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Keywords:
discrete distribution; exponential; lack of memory
discrete distribution; exponential; lack of memory
Summary:
A characterization of geometric distribution is given, which is based on the ratio of the real and imaginary part of the characteristic function.
References:
[1] Arnold B. C.: Two characterizations of the geometric distribution. J. Appl. Probab. 17 (1980), 570–573 DOI 10.2307/3213048 | MR 0568969 | Zbl 0428.60017
[2] Bary N. K.: A Treatise on Trigonometric Series. Pergamon Press, Oxford 1964 Zbl 0129.28002
[3] Crawford G. B.: Characterization of geometric and exponential distributions. Ann. Math. Statist. 37 (1966), 1790–1795 DOI 10.1214/aoms/1177699167 | MR 0207009 | Zbl 0144.42303
[4] El-Neweihi E., Govindarajulu Z.: Characterizations of geometric distributions and discrete IFR (DFR) distributions using order statistics. J. Statist. Plann. Inf. 3 (1979), 85–90 DOI 10.1016/0378-3758(79)90044-2 | MR 0529875
[5] Ferguson T. S.: A characterization of the geometric distribution. Amer. Math. Monthly 71 (1965), 256–260 DOI 10.2307/2313692 | MR 0193653 | Zbl 0127.10705
[6] Ferguson T. S.: On characterizing distributions by properties of order statistics. Sankhya Series A 20 (1967), 265–278 MR 0226804 | Zbl 0155.27302
[7] Ferguson T. S.: On a Rao-Shanbhag characterization of the exponential/geometric distribution. Sankhya Series A 64 (2002), 247–255 MR 1981756 | Zbl 1192.62033
[8] Fosam E. B., Shanbhag D. N.: Certain characterizations of exponential and geometric distributions. J. Royal Statist. Soc. Series B 56 (1994), 157–160 MR 1257803 | Zbl 0788.62016
[9] (1975) J. Galambos: Characterizations of probability distributions by properties of order statistics. In: Statistical Distributions in Scientific Work, Vol. 2: Characterizations and Appplications (G. P. Patil, S. Kotz, and J. K. Ord, eds.), D. Reidel, Boston 1975, II, pp. 89–101
[10] Henze N., Meintanis S. G.: Goodness-of-fit tests based on a new characterization of the exponential distribution. Commun. Statist. – Theory and Methods 31 (2002), 1479–1497 DOI 10.1081/STA-120013007 | MR 1925077 | Zbl 1008.62043
[11] Hitha N., Nair U. N.: Characterization of some discrete models by properties of residual life function. Cal. Statist. Assoc. Bulletin 38 (1989), 219–223 MR 1060161 | Zbl 0715.62023
[12] Kalbfleish J. D., Prentice R. L.: The Statistical Analysis of Failure Time Data. Wiley, New York 1980 MR 0570114
[13] Meintanis S. G., Iliopoulos G.: Characterizations of the exponential distribution based on certain properties of its characteristic function. Kybernetika 39 (2003), 295–298 MR 1995733
[14] Rainville E. D.: Infinite Series. The Macmillan Company, New York 1967 Zbl 0173.05702
[15] Rao B. L. S. P., Sreehari M.: On some properties of geometric distribution. Sankhya Series A 42 (1980), 120–122 MR 0637996
[16] Rogers G. S.: An alternate proof of the characterization of the density $Ax^{B}$. Amer. Math. Monthly 70 (1963), 857–858 DOI 10.2307/2312673 | MR 1532316
[17] Roy D., Gupta R. P.: Stochastic modeling through reliability measures in the discrete case. Statist. Probab. Letters 43 (1999), 197–206 DOI 10.1016/S0167-7152(98)00260-0 | MR 1693301
[18] Srivastava R. C.: Two characterizations of the geometric distribution. J. Amer. Statist. Assoc. 69 (1974), 267–269 DOI 10.1080/01621459.1974.10480169 | MR 0381074 | Zbl 0311.60012
[19] Xekalaki E.: Hazard function and life distributions in discrete time. Commun. Statist. – Theory and Methods 12 (1983), 2503–2509 DOI 10.1080/03610928308828617 | MR 0715179
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