Reliability Properties of Extended Makeham Distributions
El-Bassiouny Ahmed Habib *, Abdo Abd El Latef Noura Fakhry
Mathematics Department
Faculty of Science, Mansoura University, Mansoura, Egypt
*e-mail: bassiouny@mans.edu.eg
Received:
Received: 23 January 2009; revised: 15 June 2009; accepted: 17 July 2009; published online: 2 October 2009
DOI: 10.12921/cmst.2009.15.02.143-149
OAI: oai:lib.psnc.pl:669
Abstract:
This paper investigates reliability properties of a flexible extended Makeham family of distributions. Quantiles are obtained and a probability distribution has for particular parameter values a bathtub hazard rate function.
Key words:
Makeham distributions, moments and quantiles, reliability function
References:
[1] B.C. Arnold, N. Balakrishnan and H.N. Nagaraja, A first course in order statistics. NewYork,Wiley (1992).
[2] X. Feng, G. He and Abdurishit, Estimation of parameters of the Makeham distribution using the least squares method. Mathematics and Computers in Simulation 77, 34-44 (2008).
[3] S. Kosznik-Biernacka, Makeham’s generalised distribution. Computational Methods in Science and Technology 13(2), 113-120 (2007).
[4] S. Kotz and S. Nadarajah, Extreme value theory, theory and applications. Singapore, World Scientific Publishing Company (2001).
[5] A.W. Marshall and I. Olkin, A new method for adding a parameter to a family of distributions with application to the exponential and Weibull families. Biometrika 84, 641-652 (1997).
[6] S.M. Ross, Stochastic processes. Second edition. New York, Wiley (1996).
[7] D.P.M. Scollnik, Simulating random variates from Makeham’s distribution and from others with exact or nearly Log-Concave densities. Trans. Soc. Actuaries 47, 409-437 (1995).
This paper investigates reliability properties of a flexible extended Makeham family of distributions. Quantiles are obtained and a probability distribution has for particular parameter values a bathtub hazard rate function.
Key words:
Makeham distributions, moments and quantiles, reliability function
References:
[1] B.C. Arnold, N. Balakrishnan and H.N. Nagaraja, A first course in order statistics. NewYork,Wiley (1992).
[2] X. Feng, G. He and Abdurishit, Estimation of parameters of the Makeham distribution using the least squares method. Mathematics and Computers in Simulation 77, 34-44 (2008).
[3] S. Kosznik-Biernacka, Makeham’s generalised distribution. Computational Methods in Science and Technology 13(2), 113-120 (2007).
[4] S. Kotz and S. Nadarajah, Extreme value theory, theory and applications. Singapore, World Scientific Publishing Company (2001).
[5] A.W. Marshall and I. Olkin, A new method for adding a parameter to a family of distributions with application to the exponential and Weibull families. Biometrika 84, 641-652 (1997).
[6] S.M. Ross, Stochastic processes. Second edition. New York, Wiley (1996).
[7] D.P.M. Scollnik, Simulating random variates from Makeham’s distribution and from others with exact or nearly Log-Concave densities. Trans. Soc. Actuaries 47, 409-437 (1995).
