خلاصة:
Based on the increasing property of ratio of average reversed
hazard rates of two non-negative random variables a new stochastic order
for the sake of comparison of two lifetime distributions is proposed. This
stochastic order admits some distinguishing properties. In order to illustrate
the obtained results, a semi-parametric model which is called reverse hazard
power and a mixture model of proportional reversed hazards are taken into
account. Some examples are given to explain some facts.
ملخص الجهاز:
On the Reversed Average Intensity Order Majid Rezaei∗and Vahideh Ahrari Khalef Birjand University Based on the increasing property of ratio of average reversedhazard rates of two non-negative random variables a new stochastic orderfor the sake of comparison of two lifetime distributions is proposed.
(2014) proposed a new stochastic order based on the increasing property of ratio of two RHR functions.
To compare two mixture models of proportional reversed hazard rates (PRHR) that is essentially due to Li and Li (2008), we make use of the new stochastic order.
Let X1and X2be two non-negative random variables with respective sup- ports S1= (l1, u1)and S2= (l2, u2),having absolutely continuous distribu- ⃝c 2014, SRTC Iran tion functions F1and F2and probability density functions (pdf) f1and f2, respectively.
It is said that X1is smaller than X2in the sense of RHR order (denoted by X1≦RHR X2) if, q1(x)≦q2(x),for allx >0,or equivalently, if F2(x)/F1(x)is increasing inx∈(0,∞).
For the sake of comparison of two probability distributions according to their RAI functions, we defne a new stochastic order as follows.
1 It can be easily seen that X1≦RAI X2if and only if there exists a non- negative increasing functionβ(x)such that F2(x) = [F1(x)]β(x),for allx >0, that is the distribution function of the random variable X2is an exponenti- ated function of the distribution function of the random variable X1.
Res. Iran11(2014): 25–39 relative RHR order (denoted by X1≦RRH X2), if q2(t)/q1(t)is increasing in t >0,or equivalently if,qi(t)is TP2(i, t)in(i, t)∈ {1,2} ×(0,∞).