| fitCDF {usefr} | R Documentation |
Usually the parameter estimation of a cummulative distribution function (*CDF*) are accomplished using the corresponding probability density function (*PDF*). DIfferent optimization algorithms can be used to accomplished this task and different algorithms can yield different esitmated parameters. Hence, why not try to fit the CDF directly?
fitCDF(varobj, distNames, plot = TRUE, plot.num = 1, only.info = FALSE, maxiter = 10^4, maxfev = 1e+05, ptol = 1e-12, verbose = TRUE)
varobj |
A a vector containing observations, the variable for which the CDF parameters will be estimated. |
distNames |
a vector of distribution numbers to select from the listed below in details section, e.g. c(1:10, 15) |
plot |
Logic. Default TRUE. Whether to produce the plots for the best fitted CDF. |
plot.num |
The number of distributions to be plotted. |
only.info |
Logic. Default TRUE. If true, only information about the parameter estimation is returned. |
maxiter, maxfev, ptol |
Parameters to ontrol of various aspects of the
Levenberg-Marquardt algorithm through function
|
verbose |
Logic. If TRUE, prints the function log to stdout |
The nonlinear fit (NLF) problem for CDFs is addressed with
Levenberg-Marquardt algorithm implemented in function
nls.lm from package *minpack.lm*. This function
is inspired in a script for the function
fitDistr from the package propagate [1]. Some
parts or script ideas from function fitDistr
are used, but here we to estimate CDF and not the PDF as in the case of
"fitDistr. A more informative are also
incorporated. The studentized residuals are provided as well.
The list (so far) of possible CDFs is:
Normal (Wikipedia)
Log-normal (Wikipedia)
Half-normal (Wikipedia). An Alternatively using a scaled precision (inverse of the variance) parametrization (to avoid issues if σ is near zero), obtained by setting θ=sqrt(π)/σ*sqrt(2).
Generalized Normal (Wikipedia)
T-Generalized Normal [2].
Laplace (Wikipedia)
Gamma (Wikipedia)
3P Gamma [3].
Generalized 4P Gamma [3] (Wikipedia)
Generalized 3P Gamma [3].
Weibull (Wikipedia)
3P Weibull (Wikipedia)
Beta (Wikipedia)
3P Beta (Wikipedia)
4P Beta (Wikipedia)
Beta-Weibull ReliaWiki
Generalized Beta (Wikipedia)
Rayleigh (Wikipedia)
Exponential (Wikipedia)
2P Exponential (Wikipedia)
After return the plots, a list with following values is provided:
aic: Akaike information creterion
fit: list of results of fitted distribution, with parameter values
bestfit: the best fitted distribution according to AIC
fitted: fitted values from the best fit
rstudent: studentized residuals
residuals: residuals
After x = fitCDF( varobj, ...), attributes( x$bestfit ) yields: $names [1] "par" "hessian" "fvec" "info" "message" "diag" "niter" "rsstrace" "deviance" $class [1] "nls.lm" And fitting details can be retrived with summary(x$bestfit)
Robersy Sanchez (https://genomaths.com).
Andrej-Nikolai Spiess (2014). propagate: Propagation of Uncertainty. R package version 1.0-4. http://CRAN.R-project.org/package=propagate
Abramowitz, M. and Stegun, I. A. (1972) Handbook of Mathematical Functions. New York: Dover. Chapter 6: Gamma and Related Functions.
Hand-book on STATISTICAL DISTRIBUTIONS for experimentalists (pag 73) by Christian Walck. Particle Physics Group Fysikum. University of Stockholm (e-mail: walck@physto.se).
fitdistr and fitMixDist and
for goodness-of-fit: mcgoftest.
set.seed(1230) x1 <- rnorm(10000, mean = 0.5, sd = 1) cdfp <- fitCDF(x1, distNames = "Normal", plot = FALSE) summary(cdfp$bestfit)