Some Aging Properties Involved with Compound Geometric Distributions

Sankhya A - Tập 77 Số 2 - Trang 337-350 - 2015
Chen Li1, Rui Fang1, Xiaohu Li2
1School of Mathematical Sciences, Xiamen University, Xiamen, China
2Department of Mathematical Sciences, Stevens Institute of Technology, Hoboken, USA

Tóm tắt

Từ khóa


Tài liệu tham khảo

Abouammoh A.M., Ahmad R. and Khalique A. (2000). On new renewal better than used classes of life distributions. Stat. Probab. Lett. 48, 189–194.

Bhattacharjee M.C., Ravi S., Vasudeva R. and Mohan N.R. (2003). New order preserving properties of geometric compounds. Stat. Probab. Lett. 64, 113–120.

Brémaud P. (2014). Fourier Analysis and Stochastic Processes. Springer, Switzerland.

Dufresne F. and Gerber H.U. (1991). Risk theory for the compound Poisson process that is perturbed by diffusion. Insur. Math. Econ. 10, 51–59.

Kaas R., Goovaerts M., Dhaene J. and Denuit M. (2008). Modern Actuarial Risk Theory. Springer, Heidelberg.

Kalashnikov V. (1997). Geometric Sums: Bounds for Rare Events with Applications. Kluwer Academic Publishers, Dordrecht.

Li H. and Li X. (2013). Stochastic Orders in Reliability and Risk. Springer, New York.

Lin X.S. and Willmot G.E. (1999). Analysis of a defective renewal equation arising in ruin theory. Insur. Math. Econ. 25, 63–84.

Marshall A.W. and Olkin I. (2007). Life Distributions. Springer, New York.

Psarrakos G. (2009). A note on convolutions of compound geometric distributions. Stat. Probab. Lett. 79, 1231–1237.

Psarrakos G. (2010). On the DFR property of the compound geometric distribution with applications in risk theory. Insur. Math. Econ. 47, 428–433.

Ross S.M. (1996). Stochastic Processes. Wiley, New York.

Shaked M. and Shanthikumar J.G. (2007). Stochastic Orders. Springer, New York.

Van Hoorn M. (1984). Algorithms and Approximations for Queueing Systems. CWI Tract 8, Amsterdam.

Willmot G.E. (2002). Compound geometric residual lifetime distributions and the deficit at ruin. Insur. Math. Econ. 30, 421–438.

Willmot G.E. and Cai J. (2004). On applications of residual lifetimes of compound geometric convolutions. J. Appl. Probab. 41, 802–815.

Willmot G.E. and Lin X.S. (2001). Lundberg Approximations for Compound Distributions with Insurance Applications. Springer, New York.