Sums of Independent Random Variables of the Modified Makeham Distribution
Pomeranian University of Słupsk, Department of Statistics
ul. Słowiańska 8, 76-200 Słupsk, Poland
e-mail: sylwiakosznik@wp.pl
Received:
Received: 20 September 2010; accepted: 31 March 2011; published online: 16 May 2011
DOI: 10.12921/cmst.2011.17.01.35-40
OAI: oai:lib.psnc.pl:737
Abstract:
This paper shows how the renewal process in which the sums of independent random variables of the modified Makeham distribution appear can be approximated by the surrogate distribution.
Key words:
modified Makeham distribution, renewal function, sums of random variables
References:
[1] R.E. Barlow, F. Proshan, Statistical theory of reliability and life testing. Holt: Reinhart and Winston Inc 1975.
[2] D.R. Cox, Renewal Theory. New York, Methuen 1962.
[3] D. Cox, D. Oakes, Analysis of survival date. New York, Chapman and Hall 1990.
[4] B.S. Dhillon, A Hazard Rate Model. IEEE Transactions on Reliability R-28, 2 (1979).
[5] B.S. Dhillon, Network Reliability Evaluation: Application of Bathtub Failure Rate Curve. Microelectronics and Reliability 21, 1, 103-111 (1981).
[6] B.S. Dhillon, New Hazard Rate Function. Microelectronics and Reliability 18, 531-532 (1979).
[7] A. Drapella, Lifetime models and renewal processes. Słupsk, PAP 2002.
[8] S. Kosznik, Zrównoważenie procedury pracy próbnej i obsługi profilaktycznej w przypadku siodłowej funkcji ryzyka. Praca doktorska, PG, Gdańsk 2003.
[9] S. Kosznik-Biernacka, Makeham’s generalised distribution. Computational Methods in Science and Technology 13 (2), 113-121 (2007).
[10] S. Kosznik-Biernacka, Rodzina rozkładów Makehama. Słupsk, PAP 2006.
[11] A.W. Marshall, I. Olkin, Life Distributions. Structure of Nonparametric. Semiparametric and Parametric Families, New York, Springer 2007.
[12] E.C. Wencel, Teoria wierojatności. Moskwa, Nauka 1969.
This paper shows how the renewal process in which the sums of independent random variables of the modified Makeham distribution appear can be approximated by the surrogate distribution.
Key words:
modified Makeham distribution, renewal function, sums of random variables
References:
[1] R.E. Barlow, F. Proshan, Statistical theory of reliability and life testing. Holt: Reinhart and Winston Inc 1975.
[2] D.R. Cox, Renewal Theory. New York, Methuen 1962.
[3] D. Cox, D. Oakes, Analysis of survival date. New York, Chapman and Hall 1990.
[4] B.S. Dhillon, A Hazard Rate Model. IEEE Transactions on Reliability R-28, 2 (1979).
[5] B.S. Dhillon, Network Reliability Evaluation: Application of Bathtub Failure Rate Curve. Microelectronics and Reliability 21, 1, 103-111 (1981).
[6] B.S. Dhillon, New Hazard Rate Function. Microelectronics and Reliability 18, 531-532 (1979).
[7] A. Drapella, Lifetime models and renewal processes. Słupsk, PAP 2002.
[8] S. Kosznik, Zrównoważenie procedury pracy próbnej i obsługi profilaktycznej w przypadku siodłowej funkcji ryzyka. Praca doktorska, PG, Gdańsk 2003.
[9] S. Kosznik-Biernacka, Makeham’s generalised distribution. Computational Methods in Science and Technology 13 (2), 113-121 (2007).
[10] S. Kosznik-Biernacka, Rodzina rozkładów Makehama. Słupsk, PAP 2006.
[11] A.W. Marshall, I. Olkin, Life Distributions. Structure of Nonparametric. Semiparametric and Parametric Families, New York, Springer 2007.
[12] E.C. Wencel, Teoria wierojatności. Moskwa, Nauka 1969.
