Bivariate Discrete Modified Weibull (BDMW) Distribution
DOI:
https://doi.org/10.6092/issn.1973-2201/9775Keywords:
Weibull distribution, Joint survival function, Probability mass function, Maximum likelihood estimationAbstract
In this paper we develop a bivariate discrete modifiedWeibull (BDMW) distribution and derived some of its important properties such as joint survival function, marginal survival function, conditional survival function, joint probability generating function and hazard rate function. The significance of additional parameter in BDMW is tested using generalized likelihood ratio test. Also we construct a finite mixture ofBDMWand established its identifiability condition. Certain properties of the mixture model are derived. The parameters of BDMW are estimated through method of maximum likelihood.
References
R. H. BYRD, P. LU, J. NOCEDAL, C. ZHU (1995). A limited memory algorithm for bound constrained optimization. SIAM Journal on Scientific Computing, 16, no. 6, pp. 1190–1208.
S. CHAKRABORTY (2015). Generating discrete analogue of continuous probability distributions - a survey of methods and construction. Journal of Statistical Distributions and Applications, 2, no. 6, pp. 1–30.
A. H. EL-BASSIOUNY, H. S. SHAHEN, M. ABOUHAWWASH (2018). A new bivariate modified Weibull distribution and its extended distributions. Journal of Statisitcs Applications and Probability, 7, no. 2, pp. 217–231.
B. S. EVERITT, D. J. HANDE (1981). Finite Mixture Distribution. Chapman & Hall, London.
S. KOCHERLAKOTA, K. KOCHERLAKOTA (1992). Bivariate discrete distributions. Marcel and Dekker, New York.
D. KUNDU, A. K. GUPTA (2013). Bayes estimation for the Marshall-Olkin bivariate Weibull distribution. Computational Statistics and Data Analysis, 57, no. 1, pp. 271-281.
D. KUNDU, V. NEKOUKHOU (2018). On bivariate discreteWeibull distribution. Communications in Statistics - Theory and Methods, 48, no. 1, pp. 3464–3481.
C. D. LAI, M. XIE, D. N. P. MURTHY (2003). A modified Weibull distribution. IEEE Transactions on Reliability, 52, no. 1, pp. 33–37.
G. MCLACHLAN, D. PEEL (2000). Finite Mixture Models. Wiley, New York.
M. S. NOUGHABI, A. H. R. ROKNABADY, G. R. M. BORZADARAN (2011). Discrete modified Weibull distribution. Metron, 69, no. 2, pp. 207–222.
D. ROY (2002). Discretization of continuous distributions with an application to stressstrength reliability. Calcutta Statistical Association Bulletin, 52, pp. 205–208.
D. M. TITTERINGTON (1990). Some recent research in the analysis of mixture distributions. Statistics, 21, pp. 619–641.
D. M. TITTERINGTON, A. F. M. SMITH, U. E. MARKOV (1985). Statistical Analysis of Finite Mixture Distributions. Wiley, New York.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2021 Statistica
This work is licensed under a Creative Commons Attribution 3.0 Unported License.