dbEmpLikeGOF (version 1.2.4)

returnCutoff: Estimates the statistic cutoff for a target alpha

Description

estimates the test statistic cutoff for significance

Usage

returnCutoff(sample.size, testcall=c("uniform", "normal", "distribution.equality"), targetalpha=.05, num.mc=200, delta=0.5, delta.equality=0.10, pvl.Table=FALSE, random.seed.flag=TRUE)

Arguments

sample.size

number of observations

testcall

Type of distribution: either uniform, normal, or distribution.equality

targetalpha

The significance level for the test.

num.mc

number of simulations to estimate distribution of statistic

delta

an option for changing the minimizing range for the EL ratio test statistic for the normal and uniform distribution.

delta.equality

an option for changing the minimizing range for the EL ratio test statistic for the two sample distribution equality

pvl.Table

logical indicating if value should be calculated based on estimates from data table or by using monte carlo techniques

random.seed.flag

logical if set seed should be set

Value

level 'targetalpha'

Details

This function is designed to return the cut-off for significance for the statistics obtained from the density-based EL tests described in Vexler and Gurevich, 2010 and Gurevich and Vexler, 2011. The significance level for the associated cutoffs are specified by the user in 'targetalpha'. Note 'sample.size' should be a scalar for the normal and uniform tests, but a vector of length two for 'testcall=distribution.equality' denoting the number of observations for each sample.

The 'delta' value should remain at the default value of 0.50. The 'delta' value corresponds to the 'delta' in equation 2.10 (normal) or equation 2.3.2 (uniform) in Vexler and Gurevich, 2010. Essentially this setting controls the range over which a minimum is taken to produce the EL ratio test statistic The range is from 1 to n^(1-'delta') where 'n' represents the number of observations in 'x'. The 'delta.equality' option specifies the range over which a minimum is taken to produce the EL ratio test statistic for the two sample distribution equality test. The lower endpoint in the range is n^(0.5+delta) and upper endpoint is min(n^(1-delta),n/2) where 'n' corresponds to the number of observations. Acceptable delta values are in the interval (0,0.25).From our experiences, the two sample distribution test is rather robust to the choice of 'delta.equality'. The 'pvl.Table' is a binary option where when TRUE, the test statistic is determined by imputation from a stored table of test statistics and significance levels for common sample sizes. If 'pvl.Table' is FALSE, then the test statistic is determined from a Monte-Carlo simulation where the number of resamplings is controlled by 'num.mc'.

References

Jeffrey C. Miecznikowski, Albert Vexler, Lori A. Shepherd (2013). dbEmpLikeGOF: An R Package for Nonparametric Likelihood Ratio Tests for Goodness-of-Fit and Two-Sample Comparisons Based on Sample Entropy. Journal of Statistical Software, 54(3), 1-19. http://www.jstatsoft.org/v54/i03/

Examples

 returnCutoff(sample.size=50, testcall="normal")
 returnCutoff(sample.size=50, testcall="uniform")
 returnCutoff(sample.size=10, testcall="distribution.equality")
 returnCutoff(sample.size=c(10,15), testcall="distribution.equality")