혼합 얼랑 확률변수의 극한치Extreme Values of Mixed Erlang Random Variables
- Other Titles
- Extreme Values of Mixed Erlang Random Variables
- Authors
- 강성열
- Issue Date
- 2003
- Publisher
- 한국경영과학회
- Keywords
- Extreme Values; Erlang; Finite Mixture Distribution; Continuous Mixing; Extreme Values; Erlang; Finite Mixture Distribution; Continuous Mixing
- Citation
- 한국경영과학회지, v.28, no.4, pp.145 - 153
- Journal Title
- 한국경영과학회지
- Volume
- 28
- Number
- 4
- Start Page
- 145
- End Page
- 153
- URI
- https://scholarworks.bwise.kr/hongik/handle/2020.sw.hongik/26473
- ISSN
- 1225-1119
- Abstract
- In this paper, we examine the limiting distributional behaviour of extreme values of mixed Erlang random variables. We show that, in the finite mixture of Erlang distributions, the component distribution with an asymptotically dominant tail has a critical effect on the asymptotic extreme behavior of the mixture distribution and it converges to the Gumbel extreme-value distribution. Normalizing constants are also established. We apply this result to characterize the asymptotic distribution of maxima of sojourn times in queuing system. We also show that Erlang mixtures with continuous mixing may converge to the Gumbel or Type Ⅱ extreme-value distribution depending on their mixing distributions, considering two special cases of uniform mixing and exponential mixing.
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