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A Commentary on the Logistic Distribution

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The Legacy of Alladi Ramakrishnan in the Mathematical Sciences

Summary

The paper provides a series representation of the logistic probability density function in terms of differently scaled double exponential distributions with terms of the series alternating in signs. This representation is used to calculate moments, moment generating function, and characteristic function of a logistic distribution. The same representation is also used to derive the logistic distribution as the scale mixture of a normal distribution.

Mathematics Subject Classification (2000)62E15

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References

  1. Abramowitz, M., and Stegun, I. A. (1972). Handbook of Mathematical Functions: With Formulas, Graphs, and Mathematical Tables.Dover, New York.

    MATH  Google Scholar 

  2. Andrews, D. F., and Mallows, C. F. (1974). Scale mixtures of a normal distributions. Journal of the Royal Statistical Society, Series B, 36, 99–102.

    MathSciNet  MATH  Google Scholar 

  3. Agresti, A. (1984). Analysis of Ordinal Categorical Data.Wiley, New York.

    MATH  Google Scholar 

  4. Balakrishnan, N. (1992). Handbook of the Logistic Distribution.Marcel Dekker, New York.

    MATH  Google Scholar 

  5. Bartholomew, D. J., and Knott, M. (1999). Latent Variable Models and Factor Analysis. Edward Arnold, London.

    MATH  Google Scholar 

  6. Bateman, H. (1953). Higher Transcendental Functions, Vol. I. McGraw Hill, New York.

    MATH  Google Scholar 

  7. Breslow, N. E., and Day, N. E. (1980). Statistical Methods in Cancer Research I. The Analysis of case–Control Studies.IARC, Lyon.

    Google Scholar 

  8. Browne, W. J., Subramanian, S. V., Jones, K., and Goldstein, H. (2005). Variance partitioning in multilevel logistic models that exhibit overdispersion. Journal of the Royal Statistical Society, Series A, 168, 599–613.

    Google Scholar 

  9. Datta, G. S., and Ghosh, M. (2007). Characteristic functions without contour integration. The American Statistician, 61, 67–70.

    Article  MathSciNet  Google Scholar 

  10. Fisher, J. C., and Pry, R. H. (1971). A simple substitutional model for technological change. Technological Forecasting and Social Change, 3, 75–88.

    Article  Google Scholar 

  11. Fitzmaurice, G. M., Laird, N. M., and Ware, J. H. (2003). Applied Longitudinal Analysis. Wiley, New York.

    Google Scholar 

  12. Goldstein, H., Browne, W. J., and Rasbash, J. (2002). Partitioning variation in multilevel models. Understanding Statistics, 1, 223–232.

    Article  Google Scholar 

  13. Gradshteyn, I. S., and Ryzhik, I. M. (1980). Tables, Integrals, Series, and Products.Academic, New York.

    Google Scholar 

  14. Johnson, N. L., Kotz, S., and Balakrishnan, N. (1995). Continuous Univariate Distribution, Vol. 2. Wiley, New York.

    Google Scholar 

  15. Kalbfleisch, J. D., and Prentice, R. L. (2002). The Statistical Analysis of Failure Time Data. Wiley, New York.

    Book  MATH  Google Scholar 

  16. Kendall, S. M., and Stuart, A. (1979). The Advanced Theory of Statistics, Vol. 2. Fourth Edition. Charles Griffin & Company Limited, London.

    MATH  Google Scholar 

  17. Lord, F. M. (1965). A note on the normal ogive or logistic curve in item analysis. Psychometrika, 30, 371–372.

    Article  MATH  Google Scholar 

  18. Lotka, A. J. (1925). Elements of Physical Biology.Williams and Wilkins, Baltimore.

    MATH  Google Scholar 

  19. Modis, T. (1992). Predictions: Society’s Telltale Signature Reveals Past & Forcasts the Future.Simon and Schuster, New York, pp 97–105.

    Google Scholar 

  20. Rabe-Hesketh, S., and Skrondal, A. (2005). Multilevel and Longitudinal Modeling Using Stata. StatCorp LP, College Station, Texas.

    Google Scholar 

  21. Rasch, G. (1961). On general laws and the meaning of measurement in psychology. In Proceedings of the 4th Berkeley Symposium on Mathematical Statistics.University of California, Berkeley, pp 321–334.

    Google Scholar 

  22. Sanathanan, L. (1974). Some properties of the logistic distribution for dichotomous response. Journal of the American Statistical Association, 69, 744–749.

    Article  MATH  Google Scholar 

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Acknowledgments

This research took place when the first author was visiting the Department of Statistics and Applied Probability, National University of Singapore. He acknowledges gratefully the research opportunities made available to him during this period.

Author information

Authors and Affiliations

  1. Department of Statistics, University of Florida, 118545, Gainesville, FL, 32611-8545, USA

    Malay Ghosh

  2. Department of Statistics and Applied Probability, National University of Singapore, 6 Science Drive 2, Singapore, 117546, Singapore

    Kwok Pui Choi & Jialiang Li

Authors
  1. Malay Ghosh
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  2. Kwok Pui Choi
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  3. Jialiang Li
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Corresponding author

Correspondence to Malay Ghosh .

Editor information

Editors and Affiliations

  1. , Department of Mathematics, University of Florida, Gainesville, 32611, Florida, USA

    Krishnaswami Alladi

  2. , Department of Physics, University of Florida, Gainesville, 32611, Florida, USA

    John R. Klauder

  3. , Department of Statistics, The Pennsylvania State University, University Park, 16802, Pennsylvania, USA

    Calyampudi R. Rao

Additional information

Dedicated to the memory of Professor Alladi Ramakrishnan

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Ghosh, M., Choi, K.P., Li, J. (2010). A Commentary on the Logistic Distribution. In: Alladi, K., Klauder, J., Rao, C. (eds) The Legacy of Alladi Ramakrishnan in the Mathematical Sciences. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-6263-8_21

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