On the Comparison in Mean Residual Life Order of the Convolutions of Geometric Random Variables
نویسندگان
چکیده
Let X1, · · · , Xn and Y1, · · · , Yn be independent heterogeneous geometric random variables with parameters p1 ≤ · · · ≤ pn and q1 ≤ · · · ≤ qn, respectively. We prove that ∑k i=1Xi is larger than ∑k i=1 Yi, for k = 1, · · · , n, in mean residual life order if, and only if, the harmonic mean of p1, · · · , pk is smaller than the harmonic mean of q1, · · · , qk, for k = 1, · · · , n. In this way, we slightly improve a result of Mao, Hu and Zhao (2010). On the other hand, we present a new proof of this result. For a complete argumentation, we prove a discrete version of a well-known closure property. 2000 Mathematics Subject Classification: 60E15, 60E05.
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