Remote Access Mathematics of Computation
Green Open Access

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?)

  • 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 120725
  • F. A. Haight, Mathematical Theories of Road Traffic, Academic Press, New York, 1968, (in preparation). J. R. B. Whittlesey, “Normalized incomplete gamma function with Poisson term (UR GAMA),” SHARE Dist. #1177, IBM, New York, 1961. 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.
  • Frank A. Haight, The generalized Poisson distribution, Ann. Inst. Statist. Math. Tokyo 11 (1959), 101–105. MR 109355, DOI
  • Frank A. Haight, The generalized Poisson distribution, Ann. Inst. Statist. Math. Tokyo 11 (1959), 101–105. MR 109355, DOI
  • 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
  • William S. Jewell, The properties of recurrent-event processes, Operations Res. 8 (1960), 446–472. MR 117793, DOI
  • John R. B. Whittlesey and Frank A. Haight, Counting distributions for an Erlang process, Ann. Inst. Statist. Math. 13 (1961/62), 91–103. MR 140163, DOI
  • T. J. I’a. Bromwich & T. M. Macrobert, An Introduction to the Theory of Infinite Series, Macmillan & Co., Ltd., London, 1955, p. 330.
  • 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
  • Bateman Manuscript Project, Higher Transcendental Functions, v. 2, McGraw-Hill Book Co., Inc., New York, 1953, p. 135.
  • A. Erdélyi, Asymptotic expansions, Dover Publications, Inc., New York, 1956. MR 0078494
  • H. S. Wall, Analytic Theory of Continued Fractions, D. Van Nostrand Company, Inc., New York, N. Y., 1948. MR 0025596
  • E. B. Wilson & M. M. Hilferty, “The distribution of Chi-square,” Proc. Nat. Acad. Sci., v. 17, 1931, p. 684-688.
  • S. H. Abdel-Aty, Approximate formulae for the percentage points and the probability integral of the non-central $x^2$ distribution, Biometrika 41 (1954), 538–540. MR 65866, DOI
  • Norman C. Severo and Marvin Zelen, Normal approximation to the chi-square and non-central $F$ probability functions, Biometrika 47 (1960), 411-416. MR 119270, DOI
  • K. Pearson, Tables of the Incomplete $\Gamma$-Function, Cambridge University Press, 1951, p. xvi. 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

Article copyright: © Copyright 1963 American Mathematical Society