On bivariate geometric distribution
AbstractCharacterizations of bivariate geometric distribution using univariate and bivariate geometric compounding are obtained. Autoregressive models with marginals as bivariate geometric distribution are developed. Various bivariate geometric distributions analogous to important bivariate exponential distributions like, Marshall-Olkin’s bivariate exponential, Downton’s bivariate exponential and Hawkes’ bivariate exponential are presented.
H. W. BLOCK, (1977), A family of bivariate life distributions. “Theory and Applications of Reliability: With Emphasis on Bayesian and Nonparametric Methods”, C. P. Tsokos and I.N. Shimi, eds, Academic Press, pp. 349-372.
F. DOWNTON, (1970), Bivariate exponential distributions in reliability theory. “Journal of Royal Statistical Society”, Series B, 32, pp. 408-417.
B. V. GNEDENKO, V. KOROLEV, (1996), Random summation: Limit theorems and applications.CRC Press, New York.
A. G. HAWKES, (1972), A bivariate exponential distribution with applications to reliability. “Journal of Royal Statistical Society”, Series B, 34, pp. 129-131.
K. JAYAKUMAR, (1995), The stationary solution of a first order integer valued autoregressive processes. “Statistica”, LV, pp. 221-228.
T. J. KOZUBOWSKI, A. K. PANORSKA, (1999), Multivariate geometric stable distribution in financial applications. “Mathematical and Computer Modeling”, 29, pp. 83-92.
T. J. KOZUBOWSKI, S. T. RACHEV, (1994), The theory of geometric stable laws and its use in modeling financial data. “European Journal of Operations Research”, 74, pp. 310-324.
A. W. MARSHALL, I. OLKIN, (1967), A multivariate exponential distribution. “Journal of the American Statistical Association”, 62, pp. 30-44.
A. G. PHATAK, M. SREEHARI, (1981), Some characterizations of bivariate geometric distribution, “Journal of Indian Statistical Association”, 19, pp. 141-146.