Simulated Chi-squared goodness-of-fit test
Description
The chisq_gof() function implements Monte Carlo simulations to calculate p-values
based on the Chi-squared statistic for goodness-of-fit tests for discrete
distributions.
Usage
chisq_gof(x, p, reps = 10000, tolerance = 64 * .Machine$double.eps)
Arguments
x
a numeric vector that contains observed counts for each bin/category.
p
a vector of probabilities of the same length of x. An error is given if any entry of p is negative or if the sum of p does not equal one.
reps
an integer specifying the number of Monte Carlo simulations. The default is set to 10,000 which may be appropriate for exploratory analysis. A higher number of simulation should be selected for more precise results.
tolerance
sets an upper bound for rounding errors when evaluating
whether a statistic for a simulation is greater than or equal to the
statistic for the observed data. The default is identical to the tolerance
set for simulations in the chisq.test function from the stats
package in base R.
Value
A list with class "htest" containing the following components:
statistic
the value of the Chi-squared test statistic
p.value
the simulated p-value for the test
method
a character string describing the test
data.name
a character string give the name of the data
Examples
x <- c(15, 36, 17)
p <- c(0.25, 0.5, 0.25)
chisq_gof(x, p)
Simulated Cramer-von Mises goodness-of-fit test
Description
The cvm_gof() function implements Monte Carlo simulations to calculate p-values
based on the Cramer-von Mises statistic (W^2) for goodness-of-fit tests for discrete
distributions.
Usage
cvm_gof(x, p, reps = 10000, tolerance = 64 * .Machine$double.eps)
Arguments
x
a numeric vector that contains observed counts for each bin/category.
p
a vector of probabilities of the same length of x. An error is given if any entry of p is negative or if the sum of p does not equal one.
reps
an integer specifying the number of Monte Carlo simulations. The default is set to 10,000 which may be appropriate for exploratory analysis. A higher number of simulation should be selected for more precise results.
tolerance
sets an upper bound for rounding errors when evaluating
whether a statistic for a simulation is greater than or equal to the
statistic for the observed data. The default is identical to the tolerance
set for simulations in the chisq.test function from the stats
package in base R.
Value
A list with class "htest" containing the following components:
statistic
the value of the Cramer-von Mises test statistic (W2)
p.value
the simulated p-value for the test
method
a character string describing the test
data.name
a character string give the name of the data
Examples
x <- c(15, 36, 17)
p <- c(0.25, 0.5, 0.25)
cvm_gof(x, p)
Simulated Freeman-Tukey (Hellinger-distance) goodness-of-fit test
Description
The ft_gof() function implements Monte Carlo simulations to calculate p-values
based on the Freeman-Tukey statistic for goodness-of-fit tests for discrete
distributions. This statistic is also referred to as the Hellinger-distance.
Asymptotically, the Freeman-Tukey GOF test is identical to the Chi-squared
GOF test, but for smaller n, results may vary significantly.
Usage
ft_gof(x, p, reps = 10000, tolerance = 64 * .Machine$double.eps)
Arguments
x
a numeric vector that contains observed counts for each bin/category.
p
a vector of probabilities of the same length of x. An error is given if any entry of p is negative or if the sum of p does not equal one.
reps
an integer specifying the number of Monte Carlo simulations. The default is set to 10,000 which may be appropriate for exploratory analysis. A higher number of simulation should be selected for more precise results.
tolerance
sets an upper bound for rounding errors when evaluating
whether a statistic for a simulation is greater than or equal to the
statistic for the observed data. The default is identical to the tolerance
set for simulations in the chisq.test function from the stats
package in base R.
Value
A list with class "htest" containing the following components:
statistic
the value of the Freeman-Tukey test statistic (W2)
p.value
the simulated p-value for the test
method
a character string describing the test
data.name
a character string give the name of the data
Examples
x <- c(15, 36, 17)
p <- c(0.25, 0.5, 0.25)
ft_gof(x, p)
Simulated log-likelihood-ratio (G^2) goodness-of-fit test
Description
The g_gof() function implements Monte Carlo simulations to calculate p-values
based on the log-likelihood-ratio statistic for goodness-of-fit tests for discrete
distributions. In this context, the log-likelihood-ratio statistic is often referred
to as the G^2 statistic. Asymptotically, the G^2 GOF test is identical to the Chi-squared
GOF test, but for smaller n, results may vary significantly.
Usage
g_gof(x, p, reps = 10000, tolerance = 64 * .Machine$double.eps)
Arguments
x
a numeric vector that contains observed counts for each bin/category.
p
a vector of probabilities of the same length of x. An error is given if any entry of p is negative or if the sum of p does not equal one.
reps
an integer specifying the number of Monte Carlo simulations. The default is set to 10,000 which may be appropriate for exploratory analysis. A higher number of simulation should be selected for more precise results.
tolerance
sets an upper bound for rounding errors when evaluating
whether a statistic for a simulation is greater than or equal to the
statistic for the observed data. The default is identical to the tolerance
set for simulations in the chisq.test function from the stats
package in base R.
Value
A list with class "htest" containing the following components:
statistic
the value of the log-likelihood-ratio test statistic (G2)
p.value
the simulated p-value for the test
method
a character string describing the test
data.name
a character string give the name of the data
Examples
x <- c(15, 36, 17)
p <- c(0.25, 0.5, 0.25)
g_gof(x, p)
Simulated Kolmogorov-Smirnov goodness-of-fit test
Description
The ks_gof() function implements Monte Carlo simulations to calculate p-values
based on the Kolmogorov-Smirnov statistic for goodness-of-fit tests for discrete
distributions. The p-value expressed by ks_gof() is based on a two-sided
alternative hypothesis.
Usage
ks_gof(x, p, reps = 10000, tolerance = 64 * .Machine$double.eps)
Arguments
x
a numeric vector that contains observed counts for each bin/category.
p
a vector of probabilities of the same length of x. An error is given if any entry of p is negative or if the sum of p does not equal one.
reps
an integer specifying the number of Monte Carlo simulations. The default is set to 10,000 which may be appropriate for exploratory analysis. A higher number of simulation should be selected for more precise results.
tolerance
sets an upper bound for rounding errors when evaluating
whether a statistic for a simulation is greater than or equal to the
statistic for the observed data. The default is identical to the tolerance
set for simulations in the chisq.test function from the stats
package in base R.
Value
A list with class "htest" containing the following components:
statistic
the value of the Kolmogorov-Smirnov test statistic
p.value
the simulated p-value for the test
method
a character string describing the test
data.name
a character string give the name of the data
Examples
x <- c(15, 36, 17)
p <- c(0.25, 0.5, 0.25)
ks_gof(x, p)
Simulated root-mean-square goodness-of-fit test
Description
The rms_gof() function implements Monte Carlo simulations to calculate p-values
based on the root-mean-square statistic for goodness-of-fit tests for discrete
distributions.
Usage
rms_gof(x, p, reps = 10000, tolerance = 64 * .Machine$double.eps)
Arguments
x
a numeric vector that contains observed counts for each bin/category.
p
a vector of probabilities of the same length of x. An error is given if any entry of p is negative or if the sum of p does not equal one.
reps
an integer specifying the number of Monte Carlo simulations. The default is set to 10,000 which may be appropriate for exploratory analysis. A higher number of simulation should be selected for more precise results.
tolerance
sets an upper bound for rounding errors when evaluating
whether a statistic for a simulation is greater than or equal to the
statistic for the observed data. The default is identical to the tolerance
set for simulations in the chisq.test function from the stats
package in base R.
Value
A list with class "htest" containing the following components:
statistic
the value of the root-mean-square test statistic
p.value
the simulated p-value for the test
method
a character string describing the test
data.name
a character string give the name of the data
Examples
x <- c(15, 36, 17)
p <- c(0.25, 0.5, 0.25)
rms_gof(x, p)