Basu-Dhar's bivariate geometric distribution in presence of censored data and covariates: some computational aspects


Abstract


Some computational aspects to obtain classical and Bayesian inferences for the Basu and Dhar (1995) bivariate geometric distribution in presence of censored data and covariates are discussed in this paper. The posterior summaries of interest are obtained using standard existing MCMC (Markov Chain Monte Carlo) simulation methods available in popular free softwares  as the OpenBugs software and the R software. Numerical illustrations are introduced considering simulated and real datasets showing that the use of discrete bivariate distributions may be a good alternative to the use of continuous bivariate distributions, in many areas of application.

DOI Code: 10.1285/i20705948v11n1p108

Keywords: Basu-Dhar distribution; censored data; covariates; maximum likelihood estimates; Bayesian estimates.

References


Achcar, J., Davarzani, N., and Souza, R. (2016a). Basu–Dhar bivariate geometric distribution in the presence of covariates and censored data: a bayesian approach. Journal of Applied Statistics, 43(9):1636–1648.

Achcar, J. A. and Leandro, R. A. (1998). Use of markov chain monte carlo methods in a bayesian analysis of the block and basu bivariate exponential distribution. Annals of the Institute of Statistical Mathematics, 50(3):403–416.

Achcar, J. A., Martinez, E. Z., and Cuevas, J. R. T. (2016b). Bivariate lifetime modelling using copula functions in presence of mixture and non-mixture cure fraction models, censored data and covariates. Model Assisted Statistics and Applications, 11(4):261–276.

Arnold, B. C. (1975). A characterization of the exponential distribution by multivariate geometric compounding. Sankhya: The Indian Journal of Statistics, Series A, pages 164–173.

Arnold, B. C. and Strauss, D. (1988). Bivariate distributions with exponential conditionals. Journal of the American Statistical Association, 83(402):522–527.

Basu, A. P. and Dhar, S. (1995). Bivariate geometric distribution. Journal of Applied Statistical Science, 2(1):33–44.

Block, H. W. and Basu, A. (1974). A continuous, bivariate exponential extension. Journal of the American Statistical Association, 69(348):1031–1037.

Chib, S. and Greenberg, E. (1995). Understanding the metropolis-hastings algorithm. The american statistician, 49(4):327–335.

Davarzani, N., Achcar, J. A., Smirnov, E. N., and Peeters, R. (2015). Bivariate lifetime geometric distribution in presence of cure fractions. Journal of Data Science, 13(4):755–770.

Dhar, S. K. (1998). Data analysis with discrete analogue of freund’s model. Journal of Applied Statistical Science, 7:169–183.

Dhar, S. K. (2003). Modeling with a bivariate geometric distribution. Advances on Methodological and Applied Aspects of Probability and Statistics, 1:101–109.

Dhar, S. K. and Balaji, S. (2006). On the characterization of a bivariate geometric distribution. Communications in Statistics—Theory and Methods, 35(5):759–765.

dos Santos, C. A. and Achcar, J. A. (2011). A bayesian analysis for the block and basu bivariate exponential distribution in the presence of covariates and censored data. Journal of Applied Statistics, 38(10):2213–2223.

Downton, F. (1970). Bivariate exponential distributions in reliability theory. Journal of the Royal Statistical Society. Series B (Methodological), pages 408–417.

Freund, J. E. (1961). A bivariate extension of the exponential distribution. Journal of the American Statistical Association, 56(296):971–977.

Gelfand, A. E. and Smith, A. F. (1990). Sampling-based approaches to calculating marginal densities. Journal of the American statistical association, 85(410):398–409.

Gumbel, E. J. (1960). Bivariate exponential distributions. Journal of the American Statistical Association, 55(292):698–707.

Hanagal, D. and Ahmadi, K. (2008). Estimation of parameters by em algorithm in bivariate exponential distribution based on censored samples. Econ. Quality Control, 23(2):257–66.

Hanagal, D. D. (2006). Bivariate weibull regression model based on censored samples. Statistical Papers, 47(1):137–147.

Hawkes, A. G. (1972). A bivariate exponential distribution with applications to reliability. Journal of the Royal Statistical Society. Series B (Methodological), pages 129–131.

Henningsen, A. and Toomet, O. (2011). maxlik: A package for maximum likelihood estimation in R. Computational Statistics, 26(3):443–458.

Hougaard, P. (1986). A class of multivariate failure time distributions. Biometrika, pages 671–678.

Klein, J. P. and Moeschberger, M. L. (2005). Survival analysis: techniques for censored and truncated data. Springer Science & Business Media.

Kocherlakota, S. and Kocherlakota, K. (1992). Bivariate discrete distributions. Wiley Online Library.

Krishna, H. and Pundir, P. S. (2009). A bivariate geometric distribution with applications to reliability. Communications in Statistics—Theory and Methods, 38(7):1079–1093.

Lawless, J. F. (1982). Statistical models and methods for lifetime data. John Wiley & Sons.

Li, J. and Dhar, S. K. (2013). Modeling with bivariate geometric distributions. Communications in Statistics-Theory and Methods, 42(2):252–266.

Marshall, A. W. and Olkin, I. (1967a). A generalized bivariate exponential distribution. Journal of Applied Probability, 4(02):291–302.

Marshall, A. W. and Olkin, I. (1967b). A multivariate exponential distribution. Journal of the American Statistical Association, 62(317):30–44.

Martin, A. D., Quinn, K. M., and Park, J. H. (2011). MCMCpack: Markov chain Monte Carlo in R. Journal of Statistical Software, 42(9):22.

McGilchrist, C. and Aisbett, C. (1991). Regression with frailty in survival analysis. Biometrics, pages 461–466.

Muraleedharan Nair, K. and Unnikrishnan Nair, N. (1988). On characterizing the bivariate exponential and geometric distributions. Annals of the institute of Statistical Mathematics, 40(2):267–271.

R Core Team (2016). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria.

Sarkar, S. K. (1987). A continuous bivariate exponential distribution. Journal of the American Statistical Association, 82(398):667–675.

Spiegelhalter, D., Thomas, A., Best, N., and Lunn, D. (2007). Openbugs user manual, version 3.0. 2. MRC Biostatistics Unit, Cambridge.

Sun, K. and Basu, A. P. (1995). A characterization of a bivariate geometric distribution. Statistics & probability letters, 23(4):307–311.


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