Goodness-of-fit Test for the Bivariate Hermite Distribution

Abstract

This paper studies the goodness of fit test for the bivariate Hermite distribution. Specifically, we propose and study a Cramér-von Mises-type test based on the empirical probability generation function. The bootstrap can be used to consistently estimate the null distribution of the test statistics. A simulation study investigates the goodness of the bootstrap approach for finite sample sizes.

Implementation of a Parallel Algorithm to Simulate the Type I Error Probability

“…Additionally, implementing the algorithm developed in this research in the C programming language is planned. Furthermore, developing a package in the R language that incorporates the goodness-of-fit test studied and others proposed in [1, [19][20][21] is also planned. y_max = max(X[2,]) frec = matrix(0,x_max-x_min+1,y_max-y_min+1) for(i in x_min:x_max){ p = i -x_min + 1 for(j in y_min:y_max){ q = j -y_min + 1 for (k in 1 for(j in y_min:y_max){ q = j -y_min + 1 if(frec[p,q]>0){ prob_ij = probPB(i,j,t1,t2,t3) prob_im1jm1 = probPB(i-1,j-1,t1,t2,t3) prob_im2jm2 = probPB(i-2,j-2,t1,t2,t3) prob_im2jm1 = probPB(i-2,j-1,t1,t2,t3) prob_im1jm2 = probPB(i-1,j-2,t1,t2,t3) prob_im1j = probPB(i-1,j,t1,t2,t3) prob_ijm1 = probPB(i,j-1,t1,t2,t3) rm = rm + frec[p,q]*prob_im1jm1/prob_ij sum1 = (prob_im2jm2 -prob_im2jm1 -prob_im1jm2)/prob_ij sum2 = prob_im1jm1*(prob_im1j + prob_ijm1 -prob_im1jm1)/(prob_ij^2) der = der + frec[p,q]*(sum1 + sum2)…”

Goodness-of-fit tests for the bivariate Poisson distribution

“…where w(u) is a measurable nonnegative weight function with finite integral over [0, 1] m , and and Jiménez-Gamero (2016) With the aim of extending W n to the multivariate case, NJ (2016) proposed the following statistic for testing H 0m ,…”