Tests For An Increasing Trend In The Intensity Of A Poisson Process: A Power Study


This article concerns a comparison of several tests for testing the hypothesis of a constant intensity against the alternative of an increasing intensity function in a nonhomogeneous Poisson process (NHPP). The study includes the well-known Laplace test statistic, the most powerful test for the shape parameter in a Poisson process with Weibull intensity, the likelihood ratio test against arbitrary NHPP alternatives, two nonparametric tests for trends based on Kendall's tau and Spearman's rho, and a test based on an F statistic. The powers of the tests are determined by Monte Carlo simulation against alternatives that are increasing at an exponential rate, a power rate (Weibull intensity), and a logarithmic rate. Alternatives that are step functions with one jump are also considered. In a few cases, the exact powers are also obtained analytically. © 1985 Taylor & Francis Group, LLC.


Mathematics and Statistics

Second Department

Geosciences and Geological and Petroleum Engineering


Office of Naval Research, Grant N00014-80-C-0322

Keywords and Phrases

Increasing intensities; Laplace test; Likelihood ratio tests; Poisson processes; Wei-bull poisson processes

International Standard Serial Number (ISSN)

1537-274X; 0162-1459

Document Type

Article - Journal

Document Version


File Type





© 2023 Taylor and Francis Group; Taylor and Francis; American Statistical Association, All rights reserved.

Publication Date

01 Jan 1985