Authors:
Zainab Falih Hamza,Thaera N. Al-Ameer, Firas M. Al-Badran,DOI NO:
https://doi.org/10.26782/jmcms.2019.06.00026Keywords:
Discrete Gamma distribution, Maximum Likelihoo, Reliabilit function,Abstract
This research dials with discrete counter-part of continuous gamma distribution. In fact, the statistical and reliability properties of this distribution are discuss and some interesting interrelationships. Furthermore, an estimation of the underlying parameter and reliability for this distribution are utilized using different samples sizes, that’s done through different simulation experiments by use (R3.5.1) program, the simulation outputs proved that the Maximum likelihood method gives small bias estimators. An application done at two Soap production machines belongs to the Vegetable Oil Plant. The results show that the second machine which follows DGD (3) is more reliable from the first one.Refference:
I.Abouammoh, A. M. and Mashhour, A. F. (1981). A note on the unimodality of discrete distributions. Comm. Statistic, Ser. A, 10, 1345-1354.
II.Abouammoh, A. M. and Alhazzani, Najla. S. (2012). On discrete gamma distribution (submitted for publication).
III.Ali Khan, M. S., Khalique, A. and Abouammoh, A. M. (1989). On estimating parameters in a discrete Weibull distribution. IEEE Trans.Reliability, 38, 347-350.
IV.Bergor, J.O (1985) ” Statistics of Decision Theory and Bayesian Analysis”, 2nd Edition, Springer Verging, New York.
V.Christian, P. Robert & Gorge Casella (2010) ” Introduction Monte Carlo Methods with R”, Springer.
VI.L .Gupta, P., Gupta, R. C. and Triatic, R. C. (1997). On the monotone property of discrete failure rate. J. of Statistical Planning and Inference, 65,255-268.
VII.Hirzebruch, F. (2008). Eulerian polynomials. Munster J. of Math, 1 , 9–14.
VIII.L .Johnson, N., Kits, S. and Kemp, A. (1992). Univariate Discrete Distribution. New York, Wiley.
IX.Lawless, J. F. (2003). Statistical Models and Methods for Lifetime Data. John Wiley and Sons, New York.
X.Law, A. and Kelton, W. (1991). Simulation Modeling and Analysis. McGraw-Hill, Inc. New York.
XI.Nakagawa, T. and Osaki, S. (1975). The discrete Weibull distributions. IEEE Trans. Reliable., 24, 300-301.
XII.Padgett, W. J. and Spurries, J. D. (1985). On discrete failure models. IEEE Trans. Reliable., 34, 253–256.
XIII.Salvia, A. A. and Bollinger, R. C. (1982). On discrete hazard function. IEEE transactions on Reliability, Vol. 31, No. 5, 458-459.
XIV.Stein, W. E. and Dater, R. (1984). A new discrete Weibull distribution. IEEE Trans. Reliable., 33, 196-107.