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The burr distribution and quantal responses

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Summary

The Burr distribution, having two shape parameters in addition to the usual parameters for location and dispersion, is very flexible and has several interesting and often used special forms. A formal statement of the approximate minimum chisquare is made and then developed for the Burr.

Bias and variance functions are derived for F−1 (p). Finally, the approximate normal and six of its limit forms are also given as a prelude to a more general approach bx employing a family of response functions when analyzing ordered quantal response (binary) data.

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References

  1. Berkson, J.: “Application of the Logistric Function to Bio-Assay.” Journal of the American Statistical Association39, 357–64, 1944.

    Article  Google Scholar 

  2. Bertalanffy, L. Von: “Quantitative laws metabolism and growth.” The Quarterly Review of Biology,32, 217–31, 1957.

    Article  Google Scholar 

  3. Bratcher, T. L.: “Bayesian analysis of a dose-response experiment with serial sacrificies.” Journal of Environmental Pathology and Toxicology,1, 237–92, 1977.

    Google Scholar 

  4. Burr, I. W.: “Cumulative Frequency Functions.” Annals of Mathematical Statistics,13, 215–32, 1942.

    Article  MathSciNet  MATH  Google Scholar 

  5. Burr, I. W.: “A Useful Approximation to the Normal Distribution Function, with Application to Simulation.” Technometrics,9, 647–51, 1967.

    Article  MathSciNet  Google Scholar 

  6. Burr, I. W.: “Parameters for a general system of distributions to match a grid of α3 and α4.” Communications in Statistics,2 (1), 1–23, 1973.

    Article  MathSciNet  Google Scholar 

  7. Burr, I. W. and P. J. Cislak: “On a General System of Distributions-I. Its Curve Shape Characteristics. II. The Sample Median.” The Journal of the American Statistical Association,63, 627–35, 1968.

    Article  MathSciNet  Google Scholar 

  8. DeGroot, M. H.: Probability and Statistics. Reading, MA: Addison-Wesley Publishing Company, 1975.

    MATH  Google Scholar 

  9. Ferguson, T. S.: Mathematical Statistics a Decision Theoretic Approach. New York: Academic Press, 1967.

    MATH  Google Scholar 

  10. Moore, R. H. and R. K. Zeigler: “The Use of Non-Linear Regression Methods for Analyzing Sensitivity and Quantal Response Data.” Biometrics,23, 563, 1967.

    Article  MathSciNet  Google Scholar 

  11. Prentice, R. L.: “A log gamma model and its maximum likelihood estimation.” Biometrika,61, 545–57, 1974.

    MathSciNet  Google Scholar 

  12. “Discrimination among some parametric models.” Biometrika,62, 607–14, 1975.

  13. “A generalization of the probit and logit methods for dose response curves.” Biometrics,32, 761–68, 1976.

  14. Richards, F. J.: “A flexible growth function for empirical use.” Journal of Experimental Botany,10, 290–300, 1959.

    Article  Google Scholar 

  15. Seibert, G. B.: Estimation and confidence intervals for quantal response or sensitivity data. Tech. Report 66, Department of Statistics, Southern Methodist University, Dallas, TX 75275, 1970.

    Google Scholar 

  16. Turner, M. E., Jr.: “Some classes of hit theory models.” Mathematical Biosciences,23, 219–35, 1975.

    Article  MATH  Google Scholar 

  17. Turner, M. E., Jr.; E. L. Bradley, Jr.; K. A. Kirk and K. M. Pruitt: “A theory of growth.” Mathematical Biosciences,29, 367–73, 1976.

    Article  MATH  Google Scholar 

  18. Turner, M. E., Jr. and K. M. Pruitt: “A common basis for survival, growth and autocatalysis.” Mathematical Biosciences, in press, 1978.

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Authors
  1. J. Wanzer Drane
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  2. Donald B. Owen
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  3. Guy Burton Seibert
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Drane, J.W., Owen, D.B. & Seibert, G.B. The burr distribution and quantal responses. Statistische Hefte 19, 204–210 (1978). https://doi.org/10.1007/BF02932803

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