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,"

References

[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.

[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.