چكيده لاتين :
Consider a sequence of n independent observations from
a population of increasing size Qi, i = 1,2, ... and an absolutely
continuous initial distribution function. The distribution of the kth
record value is represented as a countable mixture, with mixing the
distribution of the kth record time and mixed the distribution of the
nth order statistic. Precisely, the distribution function and (power)
moments of the kth record value are expressed by series, with coefficients
being the signless. generalized Stirling numbers of the first
kind. Then, the probability density function and moments of the kth
record value in a geometrically increasing population are expressed by
q-series, with coefficients being the signless q-Stirling numbers of the
first kind. In the case of a uniform distribution for the initial population,
two equivalent q-series expressions of the jth (power) moment
of the kth record value are derived. Also, the distribution function
and the moments of the kth record value in a factorially increasing
population are deduced.
