Table of Contents Author Guidelines Submit a Manuscript
Journal of Probability and Statistics
Volume 2009, Article ID 310575, 16 pages
Research Article

On the Existence and Uniqueness of the Maximum Likelihood Estimators of Normal and Lognormal Population Parameters with Grouped Data

1Center on Aging and Health, John Hopkins University, Baltimore, MD 21287, USA
2Department of Statistics, Florida International University, Miami, FL 33139, USA
3Department of Statistics & Biostatistics, California State University, Hayward, CA 94542, USA

Received 11 March 2009; Accepted 16 June 2009

Academic Editor: A. Thavaneswaran

Copyright © 2009 Jin Xia 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.

Linked References

  1. P. Tai, E. Yu, R. Shiels, and J. Tonita, “Long-term survival rates of laryngeal cancer patients treated by radiation and surgery, radiation alone, and surgery alone: studied by lognormal and Kaplan-Meier survival methods,” BMC Cancer, vol. 5, article 13, 2005. View at Publisher · View at Google Scholar · View at PubMed
  2. R. F. Mould, M. Lederman, P. Tai, and J. K. M. Wong, “Methodology to predict long-term cancer survival from short-term data using Tobacco Cancer Risk and Absolute Cancer Cure models,” Physics in Medicine and Biology, vol. 47, no. 22, pp. 3893–3924, 2002. View at Publisher · View at Google Scholar
  3. M. V. Ratnaparkhi and W. J. Park, “Lognormal distribution: model for fatigue life and residual strength of composite materials,” IEEE Transactions on Reliability, vol. 35, pp. 312–315, 1986. View at Publisher · View at Google Scholar
  4. D. L. Kelly, “Use of constrained lognormal distribution in reliability analysis,” Reliability Engineering & System Safety, vol. 40, no. 1, pp. 43–47, 1993. View at Publisher · View at Google Scholar
  5. C. Kleiber and S. Kotz, Statistical Size Distributions in Economics and Actuarial Sciences, Wiley Series in Probability and Statistics, Wiley-Interscience, Hoboken, NJ, USA, 2003. View at MathSciNet
  6. J. E. Mosimann and G. Campbell, “Applications in biology of the lognormal distribution: simple growth models,” in Lognormal Distribution: Theory and Applications, pp. 287–302, 1988. View at Google Scholar
  7. T. Mäkeläinen, K. Schmidt, and G. P. H. Styan, “On the existence and uniqueness of the maximum likelihood estimate of a vector-valued parameter in fixed-size samples,” The Annals of Statistics, vol. 9, no. 4, pp. 758–767, 1981. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. W. Feller, An Introduction to Probability Theory and Its Applications: Volume 2, John Wiley & Sons, New York, NY, USA, 1957.
  9. N. Balakrishnan and J. Mi, “Existence and uniqueness of the MLEs for normal distribution based on general progressively type-II censored samples,” Statistics & Probability Letters, vol. 64, no. 4, pp. 407–414, 2003. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. USEPA, Statistical Methods for Evaluating the Attainment of Cleanup Standards. Vol. 3, 1994.