In a sequence of independent and identically distributed random variables, the $k$-th largest [lowest] observation in a partial sample is well-known as upper [lower] k-record statistic. In this paper, we consider the $k$-record statistics at the time when the $n$-th $k$-record of any kind (either an upper or lower) is observed. Then, it is shown how various exact nonparametric confidence intervals can be construct based on these information. Confidence intervals for quantile intervals and quantile differences in terms of current $k$-records are obtained. Exact expressions for the confidence coefficients of these intervals are derived without any assumption about the parent distribution function other than its continuity.

In a sequence of independent and identically distributed random variables, the $k$-th largest [lowest] observation in a partial sample is well-known as upper [lower] k-record statistic. In this paper, we consider the $k$-record statistics at the time when the $n$-th $k$-record of any kind (either an upper or lower) is observed. Then, it is shown how various exact nonparametric confidence intervals can be construct based on these information. Confidence intervals for quantile intervals and quantile differences in terms of current $k$-records are obtained. Exact expressions for the confidence coefficients of these intervals are derived without any assumption about the parent distribution function other than its continuity.

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