Geodesic
On relations for moments of the normal $k$th record values and a~characterization
Teoriâ veroâtnostej i ee primeneniâ, Tome 66 (2021) no. 3, pp. 610-618

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This paper gives the explicit expressions for moments of the $k$th record values from normal distribution and relations between the $r$th, $(r-2)$nd single, and product moments. These relations allow us to give skewness and kurtosis of record values and present a new characterization of normal distribution.
Keywords: $k$th upper record values, complete sequence of functions, characterization of probability distributions. 
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     author = {P. Pawlas and D. Szynal},
     title = {On relations for moments of the normal $k$th record values and a~characterization},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {610--618},
     publisher = {mathdoc},
     volume = {66},
     number = {3},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2021_66_3_a12/}
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P. Pawlas; D. Szynal. On relations for moments of the normal $k$th record values and a~characterization. Teoriâ veroâtnostej i ee primeneniâ, Tome 66 (2021) no. 3, pp. 610-618. http://geodesic.mathdoc.fr/item/TVP_2021_66_3_a12/