The Distribution and Frequency of Record Values

Summary The lower record values of a semi-infinite time series derived by random simple sampling from a fixed universe are defined to be those members which are less than all previous members. The probability distribution of the rth lower record value, Xr, is obtained and its probability points for r = 2, 3, …, 9, for normal and rectangular universes are tabulated. The probability distribution of the serial number, ur, of Xr in the original series xu is found and also the probability distribution of the difference of the serial numbers of Xr - 1, and Xr. These serial numbers, ur, are interesting in that they do not leave finite means. Further, they are independent of the parent universe, providing it has finite or zero probability density at all points.