It is shown that the equality in distributions of upper and lower k-records from a population with continuous distribution is a characteristic property of symmetric continuous distributions. Some characterization results for symmetric continuous distributions are obtained using moments properties of functions of upper and lower k-records. Also, spacings of k-records are considered and characterizations using equidistribution of spacing of upper and lower k-records are presented. Moreover, characterizations of symmetric distributions based on the moments’ equality of spacing of upper and lower k-records are established.

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