Various modified Bonferroni procedures (MBPs) have been proposed in order to improve the power of the classical Bonferroni procedure (CBP). In the present paper, powers of these MBPs are investigated by a Monte Carlo study for pairwise comparisons. It is shown that they can be remarkably more powerful than the CBP and Tukey's procedure with respect to all-pairs power, whereas all these procedures with respect to any-pair power are almost the same. Therefore, we recommend the use of MBPs rather than the CBP or Tukey's procedure. Shaffer's procedure sometimes shows higher power than other MBPs and would be the best choice for pairwise comparisons.

bivariate quasi-likelihood equation, integrability condition, integrating factor, multivariate (or bivariate) gamma distribution, non-integrable quasi-score function,

We propose a new bivariate negative binomial model with constant correlation structure, which was derived from a contagious bivariate distribution of two independent Poisson mass functions, by mixing the proposed bivariate gamma type density with constantly correlated covariance structure (Iwasaki & Tsubaki, 2005), which satisfies the integrability condition of McCullagh & Nelder (1989, p. 334). The proposed bivariate gamma type density comes from a natural exponential family. Joe (1997) points out the necessity of a multivariate gamma distribution to derive a multivariate distribution with negative binomial margins, and the luck of a convenient form of multivariate gamma distribution to get a model with greater flexibility in a dependent structure with indices of dispersion. In this paper we first derive a new bivariate negative binomial distribution as well as the first two cumulants, and, secondly, formulate bivariate generalized linear models with a constantly correlated negative binomial covariance structure in addition to the moment estimator of the components of the matrix. We finally fit the bivariate negative binomial models to two correlated environmental data sets.Bivariate negative binomial generalized linear models (BIVARNB GLM), bivariate negative binomial distribution, bivariate gamma type GLM, bivariate count data analysis,

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