In this paper, it is shown that a convolution of uniform distributions (a) is more dispersed and (b) has a smaller hazard rate when the scale parameters of the uniform distributions are more dispersed in the sense of majorization. It is also shown that a convolution of gamma distributions with a com
Stochastic orders of the sums of two exponential random variables
β Scribed by Kuo-Hwa Chang
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 105 KB
- Volume
- 51
- Category
- Article
- ISSN
- 0167-7152
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π SIMILAR VOLUMES
We obtain some new results on normalized spacings of independent exponential random variables with possibly different scale parameters. It is shown that the density functions of the individual normalized spacings in this case are mixtures of exponential distributions and, as a result, they are log-c
Let X 1 ; : : : ; X n be independent random variables such that X i has exponential distribution with hazard rate i ; i=1; : : : ; n. ( 1; : : : ; n) majorizes ( \* 1 ; : : : ; \* n ).
## I. fntFoduction Let {X,,, n 2 1) be a sequence of independent random variables, P, and f, the distribution function and the characteristic fundion of the X,, respectively. Let us put SN = 2 X,, where N is a pasitive integer-valued random variable independent of X,, ?t 2 1. Furthermore, let { P,
is non-decreasing. Thus, if one applies the c,-inequality, the inequality follows trivially. From this and from the preceding inequality we obtain By our condition the sums on the right hand side converge to 0 as n -+ + 00. This proves the assertion. Remarks. It is easy to see that for p > 2 our c