# NLRTest: Nonparametric likelihood ratio test to test for symmetry. In QBAsyDist: Asymmetric Distributions and Quantile Estimation

## Description

The nonparametric likelihood ratio test to test for symmetry is discussed in Gijbels et al. (2019d).

## Usage

 ```1 2``` ```NLRTest(y, f = NULL, F = NULL, QF = NULL, method = c("smooth", "parametric"), nboot = 500) ```

## Arguments

 `y` This is a vector of quantiles. `f` This is the reference density function f which is a standard version of a unimodal and symmetric around 0 density. `F` This is the cumulative distribution function F of a unimodal and symmetric around 0 reference density function f. `QF` This is the quantile function of the reference density f. `method` The method to be used for drawing bootstrap samples. The default method is a smooth bootstrap procedure. The density function f, the cumulative distribution function F and the quantile function QF are required for parametric bootstrap procedure. If QF is not given, then the numerical QF will be used. `nboot` The number of bootstrap samples desired. The default number is 500.

## Value

The nonparametric likelihood ratio test statistic with bootstrap P-value.

## References

Gijbels, I., Karim, R. and Verhasselt, A. (2019d). Test of symmetry and a quantile-based asymmetric family of densities, Manuscript.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17``` ```# Example 1: Let F be a standard normal cumulative distribution function then f_N<-function(s){dnorm(s, mean = 0,sd = 1)} # density function of N(0,1) F_N<-function(s){pnorm(s, mean = 0,sd = 1)} # distribution function of N(0,1) QF_N<-function(beta){qnorm(beta, mean = 0, sd = 1, lower.tail = TRUE, log.p = FALSE)} # Example: STRength dataset my.sample<-c(1.901,2.132,2.203,2.228,2.257,2.350,2.361,2.396,2.397, 2.445,2.454,2.474,2.518,2.522,2.525,2.532,2.575,2.614,2.616, 2.618,2.624,2.659,2.675,2.738,2.740,2.856,2.917,2.928,2.937, 2.937,2.977,2.996,3.030,3.125,3.139,3.145,3.220,3.223,3.235, 3.243,3.264,3.272,3.294,3.332,3.346,3.377,3.408,3.435,3.493, 3.501,3.537,3.554,3.562,3.628,3.852,3.871,3.886,3.971,4.024, 4.027,4.225,4.395,5.020) NLRTest(my.sample,f=NULL,F=NULL,QF=NULL,method=c("smooth"),nboot=500) NLRTest(my.sample,f=f_N,F=F_N,QF=QF_N,method=c("parametric"),nboot=500) NLRTest(my.sample,f=f_N,F=F_N,QF=NULL,method=c("parametric"),nboot=500) ```

QBAsyDist documentation built on Sept. 4, 2019, 1:05 a.m.