The complementary exponential-geometric (CEG) distribution is a useful model for analyzing lifetime data. For this distribution, some recurrence relations satisfied by marginal and joint moment generating functions of k-th lower record values were established. They enable the computation of the means, variances, and covariances of k-th lower record values for all sample sizes in a simple and efficient recursive manner. Means, variances, and covariances of lower record values were tabulated from samples of sizes up to 10 for various values of the parameters.
Kumar, D., Dey, S., Malik, M. R., & Al-Aboud, F. H. (2018). Moment Generating Functions of Complementary Exponential-Geometric Distribution Based on k-th Lower Record Values. Journal of Modern Applied Statistical Methods, 17(1), eP2479. doi: 10.22237/jmasm/1525133220