Package 'Rgof' reference manual

Title:	1d Goodness of Fit Tests
Description:	Routines that allow the user to run a large number of goodness-of-fit tests. It allows for data to be continuous or discrete. It includes routines to estimate the power of the tests and display them as a power graph. The routine run.studies allows a user to quickly study the power of a new method and how it compares to some of the standard ones.
Authors:	Wolfgang Rolke [aut, cre]
Maintainer:	Wolfgang Rolke <[email protected]>
License:	GPL (>= 2)
Version:	3.0.0
Built:	2025-03-03 06:20:52 UTC
Source:	https://github.com/cran/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)
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)
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
)
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
)
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
)
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
)
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

Find the power of various gof tests for continuous data.

Description

Find the power of various gof tests for continuous data.

Usage

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

Arguments

`pnull`	function to find cdf under null hypothesis
`vals`	=NA, values of rv, if data is discrete, NA if data is continuous
`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`	=NA, list provided to TS
`alpha`	=0.05, the level of the hypothesis test
`Range`	=c(-Inf, Inf) limits of possible observations, if any
`B`	=c(1000, 1000), number of simulation runs to find power and null distribution
`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
`maxProcessors`	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.

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=c(500, 500))
# Power of tests when null hypothesis specifies normal distribution and 
# mean and standard deviation are estimated from the data. 
# Example is not run because it takes several minutes.
# 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))
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))) 
gof_power(pnull, NA, rnull, ralt, c(0, 1), phat=phat, TSextra=TSextra, 
          B=c(200, 200), maxProcessor=2)
# 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=c(500,500))
# 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=c(200, 200), maxProcessor=2)

# 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=c(500, 500))
# Power of tests when null hypothesis specifies normal distribution and 
# mean and standard deviation are estimated from the data. 
# Example is not run because it takes several minutes.
# 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))
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))) 
gof_power(pnull, NA, rnull, ralt, c(0, 1), phat=phat, TSextra=TSextra, 
          B=c(200, 200), maxProcessor=2)
# 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=c(500,500))
# 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=c(200, 200), maxProcessor=2)

Find the power of various gof tests for continuous data.

Description

Find the power of various gof tests for continuous data.

Usage

gof_power_cont(
  pnull,
  rnull,
  ralt,
  param_alt,
  w = function(x) -99,
  phat = function(x) -99,
  TS,
  TSextra = NA,
  alpha = 0.05,
  Range = c(-Inf, Inf),
  B = c(1000, 1000),
  nbins = c(100, 10),
  rate = 0,
  maxProcessors,
  minexpcount = 5,
  ChiUsePhat = TRUE
)
gof_power_cont(
  pnull,
  rnull,
  ralt,
  param_alt,
  w = function(x) -99,
  phat = function(x) -99,
  TS,
  TSextra = NA,
  alpha = 0.05,
  Range = c(-Inf, Inf),
  B = c(1000, 1000),
  nbins = c(100, 10),
  rate = 0,
  maxProcessors,
  minexpcount = 5,
  ChiUsePhat = TRUE
)

Arguments

`pnull`	function to find cdf under null hypothesis
`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 if no parameters aare estimated
`TS`	user supplied function to find test statistics, if any
`TSextra`	=NA, list provided to TS
`alpha`	=0.05, the level of the hypothesis test
`Range`	=c(-Inf, Inf) limits of possible observations, if any
`B`	=c(1000, 1000), number of simulation runs to find power and null distribution
`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
`maxProcessors`	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.

Value

A numeric matrix of power values.

Find the power of various gof tests for discrete data.

Description

Find the power of various gof tests for discrete data.

Usage

gof_power_disc(
  pnull,
  rnull,
  vals,
  ralt,
  param_alt,
  phat = function(x) -99,
  TS,
  TSextra = NA,
  alpha = 0.05,
  B = c(1000, 1000),
  nbins = c(100, 10),
  rate = 0,
  maxProcessors,
  minexpcount = 5,
  ChiUsePhat = TRUE
)
gof_power_disc(
  pnull,
  rnull,
  vals,
  ralt,
  param_alt,
  phat = function(x) -99,
  TS,
  TSextra = NA,
  alpha = 0.05,
  B = c(1000, 1000),
  nbins = c(100, 10),
  rate = 0,
  maxProcessors,
  minexpcount = 5,
  ChiUsePhat = TRUE
)

Arguments

`pnull`	cumulative distribution function under the null hypothesis
`rnull`	a function to generate data under null hypothesis
`vals`	values of discrete rv.
`ralt`	function to generate data under alternative hypothesis
`param_alt`	vector of parameter values for distribution under alternative hypothesis
`phat`	=function(x) -99, function to estimate parameters from the data, -99 if no parameters are estimated
`TS`	user supplied function to find test statistics, if any
`TSextra`	=NA, list passed to TS, if desired
`alpha`	=0.05, the level of the hypothesis test
`B`	=c(1000, 1000), number of simulation runs to find power and null distribution
`nbins`	=c(100, 10) number of bins for chi square tests
`rate`	rate of Poisson if sample size is random
`maxProcessors`	maximum of number of processors to use, 1 if no parallel processing is needed or number of cores-1 if missing
`minexpcount`	=5 minimal number of expected counts in each bin for chi square tests
`ChiUsePhat`	= TRUE, if TRUE param is estimated parameter, otherwise minimum chi square method is used.

Value

A numeric matrix of power values.

This function performs a number of gof tests

Description

This function performs a number of gof tests

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,
  maxProcessors = 1,
  doMethods = "all"
)
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,
  maxProcessors = 1,
  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.
`maxProcessors`	=1, number of processors to use in parallel processing.
`doMethods`	Methods to include in tests

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)
# 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)
# 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")
# 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) 

# 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)
# 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)
# 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")
# 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)

This function performs a number of gof tests and finds the adjusted p value for the combined test

Description

This function performs a number of gof 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,
  doMethods
)
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,
  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.
`doMethods`	Methods to include in tests

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(1000, 200))
# 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_adjusted_pvalue(x, NA, pnull, rnull, phat=phat, TSextra=TSextra, B=c(1000, 200))
# 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(1000, 200))
# 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_adjusted_pvalue(x, vals, pnull, rnull, phat=phat, B=c(1000, 200)) 

# 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(1000, 200))
# 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_adjusted_pvalue(x, NA, pnull, rnull, phat=phat, TSextra=TSextra, B=c(1000, 200))
# 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(1000, 200))
# 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_adjusted_pvalue(x, vals, pnull, rnull, phat=phat, B=c(1000, 200))

This function performs a number of gof tests for continuous data

Description

This function performs a number of gof tests for continuous data

Usage

gof_test_cont(
  x,
  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,
  maxProcessors = 1,
  doMethods = "all"
)
gof_test_cont(
  x,
  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,
  maxProcessors = 1,
  doMethods = "all"
)

Arguments

`x`	data set
`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 aare estimated
`TS`	user supplied function to find test statistics, if any
`TSextra`	=NA, list passed to TS, if desired
`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
`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.
`maxProcessors`	=1, number of processors to use in parallel processing. If missing single processor is used.
`doMethods`	Methods to include in tests

Value

A list with vectors of test statistics and p.values

This function performs a number of gof tests for continuous data and finds the adjusted p value

Description

This function performs a number of gof tests for continuous data and finds the adjusted p value

Usage

gof_test_cont_adj(
  x,
  pnull,
  rnull,
  w = function(x) -99,
  phat = function(x) 0,
  TS,
  TSextra = NA,
  nbins = c(50, 10),
  rate = 0,
  Range = c(-Inf, Inf),
  B = c(5000, 1000),
  minexpcount = 5,
  ChiUsePhat = TRUE,
  doMethods = c("W", "ZC", "AD", "ES-s-P")
)
gof_test_cont_adj(
  x,
  pnull,
  rnull,
  w = function(x) -99,
  phat = function(x) 0,
  TS,
  TSextra = NA,
  nbins = c(50, 10),
  rate = 0,
  Range = c(-Inf, Inf),
  B = c(5000, 1000),
  minexpcount = 5,
  ChiUsePhat = TRUE,
  doMethods = c("W", "ZC", "AD", "ES-s-P")
)

Arguments

`x`	data set
`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 aare estimated
`TS`	user supplied function to find test statistics, if any
`TSextra`	=NA, list passed to TS, if desired
`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
`Range`	=c(-Inf, Inf) limits of possible observations, if any, for chi-square tests
`B`	=c(5000,1000) number of simulation runs for p values and for p value distribution
`minexpcount`	=5 minimal expected bin count required
`ChiUsePhat`	=TRUE, if TRUE param is estimated parameter, otherwise minimum chi square method is used.
`doMethods`	Methods to include in tests

Value

None

This function performs a number of gof tests for discrete data.

Description

This function performs a number of gof tests for discrete data.

Usage

gof_test_disc(
  x,
  pnull,
  rnull,
  vals,
  phat = function(x) -99,
  TS,
  TSextra = NA,
  nbins = c(50, 10),
  rate = 0,
  B = 5000,
  minexpcount = 5,
  ChiUsePhat = TRUE,
  maxProcessors = 1,
  doMethods = "Default"
)
gof_test_disc(
  x,
  pnull,
  rnull,
  vals,
  phat = function(x) -99,
  TS,
  TSextra = NA,
  nbins = c(50, 10),
  rate = 0,
  B = 5000,
  minexpcount = 5,
  ChiUsePhat = TRUE,
  maxProcessors = 1,
  doMethods = "Default"
)

Arguments

`x`	data set (the counts)
`pnull`	cumulative distribution function under the null hypothesis
`rnull`	routine to generate data under the null hypothesis
`vals`	a vector of values of discrete random variables
`phat`	=function(x) -99, function to estimate parameters from the data, or -99 if no parameters aare estimated
`TS`	=NA, user supplied function to find test statistics
`TSextra`	=NA, list passed to TS, if desired
`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
`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.
`maxProcessors`	=1, number of processors to use in parallel processing. If missing single processor is used.
`doMethods`	Methods to include in tests

Value

A numeric matrix of test statistics and p.values

This function performs a number of gof tests for discrete data and finds the adjusted p value

Description

This function performs a number of gof tests for discrete data and finds the adjusted p value

Usage

gof_test_disc_adj(
  x,
  pnull,
  rnull,
  vals,
  phat = function(x) -99,
  TS,
  TSextra = NA,
  nbins = c(50, 10),
  rate = 0,
  B = c(5000, 1000),
  minexpcount = 5,
  ChiUsePhat = TRUE,
  doMethods = c("Wassp1", "W", "AD", "s-P")
)
gof_test_disc_adj(
  x,
  pnull,
  rnull,
  vals,
  phat = function(x) -99,
  TS,
  TSextra = NA,
  nbins = c(50, 10),
  rate = 0,
  B = c(5000, 1000),
  minexpcount = 5,
  ChiUsePhat = TRUE,
  doMethods = c("Wassp1", "W", "AD", "s-P")
)

Arguments

`x`	data set (the counts)
`pnull`	cumulative distribution function under the null hypothesis
`rnull`	routine to generate data under the null hypothesis
`vals`	a vector of values of discrete random variables
`phat`	=function(x) -99, function to estimate parameters from the data, or -99 if no parameters aare estimated
`TS`	=NA, user supplied function to find test statistics
`TSextra`	=NA, list passed to TS, if desired
`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
`B`	=c(5000, 1000) number of simulation runs for p values and for adjusted p value
`minexpcount`	=5 minimal expected bin count required
`ChiUsePhat`	= TRUE, if TRUE param is estimated parameter, otherwise minimum chi square method is used.
`doMethods`	Methods to include in tests

Value

A numeric matrix of test statistics and p.values

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)
)
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
)
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)
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)
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
)
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 altenative 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
power_studies_results

Format

'power_studies_results'

A list of matrices with powers

pvaluecdf

Description

the info needed to draw a graph

Usage

pvaluecdf
pvaluecdf

Format

'pvaluecdf'

A matrix

This function runs the case studies included in the package

Description

This function runs the case studies included in the package

Usage

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

Value

A (list of ) matrices of p.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$statistic, chi, pval)
    names(out)="ChiSquare"
    out
}
TSextra=list(nbins=10, statistic=FALSE) # Use 10 bins, test routine returns p-value
Rgof::run.studies(chitest, TSextra=TSextra, With.p.value=TRUE, B=c(400,4400), maxProcessor=1)
# New test is a simple chi-square test: 
chitest=function(x, pnull, param, TSextra) {
    nbins=TSextra$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
Rgof::run.studies(chitest, TSextra=TSextra, With.p.value=TRUE, B=c(400,4400), maxProcessor=1)

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 = 4)
## S3 method for class 'digits'
signif(x, d = 4)

Arguments

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

Value

A list with rounded vectors

Find test statistics for continuous data

Description

Find test statistics for continuous data

Usage

TS_cont(x, pnull, param, qnull)
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)
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

Package 'Rgof'

Help Index

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

Description

Usage

Arguments

Value

This function checks whether the inputs have the correct format

Description

Usage

Arguments

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

Description

Usage

Arguments

Value

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

Description

Usage

Arguments

Value

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

Description

Usage

Arguments

Value

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

Description

Usage

Arguments

Value

Find the power of various gof tests for continuous data.

Description

Usage

Arguments

Value

Examples

Find the power of various gof tests for continuous data.

Description

Usage

Arguments

Value

Find the power of various gof tests for discrete data.

Description

Usage

Arguments

Value

This function performs a number of gof tests

Description

Usage

Arguments

Value

Examples

This function performs a number of gof tests and finds the adjusted p value for the combined test

Description

Usage

Arguments

Value

Examples

This function performs a number of gof tests for continuous data

Description

Usage

Arguments

Value

This function performs a number of gof tests for continuous data and finds the adjusted p value

Description

Usage

Arguments

Value

This function performs a number of gof tests for discrete data.

Description

Usage

Arguments

Value

This function performs a number of gof tests for discrete data and finds the adjusted p value

Description

Usage

Arguments

Value

This function creates several type of bins for continuous data