Package 'Rgof'

This function creates the functions needed to run the various case studies.

Description

This function creates the functions needed to run the various case studies.

Usage

case.studies(which, nsample = 500)

Arguments

which	name of the case study.
nsample	=500, sample size.

Value

a list of functions

---

This function checks whether the inputs have the correct format

Description

This function checks whether the inputs have the correct format

Usage

check.functions(pnull, rnull, phat = function(x) -99, vals, x)

Arguments

pnull	cdf under the null hypothesis
rnull	routine to generate data under the null hypothesis
phat	=function(x) -99, function to estimate parameters from the data, or -99
vals	vector of discrete values
x	data

---

This function finds the power of various chi-square tests for continuous data

Description

This function finds the power of various chi-square tests for continuous data

Usage

chi_power_cont(
  pnull,
  ralt,
  param_alt,
  qnull = NA,
  phat = function(x) -99,
  w = function(x) -99,
  alpha = 0.05,
  Range = c(-99999, 99999),
  B = 1000,
  nbins = c(50, 10),
  rate = 0,
  minexpcount = 5,
  ChiUsePhat = TRUE
)

Arguments

pnull	function to find cdf under null hypothesis
ralt	function to generate data under alternative hypothesis
param_alt	vector of parameter values for distribution under alternative hypothesis
qnull	=NA function to find quantiles under null hypothesis, if available
phat	=function(x) -99, function to estimate parameters
w	=function(x) -99, optional weight function
alpha	=0.05, the level of the hypothesis test
Range	=c(-99999, 99999) limits of possible observations, if any
B	=1000 number of simulation runs to find power
nbins	=c(50,10), number of bins for chi square tests
rate	=0 rate of Poisson if sample size is random, 0 if sample size is fixed
minexpcount	=5 minimal expected bin count required
ChiUsePhat	=TRUE, if TRUE param is estimated parameters and no minimization is used

Value

A numeric matrix of power values.

---

This function finds the power of various chi-square tests for continuous data

Description

This function finds the power of various chi-square tests for continuous data

Usage

chi_power_disc(
  pnull,
  ralt,
  param_alt,
  phat = function(x) -99,
  alpha = 0.05,
  B = 1000,
  nbins = c(50, 10),
  rate = 0,
  minexpcount = 5,
  ChiUsePhat = TRUE
)

Arguments

pnull	function to find cdf under null hypothesis
ralt	function to generate data under alternative hypothesis
param_alt	vector of parameter values for distribution under alternative hypothesis
phat	=function(x) -99, routine to estimate parameters
alpha	=0.05, the level of the hypothesis test
B	=1000 number of simulation runs to find power
nbins	=c(50,10), number of bins for chi square tests
rate	=0 rate of Poisson if sample size is random, 0 if sample size is fixed
minexpcount	=5 minimal expected bin count required
ChiUsePhat	= TRUE, should chi square use minimum chi square method?

Value

A numeric matrix of power values.

---

This function performs a number of chi-square gof tests for continuous data

Description

This function performs a number of chi-square gof tests for continuous data

Usage

chi_test_cont(
  x,
  pnull,
  w = function(x) -99,
  phat = function(x) -99,
  qnull = NA,
  nbins = c(50, 10),
  rate = 0,
  Range = c(-99999, 99999),
  minexpcount = 5,
  ChiUsePhat = TRUE,
  allbins
)

Arguments

x	data set
pnull	cdf under the null hypothesis
w	function to find weights of observations, returns -99 if data is unweighted
phat	=function(x) -99, estimated parameters, or starting values of multi-D minimum chi square minimization, or -99 if no estimation is done
qnull	=NA quantile function, if available
nbins	=c(50, 10) number of bins for chi-square tests
rate	=0, rate of Poisson if sample size is random
Range	=c(-99999, 99999) limits of possible observations, if any
minexpcount	=5 minimal expected bin count required
ChiUsePhat	=TRUE, if TRUE param is estimated parameters and no minimization is used
allbins	set of bins to use

Value

A numeric matrix of test statistics, degrees of freedom and p.values

---

This function performs a number of chi-square gof tests for continuous data

Description

This function performs a number of chi-square gof tests for continuous data

Usage

chi_test_disc(
  x,
  pnull,
  phat = function(x) -99,
  nbins = c(50, 10),
  rate = 0,
  minexpcount = 5,
  ChiUsePhat = TRUE,
  allbins
)

Arguments

x	data set
pnull	cdf under the null hypothesis
phat	=function(x) -99, function to estimate parameters, or starting values of multi-D minimum chi square minimization, or -99 if no parameters are estimated
nbins	=c(50, 10) number of bins for chi-square tests
rate	=0, rate of Poisson if sample size is random
minexpcount	=5 minimal expected bin count required
ChiUsePhat	= TRUE, if TRUE param is estimated parameter, otherwise minimum chi square method is used.
allbins	set of bins to use

Value

A numeric matrix of test statistics, degrees of freedom and p.values

---

Power estimation of goodness-of-fit tests.

Description

Find the power of various goodness-of-fit tests.

Usage

gof_power(
  pnull,
  vals = NA,
  rnull,
  ralt,
  param_alt,
  w = function(x) -99,
  phat = function(x) -99,
  TS,
  TSextra,
  With.p.value = FALSE,
  alpha = 0.05,
  Range = c(-Inf, Inf),
  B = 1000,
  nbins = c(50, 10),
  rate = 0,
  maxProcessor,
  minexpcount = 5,
  ChiUsePhat = TRUE
)

Arguments

pnull	function to find cdf under null hypothesis
vals	=NA values of discrete random variable, or NA
rnull	function to generate data under null hypothesis
ralt	function to generate data under alternative hypothesis
param_alt	vector of parameter values for distribution under alternative hypothesis
w	(Optional) function to calculate weights, returns -99 if no weights
phat	=function(x) -99 function to estimate parameters from the data, or -99
TS	user supplied function to find test statistics
TSextra	list provided to TS (optional)
With.p.value	=FALSE does user supplied routine return p values?
alpha	=0.05, the level of the hypothesis test
Range	=c(-Inf, Inf) limits of possible observations, if any
B	=1000 number of simulation runs
nbins	=c(50,10), number of bins for chi square tests.
rate	=0 rate of Poisson if sample size is random, 0 if sample size is fixed
maxProcessor	maximum of number of processors to use, 1 if no parallel processing is needed or number of cores-1 if missing
minexpcount	=5 minimal expected bin count required
ChiUsePhat	= TRUE, if TRUE param is estimated parameter, otherwise minimum chi square method is used.

Details

For details on the usage of this routine consult the vignette with vignette("Rgof","Rgof")

Value

A numeric matrix of power values.

Examples

# Power of tests when null hypothesis specifies the standard normal distribution but 
# true data comes from a normal distribution with mean different from 0.
pnull = function(x) pnorm(x)
rnull = function()  rnorm(50)
ralt = function(mu)  rnorm(50, mu)
TSextra = list(qnull=function(x) qnorm(x))
gof_power(pnull, NA, rnull, ralt, c(0.25, 0.5), TSextra=TSextra, B=200)
# Power of tests when null hypothesis specifies normal distribution and 
# mean and standard deviation are estimated from the data. 
# true data comes from a normal distribution with mean different from 0.
pnull = function(x, p=c(0, 1)) pnorm(x, p[1], ifelse(p[2]>0.001, p[2], 0.001))
rnull = function(p=c(0, 1))  rnorm(50, p[1], ifelse(p[2]>0.001, p[2], 0.001))
ralt = function(mu)  rnorm(50, mu)
phat = function(x) c(mean(x), sd(x))
TSextra = list(qnull = function(x, p=c(0, 1)) qnorm(x, p[1],  
               ifelse(p[2]>0.001, p[2], 0.001))) 
pwr=gof_power(pnull, NA, rnull, ralt, c(0, 1), phat=phat, TSextra=TSextra, B=200)
pwr
#' Compare power of a new test based on variants of the Cramer-vonMises
#' criterion to the methods included in the package: 
newTS = function(x, pnull, param) {
   Fx=sort(pnull(x, param))
   n=length(x)
   out = c(sum(abs( (2*1:n-1)/2/n-Fx )), sum(sqrt(abs( (2*1:n-1)/2/n-Fx ))))
   names(out) = c("CvM alt 1","CvM alt 2")
   out
}
#' Compare power to Lilliefors KS test, which finds its own p value:
LLtest=function(x, pnull, param) {
  out=nortest::lillie.test(x)$p.value
  names(out)="KS - Lilliefors"
  out
}
cbind(gof_power(pnull, NA, rnull, ralt, c(0, 1), TS=LLtest, phat=phat, 
       With.p.value=TRUE, TSextra=TSextra, B=200), pwr)
# Power of tests when null hypothesis specifies Poisson rv with rate 100 and 
# true rate is 100.5
vals = 0:250
pnull = function() ppois(0:250, 100)
rnull =function () table(c(0:250, rpois(1000, 100)))-1
ralt =function (p) table(c(0:250, rpois(1000, p)))-1
gof_power(pnull, vals, rnull, ralt, param_alt=100.5,  B=200)
# Power of tests when null hypothesis specifies a Binomial n=10 distribution 
# with the success probability estimated
vals = 0:10
pnull=function(p) pbinom(0:10, 10, ifelse(0<p&p<1, p, 0.001))
rnull=function(p) table(c(0:10, rbinom(1000, 10, ifelse(0<p&p<1, p, 0.001))))-1
ralt=function(p) table(c(0:10, rbinom(1000, 10, p)))-1
phat=function(x) mean(rep(0:10,x))/10
gof_power(pnull, vals, rnull, ralt, c(0.5, 0.6), phat=phat, B=200)

---

Tests for the univariate goodness-of-fit problem

Description

This function runs a number of goodness-of-fit tests using Rcpp and parallel computing.

Usage

gof_test(
  x,
  vals = NA,
  pnull,
  rnull,
  w = function(x) -99,
  phat = function(x) -99,
  TS,
  TSextra = NA,
  nbins = c(50, 10),
  rate = 0,
  Range = c(-Inf, Inf),
  B = 5000,
  minexpcount = 5,
  ChiUsePhat = TRUE,
  maxProcessor,
  doMethods = "all"
)

Arguments

x	data set
vals	=NA, values of discrete RV, or NA if data is continuous
pnull	cdf under the null hypothesis
rnull	routine to generate data under the null hypothesis
w	(Optional) function to calculate weights, returns -99 if no weights
phat	=function(x) -99, function to estimate parameters from the data, or -99 if no parameters are estimated
TS	user supplied function to find test statistics, if any
TSextra	=NA, list passed to TS, if desired, or NA
nbins	=c(100, 10) number of bins for chi-square tests
rate	=0 rate of Poisson if sample size is random, 0 if sample size is fixed
Range	=c(-Inf, Inf) limits of possible observations, if any, for chi-square tests
B	=5000 number of simulation runs
minexpcount	=5 minimal expected bin count required
ChiUsePhat	= TRUE, if TRUE param is estimated parameter, otherwise minimum chi square method is used.
maxProcessor	=1, number of processors to use in parallel processing.
doMethods	="all", a vector of codes for the methods to include or all of them.

Details

For details on the usage of this routine consult the vignette with vignette("Rgof","Rgof")

Value

A list with vectors of test statistics and p.values

Examples

# Tests to see whether data comes from a standard normal distribution.
pnull = function(x) pnorm(x)
rnull = function()  rnorm(100)
x = rnorm(100)
gof_test(x, NA, pnull, rnull, B=500)
# Tests to see whether data comes from a normal distribution with standard deviation 1 
# and the mean estimated.
pnull=function(x, m) pnorm(x, m)
rnull=function(m) rnorm(100, m)
TSextra = list(qnull=function(x, m=0) qnorm(x, m), 
          pnull=function(x, m=0) pnorm(x, m), phat=function(x) mean(x))
phat=function(x) mean(x)
x = rnorm(100, 1, 2)
gof_test(x, NA, pnull, rnull, phat=phat, TSextra=TSextra, B=500)
# Tests to see whether data comes from a binomial (10, 0.5) distribution.
vals=0:10
pnull = function() pbinom(0:10, 10, 0.5)
rnull = function() table(c(0:10, rbinom(1000, 10, 0.5)))-1
x = rnull() 
gof_test(x, vals, pnull, rnull, doMethods="all", B=500)
# Tests to see whether data comes from a binomial distribution with 
# the success probability estimated from the data.
pnull = function(p=0.5) pbinom(0:10, 10, ifelse(p>0&&p<1, p, 0.001))
rnull = function(p=0.5) table(c(0:10, rbinom(1000, 10, 
                  ifelse(p>0&&p<1, p, 0.001))))-1
phat=function(x) mean(rep(0:10,x))/10 
gof_test(x, vals, pnull, rnull, phat=phat, B=500)

---

Adjusted p values for simultaneous testing in the goodness-of-fit problem.

Description

This function performs a number of goodness-of-fit tests and finds the adjusted p value for the combined test.

Usage

gof_test_adjusted_pvalue(
  x,
  vals = NA,
  pnull,
  rnull,
  w = function(x) -99,
  phat = function(x) -99,
  TS,
  TSextra = NA,
  nbins = c(50, 10),
  rate = 0,
  Range = c(-Inf, Inf),
  B = c(5000, 1000),
  minexpcount = 5,
  ChiUsePhat = TRUE,
  maxProcessor,
  doMethods
)

Arguments

x	data set
vals	=NA, values of discrete RV, or NA if data is continuous
pnull	cdf under the null hypothesis
rnull	routine to generate data under the null hypothesis
w	(Optional) function to calculate weights, returns -99 if no weights
phat	=function(x) -99, function to estimate parameters from the data, or -99 if no parameters are estimated
TS	user supplied function to find test statistics, if any
TSextra	=NA, list passed to TS, if desired, or NA
nbins	=c(100, 10) number of bins for chi-square tests
rate	=0 rate of Poisson if sample size is random, 0 if sample size is fixed
Range	=c(-Inf, Inf) limits of possible observations, if any, for chi-square tests
B	=c(5000,1000) number of simulation runs for individual and for adjusted p values
minexpcount	=5 minimal expected bin count required
ChiUsePhat	= TRUE, if TRUE param is estimated parameter, otherwise minimum chi square method is used.
maxProcessor	number of cores to use
doMethods	a vector of codes for the methods to include. If missing, a default selection of methods are used.

Details

For details on the usage of this routine consult the vignette with vignette("Rgof","Rgof")

Value

None

Examples

# Tests to see whether data comes from a standard normal distribution.
pnull = function(x) pnorm(x)
rnull = function()  rnorm(100)
x = rnorm(100)
gof_test_adjusted_pvalue(x, NA, pnull, rnull, B=c(500, 200), 
                            maxProcessor=1)
# Tests to see whether data comes from a normal distribution with standard deviation 1 
# and the mean estimated.
pnull=function(x, m) pnorm(x, m)
rnull=function(m) rnorm(100, m)
TSextra = list(qnull=function(x, m=0) qnorm(x, m))
phat=function(x) mean(x)
x = rnorm(100, 1, 2)
gof_test_adjusted_pvalue(x, NA, pnull, rnull, phat=phat, 
                        TSextra=TSextra, B=c(500, 200), maxProcessor=1)
# Tests to see whether data comes from a binomial (10, 0.5) distribution.
vals=0:10
pnull = function() pbinom(0:10, 10, 0.5)
rnull = function() table(c(0:10, rbinom(1000, 10, 0.5)))-1
x = rnull() 
gof_test_adjusted_pvalue(x, vals, pnull, rnull, 
                        B=c(500, 200), maxProcessor=1)
# Tests to see whether data comes from a binomial distribution with 
# the success probability estimated from the data.
pnull = function(p=0.5) pbinom(0:10, 10, p)
rnull = function(p=0.5) table(c(0:10, rbinom(1000, 10, p)))-1
phat=function(x) mean(rep(0:10,x))/10 
gof_test_adjusted_pvalue(x, vals, pnull, rnull, phat=phat, 
                        B=c(500, 200), maxProcessor=1)

---

This function creates several type of bins for continuous data

Description

This function creates several type of bins for continuous data

Usage

make_bins_cont(
  x,
  pnull,
  qnull = NA,
  phat = function(x) -99,
  DataBased = FALSE,
  nbins = c(50, 10),
  minexpcount = 5,
  Range = c(-99999, 99999)
)

Arguments

x	data set
pnull	cdf under the null hypothesis
qnull	=NA quantile function, if available
phat	=function(x) -99 parameters for pnull
DataBased	=FALSE bins based on data, not expected counts
nbins	=c(50, 10) number of bins
minexpcount	=5 smallest expected count per bin
Range	=c(-99999, 99999) limits of possible observations, if any

Value

A list of bins and bin probabilities

---

This function creates several types of bins for discrete data

Description

This function creates several types of bins for discrete data

Usage

make_bins_disc(
  x,
  pnull,
  phat = function(x) -99,
  nbins = c(50, 10),
  minexpcount = 5
)

Arguments

x	counts
pnull	cumulative distribution function
phat	=function(x) -99, function to estimated parameters, or -99
nbins	=c(50, 10) number of bins
minexpcount	=5 smallest expected count per bin

Value

A list of indices

---

a local function needed for the vignette

Description

a local function needed for the vignette

Usage

newTSdisc(x, pnull, param, vals)

Arguments

x	An integer vector.
pnull	cdf.
param	parameters for pnull in case of parameter estimation.
vals	A numeric vector with the values of the discrete rv.

Value

A vector with test statistics

---

This function draws the power graph, with curves sorted by the mean power and smoothed for easier reading.

Description

This function draws the power graph, with curves sorted by the mean power and smoothed for easier reading.

Usage

plot_power(pwr, xname = " ", title, Smooth = TRUE, span = 0.25)

Arguments

pwr	a matrix of power values, usually from the twosample_power command
xname	Name of variable on x axis
title	(Optional) title of graph
Smooth	=TRUE lines are smoothed for easier reading
span	=0.25bandwidth of smoothing method

Value

plt, an object of class ggplot.

---

This function estimates the power of test routines that calculate p value(s)

Description

This function estimates the power of test routines that calculate p value(s)

Usage

power_newtest(
  TS,
  vals = NA,
  pnull,
  ralt,
  param_alt,
  phat,
  TSextra,
  alpha = 0.05,
  B = 1000
)

Arguments

TS	routine to calculate test statistics.
vals	=NA if data is discrete, a vector of possible values
pnull	routine to calculate the cdf under the null hypothesis
ralt	generate data under alternative hypothesis
param_alt	values of parameter under the alternative hypothesis.
phat	function to estimate parameters, function(x) -99 if no parameter estimation
TSextra	list (possibly) passed to TS
alpha	=0.05 type I error.
B	= 1000 number of simulation runs to estimate the power.

Value

A matrix of power values

---

power_studies_results

Description

the results of the included power studies

Usage

power_studies_results

Format

'power_studies_results'

A list of matrices with powers

---

pvaluecdf

Description

the info needed to draw a graph

Usage

pvaluecdf

Format

'pvaluecdf'

A matrix

---

Power Comparisons

Description

This function runs the case studies included in the package and compares the power of a new test to those included.

Usage

run.studies(
  TS,
  study,
  TSextra = list(aaa = 1),
  With.p.value = FALSE,
  BasicComparison = TRUE,
  nsample = 500,
  alpha = 0.05,
  param_alt,
  maxProcessor,
  B = 1000
)

Arguments

TS	routine to calculate test statistic(s) or p value(s).
study	either the name of the study, or its number. If missing all the studies are run.
TSextra	=list(aaa=1), list passed to TS.
With.p.value	=FALSE does user supplied routine return p values?
BasicComparison	=TRUE if true compares tests on one default value of parameter of the alternative distribution.
nsample	= 500, desired sample size.
alpha	=0.05 type I error
param_alt	(list of) values of parameter under the alternative hypothesis. If missing included values are used.
maxProcessor	number of cores to use for parallel programming
B	= 1000 number of simulation runs

Details

For details on the usage of this routine consult the vignette with vignette("Rgof","Rgof")

Value

A (list of ) matrices of power values

Examples

# New test is a simple chi-square test: 
chitest=function(x, pnull, param, TSextra) {
    nbins=TSextra$nbins
    bins=quantile(x, (0:nbins)/nbins)
    O=hist(x, bins, plot=FALSE)$counts
    if(param[1]!=-99) { #with parameter estimation
        E=length(x)*diff(pnull(bins, param))
        chi=sum((O-E)^2/E)
        pval=1-pchisq(chi, nbins-1-length(param))
    }
    else {
      E=length(x)*diff(pnull(bins))
      chi=sum((O-E)^2/E)
      pval=1-pchisq(chi,nbins-1)
    }  
    out=ifelse(TSextra$statistic, chi, pval)
    names(out)="ChiSquare"
    out
}
TSextra=list(nbins=10, statistic=FALSE) # Use 10 bins, test routine returns p-value
run.studies(chitest, TSextra=TSextra, With.p.value=TRUE, maxProcessor=1, B=200)

---

This function does some rounding to nice numbers

Description

This function does some rounding to nice numbers

Usage

## S3 method for class 'digits'
signif(x, d = 3)

Arguments

x	a list of two vectors
d	=4 number of digits to round to

Value

A list with rounded vectors

---

estimate run time function

Description

estimate run time function

Usage

timecheck(dta, TS, typeTS, TSextra)

Arguments

dta	data set
TS	test statistic
typeTS	format of TS
TSextra	additional info TS

Value

Mean computation time

---

Find test statistics for continuous data

Description

Find test statistics for continuous data

Usage

TS_cont(x, pnull, param, qnull)

Arguments

x	A numeric vector.
pnull	cdf.
param	parameters for pnull in case of parameter estimation.
qnull	An R function, the quantile function under the null hypothesis.

Value

A numeric vector with test statistics

---

Find test statistics for discrete data

Description

Find test statistics for discrete data

Usage

TS_disc(x, pnull, param, vals)

Arguments

x	An integer vector.
pnull	cdf.
param	parameters for pnull in case of parameter estimation.
vals	A numeric vector with the values of the discrete rv.

Value

A vector with test statistics

---