DISCRETIZATION OF BURR-TYPE III DISTRIBUTION
Keywords:
Burr-type III distribution, discrete lifetime models, reliability, failure rateAbstract
In this paper we propose a discrete analogue of Burr-type III distribution using a general approach of Discretizing a continuous distribution. It may be worth exploring the possibility of developing a discrete version of two parameter Burr-type III distribution, so that same can be used for modeling a discrete data. Discrete Burr-type III distribution is suggested as a suitable reliability model to fit a range of discrete life time data, as it is shown that hazard rate function can attain monotonic increasing (decreasing) shape for certain values of parameters. The equivalence of discrete Burr-type III (DBD-III) and continuous Burr-type III (BD-III) distributions has been established. Various theorems relating Burr Type III distribution with other statistical distributions have also been proved.
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References
Barlow, R.E. and Proschan, F. (1975). The Statistical Theory of Reliability
and Lifetesting (New York: Holt, Rinehart & Winston, Inc.).
Jazi, M.A., Lai, C.D., and Alamatsaz, M.H. (2011). A discrete inverse Weibul
distribution and estimation of its parameters, Statistical Methodology, 7, p.
-132.
Kapur, K. C. and Lamberson, L. R. (1997). Reliability in Engineering Design,
New York: John Wiley & Sons.
Krishna, H. and Pundir, P.S. (2009). Discrete burr and discrete Pareto
distributions, Statistical Methodology, 6, p. 177-188.
Krishna, H. and Pundir, P.S. (2007). Discrete Maxwell distributions, Statistical
Methodology, interstat statjournals.net/YEAR/2007/abstracts/0711003.php.
Lawless, J.F. (1982). Statistical Models and Methods for lifetime data (New
York: John Wiley & Sons).
Nakagawa, T. and Osaki, S. (1975). The Discrete Weibull Distribution, IEEE
Transactions on Reliability, R-24, 5, p. 300 –301.
Olapade, A.K (2008). On a six parameter generalized Burr XII distribution,
http://arxiv.org/abs/0806.1579v1.
Roy, D. (1993). Reliability measures in the discrete bivariate set up and related
characterization results for a bivariate geometric distribution, Journal of
Multivariate Analysis, 46, p. 362–373.
Roy, Dilip (2003). The Discrete normal Distribution, Communications in
Statistics – Theory and Methods, 32, 10, p. 1871-1883.
Roy, Dilip (2004). Discrete Rayleigh distribution, IEEE Transactions on
Reliability, 53, 2, p. 255 –260.
Sinha, S.K. (1986). Reliability and Life testing (New Delhi: Wiley Eastern
Ltd.).
Srinath, L.S. (1985). Reliability engineering (Forth edition, East-West press).
Xie, M. Gaudoin and O. Bracquemond, C. (2002). Redefining failure rate
function for discrete distributions, International Journal of Reliability, Quality
and safety Engineering, 9, 3, p.275-285