Geometric Goodness-of-fit Test

Description

Implementation of the goodness-of-fit test based on assessing the size of the area between the null hypothesis density function and a kernel density estimate of a sample.

Usage

dgeometric.test(x, fun.den, par = NULL, lower = -Inf, upper = Inf, n.sim = 101,
                bw=NULL)

Arguments

Details

dgeometric.test uses numerical integration and Monte Carlo simulation to implement the test based on assessing the extend of the area between a null hypothesis density function and a density kernel estimation. It works as follows. After computing by numerical integration the area between the density function under the null hypothesis and its sample empirical kernel estimate obtained using density.reflected, the p-value of the test is obtained by simulation as follows: (i) drawing n.sim samples from fun.den with the same size length(x) of our actual sample x; (ii) estimating the kernel density function for each of these new samples; (iii) computing the area between the theoretical density and each of the estimates obtained in (ii); and, (iv) calculating the p-value as the proportion of times the sample n.sim areas computed in (iii) exceed the value of the area computed from the observed sample.

Value

The output is an object of the class htest exactly like for the Kolmogorov-Smirnov test, ks.test. A list containing the following components:

Note

dgeometric.test calls density.reflected and area.between (and, in some circunstances, also inverse, random.function and support.facto), which are (internal) functions of the package GoFKernel.

Author(s)

Jose M. Pavia

References

Pavia, JM (2015) "Testing Goodness-of-fit with the Kernel Density Estimator: GoFKernel", Journal of Statistical Software, Code Snippets, 66(1), 1–27.

See Also

area.between, density.reflected, inverse random.function, support.facto and fan.test.

Examples

set.seed(12)
x <- rlnorm(50, meanlog=1, sdlog=1)
## test if x follows a Gamma distribution with shape .6 and rate .1
dgeometric.test(x, dgamma, par=list(shape=0.6, rate=0.1), lower=0, upper=Inf, n.sim=100)

f0 <- function(x) ifelse(x>=0 & x<=1, 2-2*x, 0)
## test if risk76.1929 follows the distribution characterized by f0
dgeometric.test(risk76.1929, f0, lower=0, upper=1, n.sim=31)

Results

R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> library(GoFKernel)
Loading required package: KernSmooth
KernSmooth 2.23 loaded
Copyright M. P. Wand 1997-2009
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/GoFKernel/dgeometric.test.Rd_%03d_medium.png", width=480, height=480)
> ### Name: dgeometric.test
> ### Title: Geometric Goodness-of-fit Test
> ### Aliases: dgeometric.test
> ### Keywords: htest
> 
> ### ** Examples
> 
> 
> set.seed(12)
> x <- rlnorm(50, meanlog=1, sdlog=1)
> ## test if x follows a Gamma distribution with shape .6 and rate .1
> dgeometric.test(x, dgamma, par=list(shape=0.6, rate=0.1), lower=0, upper=Inf, n.sim=100)

	Geometric test

data:  x
Tn = 0.58399, p-value < 2.2e-16

> 
> f0 <- function(x) ifelse(x>=0 & x<=1, 2-2*x, 0)
> ## test if risk76.1929 follows the distribution characterized by f0
> dgeometric.test(risk76.1929, f0, lower=0, upper=1, n.sim=31)

	Geometric test

data:  risk76.1929
Tn = 0.11434, p-value < 2.2e-16

> 
> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>