g_gof {discretefit}

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)