Geodesic
Exponentiality tests based on Ahsanullah's characterization and their efficiencies
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 19, Tome 412 (2013), pp. 69-87

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We construct integral and supremum type tests of exponentiality based on Ahsanullah's characterization of exponential law. We discuss limiting distributions and large deviations of new test statistics under null-hypothesis, and calculate their local Bahadur efficiency under common parametric alternatives. Conditions of local optimality of new statistics are given. 
@article{ZNSL_2013_412_a3,
     author = {K. Yu. Volkova and Ya. Yu. Nikitin},
     title = {Exponentiality tests based on {Ahsanullah's} characterization and their efficiencies},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {69--87},
     publisher = {mathdoc},
     volume = {412},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2013_412_a3/}
}
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K. Yu. Volkova; Ya. Yu. Nikitin. Exponentiality tests based on Ahsanullah's characterization and their efficiencies. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 19, Tome 412 (2013), pp. 69-87. http://geodesic.mathdoc.fr/item/ZNSL_2013_412_a3/