.3107794 1.6903990 2.0327278 2.0954383
 [64] 2.3418746 1.6046308 2.1668127 1.9220138 2.0955677 2.4186826 1.7756948
 [71] 1.8581650 2.2021594 2.1512043 0.7712528 1.6645917 1.1029077 0.6741006
 [78] 2.0401718 1.5528974 2.2235380 2.4811902 1.3320410 0.9765473 2.3920597
 [85] 1.6180805 2.2532043 2.1089776 2.4993756 2.5361994 1.9522753 1.8550015
 [92] 0.8666078 2.1456588 1.8160571 1.6351539 2.6908218 1.6379914 1.2809692
 [99] 1.8909668 2.2637689
 [1] -1.41808630  1.79161061  0.32945641 -0.40240001  0.04857878 -1.29911768
 [7]  0.24326541 -1.30372793 -0.99968661  0.73655481  1.52609023 -0.35988342
[13]  0.06745068 -1.34125194  0.06861124 -0.47717889 -1.19219900 -1.93968854
[19]  0.91166941  1.36143411

cusp documentation built on May 2, 2019, 6:51 p.m.