Exceedance statistics based on bottom-k-lists

Similar to usual lower records, Bottom-k-lists (Kozan and Tanil, & Idot;statistik J Turk Stat Assoc 13:73-79, 2013) have a wide range of practical applications in meteorology, hydrology, sports, etc. Also, exceedance statistics can be viewed as a close relative to tolerance limits-an important field of statistical science. In this study, an idea of combining these two important subjects together is studied and an exceedance statistic is defined based on bottom-k-lists in an independent and identically distributed (iid) continuous random sequence. Probability mass function (pmf) of a selected exceedance statistic is obtained. Also, an illustrative application of the exceedance statistic is given.