Characterization of Negative Exponential Distribution through Expectation
Author(s)
Milind Bhatt B.
ABSTRACT
For characterization of negative exponential distribution one needs any arbitrary non-constant function only in place of approaches such as identical distributions, absolute continuity, constant regression of order statistics, continuity and linear regression of order statistics, non-degeneracy etc. available in the literature. Path breaking different approach for characterization of negative exponential distribution through expectation of non-constant function of random variable is obtained. An example is given for illustrative purpose.
Cite this paper
M. B., "Characterization of Negative Exponential Distribution through Expectation," Open Journal of Statistics, Vol. 3 No. 5, 2013, pp. 367-369. doi: 10.4236/ojs.2013.35042.
M. B., "Characterization of Negative Exponential Distribution through Expectation," Open Journal of Statistics, Vol. 3 No. 5, 2013, pp. 367-369. doi: 10.4236/ojs.2013.35042.
References
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[1] M. Fisz, “Characterization of Some Probability Distributions,” Skandinavisk Aktuarietidskrift, Vol. 41, No. 1-2, 1958, pp. 65-70. [2] E. Tanis, “Linear Forms in the Order Statistics from an Exponential Distribution,” The Annals of Mathematical Statistics, Vol. 35, No. 1, 1964, pp. 270-276. [3] G. S. Rogers, “An Alternative Proof of the Characterization of the Density AxB,” The American Mathematical Monthly, Vol. 70, No. 8, 1963, pp. 857-858. [4] T. S. Ferguson, “A Characterization of the Negative Exponential Distribution,” The Annals of Mathematical Statistics, Vol. 35, 1964, pp. 1199-1207. [5] T. S. Ferguson, “A Characterization of the Geometric Distribution,” The American Mathematical Monthly, Vol. 72, No. 3, 1965, pp. 256-260. [6] T. S. Ferguson, “On Characterizing Distributions by Properties of Order Statistics,” Sankhyā: The Indian Journal of Statistics, Series A (1961-2002), Vol. 29, No. 3, 1967, pp. 265-278. [7] G. B. Crawford, “Characterizations of Geometric and Exponential Distributions,” The Annals of Mathematical Statistics, Vol. 37, No. 6, 1966, pp. 1790-1795. [8] H. N. Nagaraja, “On a Characterization Based on Record Values,” Australian Journal of Statistics, Vol. 19, 1977, pp. 70-73. [9] H. N. Nagaraja, “Some Characterization of Continuous Distributions Based on Adjacent Order Statistics and Record Values,” Sankhy, Series A, Vol. 50, No. 1, 1988, pp. 70-73. [10] A. H. Khan, M. Faizan and Z. Haque, “Characterization of Probability Distributions through Order Statistics,” Prob Stat Forum, Vol. 2, 2009, pp. 132-136.