Stochastic Orders in Reliability and Risk by Haijun Li & Xiaohu Li

Author:Haijun Li & Xiaohu Li
Language: eng
Format: epub
Publisher: Springer New York, New York, NY

Figure 10.6Mean residual function of convolutions of gamma random variables

We also plot the mean residual life functions of convolutions of independent gamma random variables for different sets of λ i ’s

that show how r m ordering between λ i ’s will affect the mean residual life function of convolutions of gamma random variables.

Mi, Shi and Zhou [320] studied linear combinations of independent gamma random variables with different integer shape parameters (i.e., Erlang random variables). They established the likelihood ratio ordering between two linear combinations of Erlang random variables under some restrictions on the coefficients and shape parameters. It is interesting to note that Yu [484] proved

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