Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Incomplete Gamma functions for evaluating Erlang process probabilities


Author: John R. B. Whittlesey
Journal: Math. Comp. 17 (1963), 11-17
Corrigendum: Math. Comp. 18 (1964), 536-536.
Full-text PDF Free Access

References | Additional Information

References [Enhancements On Off] (What's this?)

  • [1] Salem H. Khamis, Incomplete gamma functions expansions of statistical distribution functions, Bull. Inst. Internat. Statist. 37 (1960), no. 3, 385–396 (English, with French summary). MR 0120725 (22 #11474)
  • [2] F. A. Haight, Mathematical Theories of Road Traffic, Academic Press, New York, 1968, (in preparation).
  • [3] J. R. B. Whittlesey, ``Normalized incomplete gamma function with Poisson term (UR GAMA),'' SHARE Dist. #1177, IBM, New York, 1961.
  • [4] J. R. B. Whittlesey, `` $ {\text{Gamma}}(a,x)/{\text{Gamma}}(a) + $ Poisson term in double-precision (UR GAM2),'' SHARE Dist. #1299, IBM, New York, 1962.
  • [5] Frank A. Haight, The generalized Poisson distribution, Ann. Inst. Statist. Math. Tokyo 11 (1959), 101–105. MR 0109355 (22 #241)
  • [6] Frank A. Haight, The generalized Poisson distribution, Ann. Inst. Statist. Math. Tokyo 11 (1959), 101–105. MR 0109355 (22 #241)
  • [7] Philip M. Morse, Queues, inventories and maintenance. The analysis of operational systems with variable demand and supply, Publications in Operations Research, Operations Research Society of America, No. 1, John Wiley & Sons, Inc., New York; Chapman & Hall, Ltd., London, 1958. MR 0091216 (19,930d)
  • [8] William S. Jewell, The properties of recurrent-event processes, Operations Res. 8 (1960), 446–472. MR 0117793 (22 #8567)
  • [9] John R. B. Whittlesey and Frank A. Haight, Counting distributions for an Erlang process, Ann. Inst. Statist. Math. 13 (1961/1962), 91–103. MR 0140163 (25 #3585)
  • [10] T. J. I'a. Bromwich & T. M. Macrobert, An Introduction to the Theory of Infinite Series, Macmillan & Co., Ltd., London, 1955, p. 330.
  • [11] Cecil Hastings Jr., Approximations for digital computers, Princeton University Press, Princeton, N. J., 1955. Assisted by Jeanne T. Hayward and James P. Wong, Jr. MR 0068915 (16,963e)
  • [12] Bateman Manuscript Project, Higher Transcendental Functions, v. 2, McGraw-Hill Book Co., Inc., New York, 1953, p. 135.
  • [13] A. Erdélyi, Asymptotic expansions, Dover Publications, Inc., New York, 1956. MR 0078494 (17,1202c)
  • [14] H. S. Wall, Analytic Theory of Continued Fractions, D. Van Nostrand Company, Inc., New York, N. Y., 1948. MR 0025596 (10,32d)
  • [15] E. B. Wilson & M. M. Hilferty, ``The distribution of Chi-square,'' Proc. Nat. Acad. Sci., v. 17, 1931, p. 684-688.
  • [16] S. H. Abdel-Aty, Approximate formulae for the percentage points and the probability integral of the non-central 𝑥² distribution, Biometrika 41 (1954), 538–540. MR 0065866 (16,497c)
  • [17] Norman C. Severo and Marvin Zelen, Normal approximation to the chi-square and non-central 𝐹\ probability functions, Biometrika 47 (1960), 411-416. MR 0119270 (22 #10036)
  • [18] K. Pearson, Tables of the Incomplete $ \Gamma $-Function, Cambridge University Press, 1951, p. xvi.
  • [19] F. A. Haight, B. F. Whisler, & W. W. Mosher, Jr., ``New statistical method for describing highway distribution of cars,'' Proc. Highway Res. Board, v. 40, 1961, p. 557-564.


Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-63-99188-9
PII: S 0025-5718(63)99188-9
Article copyright: © Copyright 1963 American Mathematical Society