Journal of Applied Mathematics and Decision Sciences
Volume 2008 (2008), Article ID 463781, 8 pages
Research Article

Tests of Fit for the Logarithmic Distribution

D. J. Best,1 J. C. W. Rayner,1 and O. Thas2

1School of Mathematical and Physical Sciences, University of Newcastle, NSW 2308, Australia
2Department of Applied Mathematics, Biometrics and Process Control, Ghent University, 9000 Gent, Belgium

Received 21 September 2007; Accepted 25 February 2008

Academic Editor: Chin Lai

Copyright © 2008 D. J. Best et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Smooth tests for the logarithmic distribution are compared with three tests: the first is a test due to Epps and is based on a probability generating function, the second is the Anderson-Darling test, and the third is due to Klar and is based on the empirical integrated distribution function. These tests all have substantially better power than the traditional Pearson-Fisher X2 test of fit for the logarithmic. These traditional chi-squared tests are the only logarithmic tests of fit commonly applied by ecologists and other scientists.