Geodesic
Record and interrecord times for sequences of nonidentically distributed random variables
Zapiski Nauchnykh Seminarov POMI, Problems of the theory of probability distributions. Part IX, Tome 142 (1985), pp. 109-118

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Assume that the independent random variables $X_1$, $X_2,\dots$ have the distribution functions $F^{\alpha_1}$, $F^{\alpha_2},\dots$, respectively, where $F$ is an arbitrary continuous distribution function, while $\alpha_i$ are positive constants. In this situation, one obtains some theorems for the record moments and interrecord times. 
@article{ZNSL_1985_142_a10,
     author = {V. B. Nevzorov},
     title = {Record and interrecord times for sequences of nonidentically distributed random variables},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {109--118},
     publisher = {mathdoc},
     volume = {142},
     year = {1985},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1985_142_a10/}
}
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V. B. Nevzorov. Record and interrecord times for sequences of nonidentically distributed random variables. Zapiski Nauchnykh Seminarov POMI, Problems of the theory of probability distributions. Part IX, Tome 142 (1985), pp. 109-118. http://geodesic.mathdoc.fr/item/ZNSL_1985_142_a10/