AdequacyModel (version 1.0.1)

goodness.fit: Adequacy of models

Description

This package provides some useful functions for calculating measures of goodness of fit, including statistics Cramer-von Mises and Anderson-Darling. These statistics are often used to compare models not fitted. You can also calculate other medias goodness of fit as the AIC, CAIC and BIC.

Usage

goodness.fit(fdp, fda, starts, datas, method = "SANN")

Arguments

fdp

Specification of the probability density function.

fda

Specification of cumulative distribution function.

starts

Initial parameters to maximize the likelihood function.

datas

Data vector considered.

method

This option refers to the choice of method to be used to maximize the log-likelihood function. The default method is the SANN (Simulated Annealing). Outas options accepted are: BFGS and CG. It is also accepted as the

encoding

latin1

Details

The function returns the maximum likelihood estimates as well as some statistical goodness of fit. The goodness of fit statistics are returned: Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC) and Consistent Akaikes Information Criterion (CAIC). Such measures are commonly used to compare two models fitted. For models not fitted comparing statistics is returned Cramer-von Mises (W) and Anderson-Darling (A). These statistics are described in detail in Chen and Balakrishnan (1995).

References

Chen, G., Balakrishnan, N. (1995). A general purpose approximate goodness-of-fit test. Journal of Quality Technology 27, 154-161.

See Also

nlminb, optim

Examples

data(carbone)
carbone = c(3.70, 2.74, 2.73, 2.50, 3.60, 3.11, 3.27, 2.87, 1.47,
            3.11, 4.42, 2.4, 3.19, 3.22, 1.69, 3.28, 3.09, 1.87,
            3.15, 4.90, 3.75,2.43, 2.95, 2.97, 3.39, 2.96, 2.53,
           2.67, 2.93, 3.22, 3.39, 2.81, 4.20, 3.33, 2.55, 3.31,
           3.31, 2.85, 2.56, 3.56, 3.15, 2.35, 2.55, 2.59, 2.38,
           2.81, 2.77, 2.17, 2.83, 1.92, 1.41, 3.68, 2.97, 1.36,
           0.98, 2.76, 4.91, 3.68, 1.84, 1.59, 3.19, 1.57, 0.81,
           5.56, 1.73, 1.59, 2.00, 1.22, 1.12, 1.71, 2.17, 1.17, 
           5.08, 2.48, 1.18, 3.51, 2.17, 1.69, 1.25, 4.38, 1.84,
           0.39, 3.68, 2.48, 0.85, 1.61, 2.79, 4.70, 2.03, 1.80,
           1.57, 1.08, 2.03, 1.61, 2.12, 1.89, 2.88, 2.82, 2.05,
           3.65)
           
we <- function(par,x){
  c = par[1]
  theta = par[2]
  alpha = par[3]
  ((c*theta)/alpha)*((x/alpha)^(c-1))*exp(-(x/alpha)^c)*((1 - exp(-(x/alpha)^c))^(theta-1))
}

fda_we <- function(par,x){
  c = par[1]
  theta = par[2]
  alpha = par[3]
  (1-exp(-(x/alpha)^c))^theta
}

goodness.fit(fdp=we,fda = fda_we, start=c(1,2,1,1), method="Nelder-Mead",
             datas=carbone)