Univariate distribution relationships

American Statistician

Volumn 62, Issue 1, 2008, Pages 45-53

  Leemis, Lawrence M ^a   McQueston, Jacquelyn T ^b  

^a The College of William and Mary   (United States)

^b NORTHROP GRUMMAN CORPORATION   (United States)

Author keywords

Asymptotic relationships; Distribution properties; Limiting distributions; Stochastic parameters; Transformations

Indexed keywords

EID: 39049147084     PISSN: 00031305     EISSN: None     Source Type: Journal    
DOI: 10.1198/000313008X270448     Document Type: Article

References (44)

1. Balakrishnan, N., and Nevzorov, V.B. (2003), A Primer on Statistical Distributions, Hoboken, NJ: Wiley.
2. Benford, F. (1938), "The Law of Anomalous Numbers," Proceedings of the American Philosophical Society, 78, 551-572.
3. Boomsma, A., and Molenaar, I.W. (1994), "Four Electronic Tables for Probability Distributions," The American Statistician, 48, 153-162.
4. Casella, G., and Berger, R. (2002), Statistical Inference (2nd ed.), Belmont, CA: Duxbury.
5. Chhikara, R.S., and Folks, L.S. (1989), The Inverse Gaussian Distribution: Theory, Methodology and Applications, New York: Marcel Dekker, Inc.
6. Crowder, M.J., Kimber, A.C., Smith, R.L., and Sweeting, T.J. (1991), Statistical Analysis of Reliability Data, New York: Chapman and Hall.
7. Davis, H.T., and Feldstein, M.L (1979), "The Generalized Pareto Law as a Model for Progressively Censored Survival Data," Biometrika, 66, 299-306.
8. Devroye, L. (2006), "Nonuniform Random Variate Generation," in Simulation, eds. S.G. Henderson and B.L. Nelson, Vol. 13, Handbooks in Operations Research and Management Science, Amsterdam: North-Holland.
9. Drew, J.H., Glen, A.G., and Leemis, L.M. (2000), "Computing the Cumulative Distribution Function of the Kolmogorov-Smimov Statistic," Computational Statistics and Data Analysis, 34, 1-15.
10. Evans, M., Hastings, N., and Peacock, B. (2000), Statistical Distributions (3rd ed.), New York: Wiley.
11. Flanigan-Wagner, M., and Wilson, J.R. (1993), "Using Univariate Bézier Distributions to Model Simulation Input Processes," in Proceedings of the 1993 Winter Simulation Conference, eds. G. W. Evans, M. Mollaghasemi, E. C. Russell, and W. E. Biles, Institute of Electrical and Electronics Engineers, pp. 365-373.
12. Glen, A., and Leemis, L.M. (1997), "The Arctangent Survival Distribution," Journal of Quality Technology, 29, 205-210.
13. Gupta, R.D., and Kundu, D. (2007), "Generalized Exponential Distribution: Existing Results and Some Recent Developments," Journal of Statistical Planning and Research, 137, 3537-3547.
14. de Haan, L., and Ferreira, A. (2006), Extreme Value Theory: An Introduction, New York: Springer.
15. Hjorth, U. (1980), "A Reliability Distribution with Increasing, Decreasing, Constant and Bathtub-Shaped Failure Rates," Technometrics, 22, 99-107.
16. Hogg, R. V., McKean, J.W., and Craig, A.T. (2005), Introduction to Mathematical Statistics (6th ed.), Upper Saddle River, NJ: Prentice Hall.
17. Hosking, J.R.M. (1994), "The Four-Parameter Kappa Distribution," IBM Journal of Research and Development, 38, 251-258.
18. Johnson, N.L., Kemp, A.W., and Kotz, S. (2005), Univariate Discrete Distributions (3rd ed.), New York: Wiley.
19. Johnson, N.L., Kotz, S., and Balakrishnan, N. (1994), Continuous Univariate Distributions (Vol. I, 2nd ed.), New York: Wiley.
20. (1995), Continuous Univariate Distributions (Vol. II, 2nd ed.), New York: Wiley.
21. Jones, M.C. (2002), "The Complementary Beta Distribution," Journal of Statistical Planning and Inference, 104, 329-337.
22. Jordan, C.W. (1967), Life Contingencies, Chicago: Society of Actuaries.
23. Kotz, S., and van Dorp, J.R. (2004), Beyond Beta: Other Continuous Families of Distributions with Bounded Support and Applications, Hackensack, NJ: World Scientific.
24. Lan, L., and Leemis, L. (2007), "The Logistic-Exponential Survival Distribution," Technical Report, The College of William & Mary, Department of Mathematics.
25. Leemis, L. (1986), "Relationships Among Common Univariate Distributions," The American Statistician, 40, 143-146.
26. Marshall, A.W., and Olkin, I. (1985), "A Family of Bivariate Distributions Generated by the Bivariate Bernoulli Distribution," Journal of the American Statistical Association, 80, 332-338.
27. McDonald, J.B. (1984), "Some Generalized Functions for the Size Distribution of Income," Econometrica, 52, 647-663.
28. Miller, G.K., and Fridell, S.L. (2007), "A Forgotten Discrete Distribution? Reviving the Negative Hypergeometric Model," The American Statistician, 61, 347-350.
29. Muth, E.J. (1977), "Reliability Models with Positive Memory Derived from the Mean Residual Life Function" in The Theory and Applications of Reliability, eds. C.P. Tsokos and I. Shimi, New York: Academic Press, Inc., pp. 401-435.
30. Nakagawa, T., and Yoda, H. (1977), "Relationships Among Distributions," IEEE Transactions on Reliability, 26, 352-353.
31. Ord, J.K. (1972), Families of Frequency Distributions, New York: Hafner Publishing.
32. Patel, J.K., Kapadia, C.H., and Owen, D.B. (1976), Handbook of Statistical Distributions, New York: Marcel Dekker, Inc.
33. Patil, G.P., Boswell, M.T., Joshi, S.W., and Ratnaparkhi, M.V. (1985), Discrete Models, Burtonsville, MD: International Co-operative Publishing House.
34. Patil, G.P., Boswell, M.T., and Ratnaparkhi, M.V. (1985), Univariate Continuous Models, Burtonsville, MD: International Co-operative Publishing House.
35. Prentice, R.L. (1975), "Discrimination Among Some Parametric Models," Biometrika, 62, 607-619.
36. Ramberg, J.S., and Schmeiser, B.W. (1974), "An Approximate Method for Generating Asymmetric Random Variables," Communications of the Association for Computing Machinery, 17, 78-82.
37. Ross, S. (2006), A First Course In Probability (7th ed.), Upper Saddle River, NJ: Prentice Hall.
38. (2007), Introduction to Probability Models (9th ed.), New York: Academic Press.
39. Seshadri, V. (1993), The Inverse Gaussian Distribution, Oxford: Oxford University Press.
40. Shapiro, S.S., and Gross, A.J. (1981), Statistical Modeling Techniques, New York: Marcel Dekker.
41. Smith, R.M., and Bain, L.J. (1975), "An Exponential Power Life-Testing Distribution," Communications in Statistics, 4, 469-481.
42. Song, W.T. (2005), "Relationships Among Some Univariate Distributions," IIE Transactions, 37, 651-656.
43. Stacy, E.W. (1962), "A Generalization of the Gamma Distribution," Annals of Mathematical Statistics, 33, 1187-1192.
44. Taha, H.A. (1982), Operations Research: An Introduction (3rd ed.), New York: Macmillan.