fitctp {cpd}R Documentation

Maximum-likelihood fitting of the CTP distribution

Description

Maximum-likelihood fitting of the Complex Triparametric Pearson (CTP) distribution with parameters aa, bb and γ\gamma. Generic methods are print, summary, coef, logLik, AIC, BIC and plot.

Usage

fitctp(x, astart = NULL, bstart = NULL, gammastart = NULL, 
          method = "L-BFGS-B", control = list(), ...)

Arguments

x

A numeric vector of length at least one containing only finite values.

astart

A starting value for the parameter a>0a>0; by default NULL.

bstart

A starting value for the parameter bb; by default NULL.

gammastart

A starting value for the parameter γ>max(0,2a)\gamma>max(0,2a); by default NULL.

method

The method to be used in fitting the model. See 'Details'.

control

A list of parameters for controlling the fitting process.

...

Additional parameters.

Details

If the starting values of the parameters aa, bb and γ\gamma are omitted (default option), they are computing by the method of moments (if possible; otherwise they must be entered).

The default method is "L-BFGS-B" (see details in optim function), but non-linear minimization (nlm) or those included in the optim function ("Nelder-Mead", "BFGS", "CG" and "SANN") may be used.

Standard error (SE) estimates for aa, bb and γ\gamma are provided by the default method; otherwise, SE for γ0\gamma_0 where γ=exp(γ0)\gamma=exp(\gamma_0) is computed.

Value

An object of class 'fitCTP' is a list containing the following components:

Generic functions:

References

Rodriguez-Avi J, Conde-Sanchez A, Saez-Castillo AJ, Olmo-Jimenez MJ (2004). “A triparametric discrete distribution with complex parameters.” Stat. Pap., 45, 81-95. doi:10.1007/BF02778271.

Olmo-Jimenez MJ, Rodriguez-Avi J, Cueva-Lopez V (2018). “A review of the CTP distribution: a comparison with other over- and underdispersed count data models.” Journal of Statistical Computation and Simulation, 88(14), 2684-2706. doi:10.1080/00949655.2018.1482897.

See Also

Plot of observed and theoretical frequencies for a CTP fit: plot.fitCTP

Maximum-likelihood fitting for the CBP distribution: fitcbp.

Maximum-likelihood fitting for the EBW distribution: fitebw.

Examples

set.seed(123)
x <- rctp(500, -0.5, 1, 2)
fitctp(x)
summary(fitctp(x, astart = 1, bstart = 1.1, gammastart = 3))

[Package cpd version 0.3.2 Index]