Exponential distributions are characterized by distributional properties of generalized order statistics. These characterizations include known results for ordinary order statistics and record values as particular cases.
@article{bwmeta1.element.bwnjournal-article-zmv24i4p383bwm, author = {Udo Kamps and Ursula Gather}, title = {Characteristic properties of generalized order statistics from exponential distributions}, journal = {Applicationes Mathematicae}, volume = {24}, year = {1997}, pages = {383-391}, zbl = {0884.62018}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-zmv24i4p383bwm} }
Kamps, Udo; Gather, Ursula. Characteristic properties of generalized order statistics from exponential distributions. Applicationes Mathematicae, Tome 24 (1997) pp. 383-391. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-zmv24i4p383bwm/
[000] M. Ahsanullah (1978), A characterization of the exponential distribution by spacings, Ann. Inst. Statist. Math. 30A, 163-166. | Zbl 0444.62015
[001] M. Ahsanullah (1981a), Record values of exponentially distributed random variables, Statist. Hefte 22, 121-127. | Zbl 0471.62017
[002] M. Ahsanullah (1981b), On characterizations of the exponential distribution by spacings, ibid., 316-320. | Zbl 0479.62009
[003] L. Gajek and U. Gather (1989), Characterizations of the exponential distribution by failure rate- and moment properties of order statistics, in: J. Hüsler and R. D. Reiss (eds.), Extreme Value Theory, Springer, Berlin, 114-124. | Zbl 0672.62021
[004] U. Gather (1988), On a characterization of the exponential distribution by properties of order statistics, Statist. Probab. Lett. 7, 93-96. | Zbl 0655.62008
[005] U. Gather, U. Kamps and N. Schweitzer (1997), Characterizations of distributions via identically distributed functions of order statistics, in: C. R. Rao and N. Balakrishnan (eds.), Handbook of Statistics-16, Order Statistics and Their Applications, North-Holland, Amsterdam, to appear. | Zbl 0905.62008
[006] M. Iwińska (1986), On the characterizations of the exponential distribution by order statistics and record values, Fasc. Math. 16, 101-107. | Zbl 0622.62014
[007] U. Kamps (1995), A Concept of Generalized Order Statistics, Teubner, Stuttgart. | Zbl 0838.62038
[008] P. V. Sukhatme (1937), Tests of significance for samples of the population with two degrees of freedom, Ann. Eugenics 8, 52-56.