OpVaR (version 1.0.5)

goftest: Goodness of fit tests for severity distributions

Description

Testing the goodness-of-fit of the distributions given in a sevdist or a freqdist object to the loss data.

Usage

goftest(cell, object)

Arguments

cell

A data frame giving the losses (cell$Loss) and the user-defined period (cell$Period) in which the loss occured.

object

A loss severity model (sevdist object) or a loss frequency model (freqdist object)

Value

If object is of type sevdist, then the return is a list with the test results from all three tests: [[1]] Anderson-Darling, [[2]] Cramer-von-Mises, [[3]] Kolmogorow-Smirnov.

If object is of type freqdist, then the functions returns the result of the \(\chi^2\) test.

Refer with $p.value to the p-values and $statistic to the test statistic of each of the tests.

Details

If object is of type sevdist, then Anderson-Darling, Cramer-von-Mises and Kolmogorov-Smirnov test is performed on the loss data of a single cell and the respected fitted distribution given by the sevdist object.

If object is of type freqdist, then a \(\chi^2\) goodness-of-fit test will be performed.

References

Anderson, Theodore W., and Donald A. Darling. Asymptotic theory of certain "goodness of fit" criteria based on stochastic processes. The annals of mathematical statistics (1952): 193-212.

Anderson, Theodore W., and Donald A. Darling. "A test of goodness of fit". Journal of the American statistical association 49.268 (1954): 765-769.

Birnbaum, Z. W., and Fred H. Tingey. "One-sided confidence contours for probability distribution functions". The Annals of Mathematical Statistics 22.4 (1951): 592-596.

Conover, William Jay, and William Jay Conover. "Practical nonparametric statistics" (1980).

Csorgo, Sandor, and Julian J. Faraway. "The exact and asymptotic distributions of Cramer-von Mises statistics". Journal of the Royal Statistical Society. Series B (Methodological) (1996): 221-234.

Durbin, James. "Distribution theory for tests based on the sample distribution function". Society for Industrial and Applied Mathematics, 1973.

See Also

We use the goodness-of-fit tests ad.test, cvm.test from the package goftest and ks.test and chisq.test from stats.

Examples

# NOT RUN {
data("lossdat")
opriskmodel = list()
opriskmodel[[1]] = list()
opriskmodel[[1]]$freqdist = fitFreqdist(lossdat[[1]],"pois")
opriskmodel[[1]]$sevdist = fitPlain(lossdat[[1]],"gamma")

# perform test on the sevdist object
goftest(lossdat[[1]], opriskmodel[[1]]$sevdist)

# show result for e.g. only the Kolmogorow-Smirnov test
test = goftest(lossdat[[1]], opriskmodel[[1]]$sevdist)
test[[3]]$p.value
test[[3]]$statistic

# perform test on the freqdist object
goftest(lossdat[[1]], opriskmodel[[1]]$freqdist)

# the p-value is given by 
goftest(lossdat[[1]], opriskmodel[[1]]$freqdist)$p.value
# }