AD {gofIG}R Documentation

Description

This function computes the test statistic of the goodness-of-fit test for the inverse Gaussian family in the spirit of Anderson and Darling.

Usage

AD(data)

Arguments

data

a vector of positive numbers.

Details

Let X_{(j)} denote the jth order statistic of X_1, \ldots, X_n, a sequence of independent observations of a positive random variable X. Furthermore, let \hat{F}(x) = F(x; \hat{\mu}_n, \hat{\lambda}_n), where F is the distribution function of the inverse Gaussian distribution. Note that \hat{\mu}_n,\hat{\lambda}_n are the maximum likelihood estimators for \mu and \lambda, respectively, the parameters of the inverse Gaussian distribution. The null hypothesis is rejected for large values of the test statistic:

AD = -n - \frac{1}{n} \sum_{j=1}^{n} \left[ (2j-1) \log \hat{F}(X_{(j)}) + (2(n-j) + 1) \log \left( 1 - \hat{F}(X_{(j)}) \right) \right].

Value

value of the test statistic.

References

Allison, J.S., Betsch, S., Ebner, B., Visagie, I.J.H. (2022) "On Testing the Adequacy of the Inverse Gaussian Distribution". LINK

Examples

AD(rmutil::rinvgauss(20,2,1))


[Package gofIG version 1.0 Index]