dbEmpLikeGOF (version 1.2.4)

dbEmpLikeGOF: Density Based Empirical Likelihood Goodness of Fit

Description

Performs density based empirical likelihood goodness of fit tests for normality, uniformity, and distribution equality.

Usage

dbEmpLikeGOF(x, y=NA, testcall=c("uniform", "normal"), delta=0.50, delta.equality=0.10, num.mc=1000, pvl.Table=TRUE, vrb=TRUE, random.seed.flag=TRUE)

Arguments

x

vector of data values

y

an optional vector of data values when testing for distribution equality

testcall

Type of distribution: either uniform or normal

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.

num.mc

number of simulations to use when calculating p-value

pvl.Table

logical indicating if p-value should be calculated based on estimates from stored data tables or by using Monte Carlo techniques

vrb

logical indicating if status messages should be printed

random.seed.flag

logical if set seed should be set

Value

Returns a vector of length 2 with test statistic and p-value.

teststat

the value of the test statistic

pvalue

the p-value for the test

Details

The method employs a density-based empirical likelihood approach to obtain test statistic and p-values for a goodness-of-fit tests for uniformity, normality, and two sample distribution equality.

If both 'x' and 'y' are specified then a two sample distribution is performed to evaluate the null hypothesis of equal distributions.

If only 'x' is specified, then the 'testcall' option must be specified as either 'uniform' (uniform) or 'normal' (normal) denoting whether the distribution of the 'x' vector of observations should be tested against the normal or uniform distribution. 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 p-value for 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 p-value is determined from Monte-Carlo simulations where the number of resamplings is set 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/

Vexler A, Gurevich G, Empirical likelihood ratios applied to goodness-of-fit tests based on sample entropy. Computational Statistics and Data Analysis 54(2010) 531-545.

Gurevich G, Vexler A, A two-sample empirical likelihood ratio test based on samples entropy. Statistics and Computing, 2011.

Examples

 x <- rnorm(100)
 testNorm <- dbEmpLikeGOF(x, testcall="normal")
 testUni <- dbEmpLikeGOF(x, testcall="uniform")
 testNorm
 testUni
 y=rnorm(40)
 testDist <- dbEmpLikeGOF(x,y)
 testDist