Testing for a trend in exponential means: A two-moment approximation to the null distribution of the likelihood-ratio statistic

The likelihood-ratio test statistic for testing homogeneity of exponential means with an ordered alternative has a rather complex null distribution. Expressions for the mean and variance of its null distribution are derived, and the accuracy of a two-moment chi-squared approximation is studied. The coefficients needed to implement the approximation are tabled. The application of these results in testing for a constant versus a nondecreasing intensity in a nonhomogeneous Poisson process is also discussed.