Nothing
R/gofstat.R
In fitdistrplus: Help to Fit of a Parametric Distribution to Non-Censored or Censored Data
Defines functions
print.gofstat.fitdistcens
print.gofstat.fitdist
computegofstatChi2
computegofstatKSCvMAD
Documented in
print.gofstat.fitdist
print.gofstat.fitdistcens
#############################################################################
# Copyright (c) 2009 Marie Laure Delignette-Muller, Christophe Dutang
#
# This program is free software; you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation; either version 2 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program; if not, write to the
# Free Software Foundation, Inc.,
# 59 Temple Place, Suite 330, Boston, MA 02111-1307, USA
#
#############################################################################
### calculate goodness-of-fit statistics for
### fit of a parametric distribution on non-censored data
###
### R functions
###
gofstat <- function (f, chisqbreaks, meancount, discrete,
fitnames=NULL)
{
# Check of the first argument
if(inherits(f, "fitdist"))
{
type <- "fitdist"
f <- list(f)
}else if(inherits(f, "fitdistcens"))
{
type <- "fitdistcens"
f <- list(f)
}else if(length(f) == 1 & !inherits(f, "fitdist") & !inherits(f, "fitdistcens"))
{
stop("argument f must a 'fitdist' or 'fitdistcens' object or a list of 'fitdist' or 'fitdistcens' objects.")
}else if(!is.list(f))
{
stop("argument f must be a list of 'fitdist' or 'fitdistcens' objects")
}else if (inherits(f[[1]], "fitdist"))
{
type <- "fitdist"
if(any(sapply(f, function(x) !inherits(x, "fitdist"))))
stop("argument f must be a list of 'fitdist' or 'fitdistcens' objects")
} else if (inherits(f[[1]], "fitdistcens"))
{
type <- "fitdistcens"
if(any(sapply(f, function(x) !inherits(x, "fitdistcens"))))
stop("argument f must be a list of 'fitdist' or 'fitdistcens' objects")
} else
{
stop("argument f must a 'fitdist' or 'fitdistcens' object or a list of 'fitdist' or 'fitdistcens' objects.")
}
# In the future developments, it will be necessary to check that all the fits share the same weights
if(!is.null(f[[1]]$weights))
stop("gofstat is not yet available when using weights")
############# for uncensored data ########################
if (type == "fitdist")
{
odata <- f[[1]]$data
sdata <- sort(odata)
n <- f[[1]]$n
distname <- f[[1]]$distname
pdistname <- paste("p", distname, sep="")
estimate <- f[[1]]$estimate
fix.arg <- f[[1]]$fix.arg
verif.ftidata <- function(fti)
{
if (any(fti$data != odata))
stop("All compared fits must have been obtained with the same dataset")
invisible()
}
lapply(f, verif.ftidata)
# initiate discrete if not given
if(missing(discrete))
{
discrete <- f[[1]]$discrete
}
if(!is.logical(discrete))
stop("wrong argument 'discrete'.")
#define chisqbreaks if not defined
if (missing(chisqbreaks))
{
if (missing(meancount))
meancount <- round( n / ((4*n)^(2/5)) )
if (length(sdata)>ceiling(1.5*meancount))
{
limit <- sdata[meancount]
sdata <- sdata[sdata>limit]
chisqbreaks <- limit
}else
{
warnings("The sample is too small to automatically define chisqbreaks")
chisq <- NULL
chisqbreaks <- NULL
chisqpvalue <- NULL
chisqtable <- NULL
chisqdf <- NULL
}
while (length(sdata)>ceiling(1.5*meancount))
{
limit <- sdata[meancount]
sdata <- sdata[sdata>limit]
chisqbreaks <- c(chisqbreaks,limit)
}
sdata <- sort(odata)
}
nbfit <- length(f)
if(is.null(fitnames))
fitnames <- paste(1:nbfit, sapply(f, function(x) x$method),
sapply(f, function(x) x$distname), sep="-")
else
fitnames <- rep(fitnames, length.out=nbfit)
Chi2 <- computegofstatChi2(sdata, n, distname, pdistname, estimate, fix.arg,
chisqbreaks)
if(length(f) > 1)
{
#renaming
names(Chi2$chisq) <- names(Chi2$chisqpvalue) <- names(Chi2$chisqdf) <- fitnames[1]
colnames(Chi2$chisqtable)[2] <- paste("theo", fitnames[1], sep=" ")
#computation and storing
for(i in 2:nbfit)
{
Chi2temp <- computegofstatChi2(sdata, n, f[[i]]$distname, paste("p", f[[i]]$distname, sep=""),
f[[i]]$estimate, f[[i]]$fix.arg, chisqbreaks)
names(Chi2temp$chisq) <- names(Chi2temp$chisqpvalue) <- names(Chi2temp$chisqdf) <- fitnames[i]
Chi2$chisq <- c(Chi2$chisq, Chi2temp$chisq)
Chi2$chisqpvalue <- c(Chi2$chisqpvalue, Chi2temp$chisqpvalue)
Chi2$chisqdf <- c(Chi2$chisqdf, Chi2temp$chisqdf)
Chi2$chisqtable <- cbind(Chi2$chisqtable, Chi2temp$chisqtable[,2])
colnames(Chi2$chisqtable)[NCOL(Chi2$chisqtable)] <- paste("theo", fitnames[i], sep=" ")
}
}
if(discrete)
{
addres <- Chi2
}else
{
KSCvMAD <- computegofstatKSCvMAD(sdata, n, distname, pdistname, estimate,
fix.arg, f[[1]]$method)
#renaming
names(KSCvMAD$cvm) <- names(KSCvMAD$ad) <- names(KSCvMAD$ks) <- fitnames[1]
if(!is.null(KSCvMAD$cvmtest))
names(KSCvMAD$cvmtest) <- names(KSCvMAD$adtest) <- names(KSCvMAD$kstest) <- fitnames[1]
if(length(f) > 1)
{
#computation and storing
for(i in 2:nbfit)
{
KSCvMADtemp <- computegofstatKSCvMAD(sdata, n, f[[i]]$distname, paste("p", f[[i]]$distname, sep=""),
f[[i]]$estimate, f[[i]]$fix.arg, f[[i]]$method)
names(KSCvMADtemp$cvm) <- names(KSCvMADtemp$ad) <- names(KSCvMADtemp$ks) <- fitnames[i]
if(!is.null(KSCvMADtemp$cvmtest))
names(KSCvMADtemp$cvmtest) <- names(KSCvMADtemp$adtest) <- names(KSCvMADtemp$kstest) <- fitnames[i]
KSCvMAD$cvm <- c(KSCvMAD$cvm, KSCvMADtemp$cvm)
KSCvMAD$cvmtest <- c(KSCvMAD$cvmtest, KSCvMADtemp$cvmtest)
KSCvMAD$ad <- c(KSCvMAD$ad, KSCvMADtemp$ad)
KSCvMAD$adtest <- c(KSCvMAD$adtest, KSCvMADtemp$adtest)
KSCvMAD$ks <- c(KSCvMAD$ks, KSCvMADtemp$ks)
KSCvMAD$kstest <- c(KSCvMAD$kstest, KSCvMADtemp$kstest)
}
}
addres <- c(Chi2, KSCvMAD)
}
aics <- sapply(f, function(x) x$aic)
names(aics) <- fitnames
bics <- sapply(f, function(x) x$bic)
names(bics) <- fitnames
res <- c(addres, aic=list(aics), bic=list(bics), discrete=discrete, nbfit=nbfit)
class(res) <- c("gofstat.fitdist", "fitdist")
res
} else # so if if type == "fitdistcens"
############# for censored data ########################
{
censdata <- f[[1]]$censdata
verif.ftidata <- function(fti)
{
if (any(!identical(fti$censdata, censdata)))
stop("All compared fits must have been obtained with the same dataset")
invisible()
}
lapply(f, verif.ftidata)
# check discrete
if(!missing(discrete))
{
if(!is.logical(discrete))
{
stop("wrong argument 'discrete'.")
} else if (discrete)
{
warning("Censored data cannot be considered as discrete data")
}
}
# warning about absence of chisq
if (!missing(chisqbreaks) | !missing(meancount))
{
warning("The chi-squared statistic is not calculated for fits using censored data")
}
nbfit <- length(f)
if(is.null(fitnames))
fitnames <- paste(1:nbfit, sapply(f, function(x) x$method),
sapply(f, function(x) x$distname), sep="-")
else
fitnames <- rep(fitnames, length.out=nbfit)
aics <- sapply(f, function(x) x$aic)
names(aics) <- fitnames
bics <- sapply(f, function(x) x$bic)
names(bics) <- fitnames
res <- c(aic=list(aics), bic=list(bics), nbfit=nbfit)
class(res) <- c("gofstat.fitdistcens", "fitdistcens")
res
}
}
#----------------------------------------------------------------------
#KS, CvM, AD statistics : only for continuous distributions
computegofstatKSCvMAD <- function(sdata, n, distname, pdistname, estimate,
fix.arg, method)
{
obspu <- seq(1,n)/n
obspl <- seq(0,n-1)/n
theop <- do.call(pdistname, c(list(sdata), as.list(estimate), fix.arg))
# Kolmogorov-Smirnov statistic
ks <- max(pmax(abs(theop-obspu), abs(theop-obspl)))
Dmod <- ks*(sqrt(n)+0.12+0.11/sqrt(n))
# Kolmogorov-Smirnov test
if (n>=30)
kstest <- ifelse(Dmod>1.358,"rejected","not rejected")
else
kstest <- "not computed"
# Anderson-Darling statistic
ad <- - n - mean( (2 * 1:n - 1) * (log(theop) + log(1 - rev(theop))) )
# ad <- -n-sum((2*(1:n)-1)*log(theop) + (2*n+1-2*(1:n))*log(1-theop))/n
# Anderson-Darling test
if (is.null(fix.arg) & method == "mle")
{
# the following test does not correspond to MLE estimate but to unbiased
# estimate of the variance
#if ((distname == "norm" | distname == "lnorm") & n>=5) {
# a2mod <- ad*(1+0.75/n+2.25/n^2)
# adtest <- ifelse(a2mod>0.752,"rejected","not rejected")
#}
#else
if (distname == "exp" & n>=5)
{
a2mod <- ad*(1+0.6/n)
adtest <- ifelse(a2mod>1.321, "rejected", "not rejected")
}else if (distname == "gamma" & n>=5)
{
m <- as.list(estimate)$shape
interp <- approxfun(c(1,2,3,4,5,6,8,10,12,15,20),
c(0.786,0.768,0.762,0.759,0.758,0.757,0.755,0.754,0.754,0.754,0.753),
yright=0.752)
adtest <- ifelse(ad>interp(m), "rejected", "not rejected")
}else if (distname == "weibull" & n>=5)
{
a2mod <- ad*(1+0.2/sqrt(n))
adtest <- ifelse(a2mod>0.757, "rejected", "not rejected")
}else if (distname == "logis" & n>=5)
{
a2mod <- ad*(1+0.25/n)
adtest <- ifelse(a2mod>0.66,"rejected","not rejected")
}else adtest <- "not computed"
}else # if (is.null(fix.arg)...)
adtest <- "not computed"
# Cramer-von Mises statistic
cvm <- 1/(12*n) + sum( ( theop - (2 * 1:n - 1)/(2 * n) )^2 )
# Cramer-von Mises test
if (is.null(fix.arg) & method == "mle")
{
# the following test does not correspond to MLE estimate but to unbiased
# estimate of the variance
# if ((distname == "norm" | distname == "lnorm") & n>=5) {
# w2mod <- cvm*(1+0.5/n)
# cvmtest <- ifelse(w2mod>0.126,"rejected","not rejected")
# }
# else
if (distname == "exp" & n>=5)
{
w2mod <- cvm*(1+0.16/n)
cvmtest <- ifelse(w2mod>0.222,"rejected","not rejected")
}else if (distname == "gamma" & n>=5)
{
m <- as.list(estimate)$shape
interp <- approxfun(c(1,2,3,4,5,6,8,10,12,15,20),
c(0.136,0.131,0.129,0.128,0.128,0.128,0.127,0.127,0.127,0.127,0.126),
yright=0.126)
cvmtest <- ifelse(cvm>interp(m),"rejected","not rejected")
}else if (distname == "weibull" & n>=5)
{
w2mod <- cvm*(1+0.2/sqrt(n))
cvmtest <- ifelse(w2mod>0.124,"rejected","not rejected")
}else if (distname == "logis" & n>=5)
{
w2mod <- (n*cvm - 0.08)/(n - 1)
cvmtest <- ifelse(w2mod>0.098,"rejected","not rejected")
}else cvmtest <- "not computed"
} else # if (is.null(fix.arg))
cvmtest <- "not computed"
if (length(table(sdata)) != length(sdata))
warnings("Kolmogorov-Smirnov, Cramer-von Mises and Anderson-Darling statistics may not be correct with ties")
list(cvm = cvm, cvmtest = cvmtest, ad = ad,adtest = adtest, ks = ks, kstest=kstest)
}
#----------------------------------------------------------------------
#chi-squared statistic : both for continuous and discrete distributions
computegofstatChi2 <- function(sdata, n, distname, pdistname, estimate, fix.arg, chisqbreaks)
{
# chi-squared statistic and pvalues
if (!is.null(chisqbreaks))
{
if(!is.numeric(chisqbreaks))
stop("chisqbreaks must be a numeric vector defining the cell boundaries")
nbreaks <- length(chisqbreaks)
pbreaks <- do.call(pdistname, c(list(chisqbreaks), as.list(estimate), fix.arg))
Fobsbreaks <- ecdf(sdata)(chisqbreaks)
Fobsunder <- c(0, Fobsbreaks[1:nbreaks-1])
punder <- c(0, pbreaks[1:nbreaks-1])
if (pbreaks[nbreaks]==1 & Fobsbreaks[nbreaks]==1)
{
p <- pbreaks-punder
Fobs <- Fobsbreaks-Fobsunder
}else
{
p <- c(pbreaks-punder, 1-pbreaks[nbreaks])
Fobs <- c(Fobsbreaks-Fobsunder, 1-Fobsbreaks[nbreaks])
}
obscounts <- round(Fobs*n)
theocounts <- p*n
chisq <- sum(((obscounts-theocounts)^2)/theocounts)
chisqdf <- length(obscounts)-1-length(estimate)
# replacing of the line below which causes an error message for chisqdf <=0
# chisqpvalue <- ifelse(chisqdf>0, pchisq(chisq, df=chisqdf, lower.tail=FALSE), NULL)
if (chisqdf>0)
{
chisqpvalue <- pchisq(chisq, df=chisqdf, lower.tail=FALSE)
} else
{
chisqpvalue <- NULL
}
chisqtable <- as.table(cbind(obscounts, theocounts))
for (i in 1:length(obscounts)-1)
rownames(chisqtable)[i] <- paste("<=", signif(chisqbreaks[i], digits=4))
rownames(chisqtable)[length(obscounts)] <- paste(">", signif(chisqbreaks[i], digits=4))
return( list(chisq = chisq, chisqbreaks=chisqbreaks, chisqpvalue = chisqpvalue,
chisqdf = chisqdf, chisqtable = chisqtable) )
}else
return(NULL)
}
print.gofstat.fitdist <- function(x, ...)
{
if (!inherits(x, "gofstat.fitdist"))
stop("Use only with 'gofstat.fitdist' objects")
if (x$discrete) #discrete distribution
{
if(!is.null(x$chisq))
{
cat("Chi-squared statistic: ",x$chisq,"\n")
cat("Degree of freedom of the Chi-squared distribution: ",x$chisqdf,"\n")
if (any(x$chisqdf <= 0))
{
cat(" The degree of freedom of the chi-squared distribution is less than 1 \n")
cat(" The number of cells is insufficient to calculate the p-value. \n")
}else
{
cat("Chi-squared p-value: ",x$chisqpvalue,"\n")
if (any(x$chisqtable[,-1] < 5))
cat(" the p-value may be wrong with some theoretical counts < 5 \n")
}
cat("Chi-squared table:\n")
print(x$chisqtable)
cat("\nGoodness-of-fit criteria\n")
mm <- rbind(AIC=x$aic, BIC=x$bic)
rownames(mm) <- c("Akaike's Information Criterion",
"Bayesian Information Criterion")
print(mm)
}else
cat("The sample is too small to automatically define cells for Chi-squared test \n")
}else # continuous distribution
{
cat("Goodness-of-fit statistics\n")
mm <- rbind(KS=x$ks, CvM=x$cvm, AD=x$ad)
rownames(mm) <- c("Kolmogorov-Smirnov statistic", "Cramer-von Mises statistic",
"Anderson-Darling statistic")
print(mm)
cat("\nGoodness-of-fit criteria\n")
mm <- rbind(AIC=x$aic, BIC=x$bic)
rownames(mm) <- c("Akaike's Information Criterion",
"Bayesian Information Criterion")
print(mm)
}
invisible(x)
}
print.gofstat.fitdistcens <- function(x, ...)
{
if (!inherits(x, "gofstat.fitdistcens"))
stop("Use only with 'gofstat.fitdistcens' objects")
cat("\nGoodness-of-fit criteria\n")
mm <- rbind(AIC=x$aic, BIC=x$bic)
rownames(mm) <- c("Akaike's Information Criterion",
"Bayesian Information Criterion")
print(mm)
invisible(x)
}
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Defines functions print.gofstat.fitdistcens print.gofstat.fitdist computegofstatChi2 computegofstatKSCvMAD
Documented in print.gofstat.fitdist print.gofstat.fitdistcens
#############################################################################
# Copyright (c) 2009 Marie Laure Delignette-Muller, Christophe Dutang
#
# This program is free software; you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation; either version 2 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program; if not, write to the
# Free Software Foundation, Inc.,
# 59 Temple Place, Suite 330, Boston, MA 02111-1307, USA
#
#############################################################################
### calculate goodness-of-fit statistics for
### fit of a parametric distribution on non-censored data
###
### R functions
###
gofstat <- function (f, chisqbreaks, meancount, discrete,
fitnames=NULL)
{
# Check of the first argument
if(inherits(f, "fitdist"))
{
type <- "fitdist"
f <- list(f)
}else if(inherits(f, "fitdistcens"))
{
type <- "fitdistcens"
f <- list(f)
}else if(length(f) == 1 & !inherits(f, "fitdist") & !inherits(f, "fitdistcens"))
{
stop("argument f must a 'fitdist' or 'fitdistcens' object or a list of 'fitdist' or 'fitdistcens' objects.")
}else if(!is.list(f))
{
stop("argument f must be a list of 'fitdist' or 'fitdistcens' objects")
}else if (inherits(f[[1]], "fitdist"))
{
type <- "fitdist"
if(any(sapply(f, function(x) !inherits(x, "fitdist"))))
stop("argument f must be a list of 'fitdist' or 'fitdistcens' objects")
} else if (inherits(f[[1]], "fitdistcens"))
{
type <- "fitdistcens"
if(any(sapply(f, function(x) !inherits(x, "fitdistcens"))))
stop("argument f must be a list of 'fitdist' or 'fitdistcens' objects")
} else
{
stop("argument f must a 'fitdist' or 'fitdistcens' object or a list of 'fitdist' or 'fitdistcens' objects.")
}
# In the future developments, it will be necessary to check that all the fits share the same weights
if(!is.null(f[[1]]$weights))
stop("gofstat is not yet available when using weights")
############# for uncensored data ########################
if (type == "fitdist")
{
odata <- f[[1]]$data
sdata <- sort(odata)
n <- f[[1]]$n
distname <- f[[1]]$distname
pdistname <- paste("p", distname, sep="")
estimate <- f[[1]]$estimate
fix.arg <- f[[1]]$fix.arg
verif.ftidata <- function(fti)
{
if (any(fti$data != odata))
stop("All compared fits must have been obtained with the same dataset")
invisible()
}
lapply(f, verif.ftidata)
# initiate discrete if not given
if(missing(discrete))
{
discrete <- f[[1]]$discrete
}
if(!is.logical(discrete))
stop("wrong argument 'discrete'.")
#define chisqbreaks if not defined
if (missing(chisqbreaks))
{
if (missing(meancount))
meancount <- round( n / ((4*n)^(2/5)) )
if (length(sdata)>ceiling(1.5*meancount))
{
limit <- sdata[meancount]
sdata <- sdata[sdata>limit]
chisqbreaks <- limit
}else
{
warnings("The sample is too small to automatically define chisqbreaks")
chisq <- NULL
chisqbreaks <- NULL
chisqpvalue <- NULL
chisqtable <- NULL
chisqdf <- NULL
}
while (length(sdata)>ceiling(1.5*meancount))
{
limit <- sdata[meancount]
sdata <- sdata[sdata>limit]
chisqbreaks <- c(chisqbreaks,limit)
}
sdata <- sort(odata)
}
nbfit <- length(f)
if(is.null(fitnames))
fitnames <- paste(1:nbfit, sapply(f, function(x) x$method),
sapply(f, function(x) x$distname), sep="-")
else
fitnames <- rep(fitnames, length.out=nbfit)
Chi2 <- computegofstatChi2(sdata, n, distname, pdistname, estimate, fix.arg,
chisqbreaks)
if(length(f) > 1)
{
#renaming
names(Chi2$chisq) <- names(Chi2$chisqpvalue) <- names(Chi2$chisqdf) <- fitnames[1]
colnames(Chi2$chisqtable)[2] <- paste("theo", fitnames[1], sep=" ")
#computation and storing
for(i in 2:nbfit)
{
Chi2temp <- computegofstatChi2(sdata, n, f[[i]]$distname, paste("p", f[[i]]$distname, sep=""),
f[[i]]$estimate, f[[i]]$fix.arg, chisqbreaks)
names(Chi2temp$chisq) <- names(Chi2temp$chisqpvalue) <- names(Chi2temp$chisqdf) <- fitnames[i]
Chi2$chisq <- c(Chi2$chisq, Chi2temp$chisq)
Chi2$chisqpvalue <- c(Chi2$chisqpvalue, Chi2temp$chisqpvalue)
Chi2$chisqdf <- c(Chi2$chisqdf, Chi2temp$chisqdf)
Chi2$chisqtable <- cbind(Chi2$chisqtable, Chi2temp$chisqtable[,2])
colnames(Chi2$chisqtable)[NCOL(Chi2$chisqtable)] <- paste("theo", fitnames[i], sep=" ")
}
}
if(discrete)
{
addres <- Chi2
}else
{
KSCvMAD <- computegofstatKSCvMAD(sdata, n, distname, pdistname, estimate,
fix.arg, f[[1]]$method)
#renaming
names(KSCvMAD$cvm) <- names(KSCvMAD$ad) <- names(KSCvMAD$ks) <- fitnames[1]
if(!is.null(KSCvMAD$cvmtest))
names(KSCvMAD$cvmtest) <- names(KSCvMAD$adtest) <- names(KSCvMAD$kstest) <- fitnames[1]
if(length(f) > 1)
{
#computation and storing
for(i in 2:nbfit)
{
KSCvMADtemp <- computegofstatKSCvMAD(sdata, n, f[[i]]$distname, paste("p", f[[i]]$distname, sep=""),
f[[i]]$estimate, f[[i]]$fix.arg, f[[i]]$method)
names(KSCvMADtemp$cvm) <- names(KSCvMADtemp$ad) <- names(KSCvMADtemp$ks) <- fitnames[i]
if(!is.null(KSCvMADtemp$cvmtest))
names(KSCvMADtemp$cvmtest) <- names(KSCvMADtemp$adtest) <- names(KSCvMADtemp$kstest) <- fitnames[i]
KSCvMAD$cvm <- c(KSCvMAD$cvm, KSCvMADtemp$cvm)
KSCvMAD$cvmtest <- c(KSCvMAD$cvmtest, KSCvMADtemp$cvmtest)
KSCvMAD$ad <- c(KSCvMAD$ad, KSCvMADtemp$ad)
KSCvMAD$adtest <- c(KSCvMAD$adtest, KSCvMADtemp$adtest)
KSCvMAD$ks <- c(KSCvMAD$ks, KSCvMADtemp$ks)
KSCvMAD$kstest <- c(KSCvMAD$kstest, KSCvMADtemp$kstest)
}
}
addres <- c(Chi2, KSCvMAD)
}
aics <- sapply(f, function(x) x$aic)
names(aics) <- fitnames
bics <- sapply(f, function(x) x$bic)
names(bics) <- fitnames
res <- c(addres, aic=list(aics), bic=list(bics), discrete=discrete, nbfit=nbfit)
class(res) <- c("gofstat.fitdist", "fitdist")
res
} else # so if if type == "fitdistcens"
############# for censored data ########################
{
censdata <- f[[1]]$censdata
verif.ftidata <- function(fti)
{
if (any(!identical(fti$censdata, censdata)))
stop("All compared fits must have been obtained with the same dataset")
invisible()
}
lapply(f, verif.ftidata)
# check discrete
if(!missing(discrete))
{
if(!is.logical(discrete))
{
stop("wrong argument 'discrete'.")
} else if (discrete)
{
warning("Censored data cannot be considered as discrete data")
}
}
# warning about absence of chisq
if (!missing(chisqbreaks) | !missing(meancount))
{
warning("The chi-squared statistic is not calculated for fits using censored data")
}
nbfit <- length(f)
if(is.null(fitnames))
fitnames <- paste(1:nbfit, sapply(f, function(x) x$method),
sapply(f, function(x) x$distname), sep="-")
else
fitnames <- rep(fitnames, length.out=nbfit)
aics <- sapply(f, function(x) x$aic)
names(aics) <- fitnames
bics <- sapply(f, function(x) x$bic)
names(bics) <- fitnames
res <- c(aic=list(aics), bic=list(bics), nbfit=nbfit)
class(res) <- c("gofstat.fitdistcens", "fitdistcens")
res
}
}
#----------------------------------------------------------------------
#KS, CvM, AD statistics : only for continuous distributions
computegofstatKSCvMAD <- function(sdata, n, distname, pdistname, estimate,
fix.arg, method)
{
obspu <- seq(1,n)/n
obspl <- seq(0,n-1)/n
theop <- do.call(pdistname, c(list(sdata), as.list(estimate), fix.arg))
# Kolmogorov-Smirnov statistic
ks <- max(pmax(abs(theop-obspu), abs(theop-obspl)))
Dmod <- ks*(sqrt(n)+0.12+0.11/sqrt(n))
# Kolmogorov-Smirnov test
if (n>=30)
kstest <- ifelse(Dmod>1.358,"rejected","not rejected")
else
kstest <- "not computed"
# Anderson-Darling statistic
ad <- - n - mean( (2 * 1:n - 1) * (log(theop) + log(1 - rev(theop))) )
# ad <- -n-sum((2*(1:n)-1)*log(theop) + (2*n+1-2*(1:n))*log(1-theop))/n
# Anderson-Darling test
if (is.null(fix.arg) & method == "mle")
{
# the following test does not correspond to MLE estimate but to unbiased
# estimate of the variance
#if ((distname == "norm" | distname == "lnorm") & n>=5) {
# a2mod <- ad*(1+0.75/n+2.25/n^2)
# adtest <- ifelse(a2mod>0.752,"rejected","not rejected")
#}
#else
if (distname == "exp" & n>=5)
{
a2mod <- ad*(1+0.6/n)
adtest <- ifelse(a2mod>1.321, "rejected", "not rejected")
}else if (distname == "gamma" & n>=5)
{
m <- as.list(estimate)$shape
interp <- approxfun(c(1,2,3,4,5,6,8,10,12,15,20),
c(0.786,0.768,0.762,0.759,0.758,0.757,0.755,0.754,0.754,0.754,0.753),
yright=0.752)
adtest <- ifelse(ad>interp(m), "rejected", "not rejected")
}else if (distname == "weibull" & n>=5)
{
a2mod <- ad*(1+0.2/sqrt(n))
adtest <- ifelse(a2mod>0.757, "rejected", "not rejected")
}else if (distname == "logis" & n>=5)
{
a2mod <- ad*(1+0.25/n)
adtest <- ifelse(a2mod>0.66,"rejected","not rejected")
}else adtest <- "not computed"
}else # if (is.null(fix.arg)...)
adtest <- "not computed"
# Cramer-von Mises statistic
cvm <- 1/(12*n) + sum( ( theop - (2 * 1:n - 1)/(2 * n) )^2 )
# Cramer-von Mises test
if (is.null(fix.arg) & method == "mle")
{
# the following test does not correspond to MLE estimate but to unbiased
# estimate of the variance
# if ((distname == "norm" | distname == "lnorm") & n>=5) {
# w2mod <- cvm*(1+0.5/n)
# cvmtest <- ifelse(w2mod>0.126,"rejected","not rejected")
# }
# else
if (distname == "exp" & n>=5)
{
w2mod <- cvm*(1+0.16/n)
cvmtest <- ifelse(w2mod>0.222,"rejected","not rejected")
}else if (distname == "gamma" & n>=5)
{
m <- as.list(estimate)$shape
interp <- approxfun(c(1,2,3,4,5,6,8,10,12,15,20),
c(0.136,0.131,0.129,0.128,0.128,0.128,0.127,0.127,0.127,0.127,0.126),
yright=0.126)
cvmtest <- ifelse(cvm>interp(m),"rejected","not rejected")
}else if (distname == "weibull" & n>=5)
{
w2mod <- cvm*(1+0.2/sqrt(n))
cvmtest <- ifelse(w2mod>0.124,"rejected","not rejected")
}else if (distname == "logis" & n>=5)
{
w2mod <- (n*cvm - 0.08)/(n - 1)
cvmtest <- ifelse(w2mod>0.098,"rejected","not rejected")
}else cvmtest <- "not computed"
} else # if (is.null(fix.arg))
cvmtest <- "not computed"
if (length(table(sdata)) != length(sdata))
warnings("Kolmogorov-Smirnov, Cramer-von Mises and Anderson-Darling statistics may not be correct with ties")
list(cvm = cvm, cvmtest = cvmtest, ad = ad,adtest = adtest, ks = ks, kstest=kstest)
}
#----------------------------------------------------------------------
#chi-squared statistic : both for continuous and discrete distributions
computegofstatChi2 <- function(sdata, n, distname, pdistname, estimate, fix.arg, chisqbreaks)
{
# chi-squared statistic and pvalues
if (!is.null(chisqbreaks))
{
if(!is.numeric(chisqbreaks))
stop("chisqbreaks must be a numeric vector defining the cell boundaries")
nbreaks <- length(chisqbreaks)
pbreaks <- do.call(pdistname, c(list(chisqbreaks), as.list(estimate), fix.arg))
Fobsbreaks <- ecdf(sdata)(chisqbreaks)
Fobsunder <- c(0, Fobsbreaks[1:nbreaks-1])
punder <- c(0, pbreaks[1:nbreaks-1])
if (pbreaks[nbreaks]==1 & Fobsbreaks[nbreaks]==1)
{
p <- pbreaks-punder
Fobs <- Fobsbreaks-Fobsunder
}else
{
p <- c(pbreaks-punder, 1-pbreaks[nbreaks])
Fobs <- c(Fobsbreaks-Fobsunder, 1-Fobsbreaks[nbreaks])
}
obscounts <- round(Fobs*n)
theocounts <- p*n
chisq <- sum(((obscounts-theocounts)^2)/theocounts)
chisqdf <- length(obscounts)-1-length(estimate)
# replacing of the line below which causes an error message for chisqdf <=0
# chisqpvalue <- ifelse(chisqdf>0, pchisq(chisq, df=chisqdf, lower.tail=FALSE), NULL)
if (chisqdf>0)
{
chisqpvalue <- pchisq(chisq, df=chisqdf, lower.tail=FALSE)
} else
{
chisqpvalue <- NULL
}
chisqtable <- as.table(cbind(obscounts, theocounts))
for (i in 1:length(obscounts)-1)
rownames(chisqtable)[i] <- paste("<=", signif(chisqbreaks[i], digits=4))
rownames(chisqtable)[length(obscounts)] <- paste(">", signif(chisqbreaks[i], digits=4))
return( list(chisq = chisq, chisqbreaks=chisqbreaks, chisqpvalue = chisqpvalue,
chisqdf = chisqdf, chisqtable = chisqtable) )
}else
return(NULL)
}
print.gofstat.fitdist <- function(x, ...)
{
if (!inherits(x, "gofstat.fitdist"))
stop("Use only with 'gofstat.fitdist' objects")
if (x$discrete) #discrete distribution
{
if(!is.null(x$chisq))
{
cat("Chi-squared statistic: ",x$chisq,"\n")
cat("Degree of freedom of the Chi-squared distribution: ",x$chisqdf,"\n")
if (any(x$chisqdf <= 0))
{
cat(" The degree of freedom of the chi-squared distribution is less than 1 \n")
cat(" The number of cells is insufficient to calculate the p-value. \n")
}else
{
cat("Chi-squared p-value: ",x$chisqpvalue,"\n")
if (any(x$chisqtable[,-1] < 5))
cat(" the p-value may be wrong with some theoretical counts < 5 \n")
}
cat("Chi-squared table:\n")
print(x$chisqtable)
cat("\nGoodness-of-fit criteria\n")
mm <- rbind(AIC=x$aic, BIC=x$bic)
rownames(mm) <- c("Akaike's Information Criterion",
"Bayesian Information Criterion")
print(mm)
}else
cat("The sample is too small to automatically define cells for Chi-squared test \n")
}else # continuous distribution
{
cat("Goodness-of-fit statistics\n")
mm <- rbind(KS=x$ks, CvM=x$cvm, AD=x$ad)
rownames(mm) <- c("Kolmogorov-Smirnov statistic", "Cramer-von Mises statistic",
"Anderson-Darling statistic")
print(mm)
cat("\nGoodness-of-fit criteria\n")
mm <- rbind(AIC=x$aic, BIC=x$bic)
rownames(mm) <- c("Akaike's Information Criterion",
"Bayesian Information Criterion")
print(mm)
}
invisible(x)
}
print.gofstat.fitdistcens <- function(x, ...)
{
if (!inherits(x, "gofstat.fitdistcens"))
stop("Use only with 'gofstat.fitdistcens' objects")
cat("\nGoodness-of-fit criteria\n")
mm <- rbind(AIC=x$aic, BIC=x$bic)
rownames(mm) <- c("Akaike's Information Criterion",
"Bayesian Information Criterion")
print(mm)
invisible(x)
}
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