Finite mixtures of geometric random variables X 1 and X 2 are identified in terms of relations between the best predictor of X 2:2 given X 1:2 and the functions of the failure rate (or hazard function) of the distribution. Here X 1:2 and X 2:2 denote the corresponding order statistics. In addition, we also use the relation between the mean residual life (MRL) of X 1 and the functions of the failure rate of the distribution to characterize the finite mixture of geometric distributions. The characterizing relations were motivated by the work of A. N. Ahmed and A. Y. Yehia [J. Jap. Stat. Soc. 23, No. 1, 49-55 (1993; Zbl 0782.62016)], S. N. U. A. Kirmani and S. N. Alam [Commun. Stat., Theory Methods A9, 541-547 (1980; Zbl 0454.62015)] and D. N. Shanbhag [J. Am. Stat. Assoc. 65, 1256-1259 (1970; Zbl 0224.62007)].
Journal of applied statistical science 10, pp.167-180