Journal of Statistical Theory and Practice

, Volume 6, Issue 4, pp 783–792 | Cite as

Combined Tests for the Homogeneity of Weibull (or Extreme Value) Populations With Censored Data

  • K. ThiagarajahEmail author


A method of combining two independent test statistics to test the homogeneity of several Weibull (or extreme value) populations under censoring is considered. The procedures developed in this paper are based on Fisher’s method of combining two likelihood ratio statistics and two score statistics. The performance of these procedures are examined, through simulations, in terms of empirical size and power of the test statistics. We also develop two other statistics to test the equality of several Weibull scale parameters and shape parameters (or extreme value location and scale parameters) simultaneously. Simulation results show that the Fisher’s method of combining two independent statistics performs reasonably well under censoring.


Likelihood ratio statistic Score statistic Fisher’s method Extreme value distribution Censored data 

AMS 2000 Subject Classification

62N05 62N01 62F03 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Durairajan, T. M. 1985. Bahadur efficient test for the parameter of inverse Gaussian distribution. J. Agric. Stat., 37, 192–197.MathSciNetGoogle Scholar
  2. Fisher, R. A. 1950. Statistical methods for research workers, 11th ed., Edinburgh, Oliver & Boyd.zbMATHGoogle Scholar
  3. Jiang, X., and S. R. Paul. 2004. Testing the equality of means and variances of several Weibull populations. Int. J. Stat. Sci., 3, 179–190.Google Scholar
  4. Lawless, J. F. 1982. Statistical models and methods for lifetime data. New York, Wiley.zbMATHGoogle Scholar
  5. Lawless, J. F., and N. R. Mann. 1976. Tests for homogeneity of extreme value scale parameters. Communi. Stat. Theory Methods, 5, 389–405.MathSciNetCrossRefGoogle Scholar
  6. Littell, R., and J. L. Folks. 1973. Asymptotic optimality of Fisher’s method of combining independent tests II. J. Am. Stat. Assoc., 68, 193–194.MathSciNetCrossRefGoogle Scholar
  7. McCool, J. I. 1975. Multiple comparisons for Weibull parameters. IEEE Trans. Reliability, R24, 186–192.MathSciNetCrossRefGoogle Scholar
  8. McCool, J. I. 1979. Analysis of single classification experiments based on censored samples from the two-parameter Weibull distribution. J. Stat. Plan. Inference, 3, 39–68.MathSciNetCrossRefGoogle Scholar
  9. Paul, S. R., and X. Jiang. 2005. Testing the homogeneity of several two-parameter populations. Can. J. Stat., 33, 131–143.MathSciNetCrossRefGoogle Scholar
  10. Paul, S. R., and K. Thiagarajah. 1992. Hypothesis tests for the one-way layout of type II censored data from Weibull populations. J. Stat. Plan. Inference, 33, 367–380.CrossRefGoogle Scholar
  11. Singh, N. 1986. A simple and asymptotically optimal test for the equality of normal populations. A pragmatic approach to one-way classification. J. Am. Stat. Assoc., 81, 703–704.MathSciNetCrossRefGoogle Scholar
  12. Thiagarajah, K., 1992. Inference procedures in some lifetime models, Ph.D. thesis, University of Windsor, Canada.Google Scholar
  13. Thiagarajah, K., and S. R. Paul. 1993. C(α) tests for the analysis of one-way layout of data having extreme value distribution. Statistician, 42, 85–100.CrossRefGoogle Scholar

Copyright information

© Grace Scientific Publishing 2012

Authors and Affiliations

  1. 1.Department of MathematicsIllinois State UniversityNormalUSA

Personalised recommendations