covbivgeo function

Covariance for the Basu-Dhar Bivariate Geometric Distribution

Covariance for the Basu-Dhar Bivariate Geometric Distribution

This function computes the covariance for the Basu-Dhar bivariate geometric distribution assuming arbitrary parameter values.

Source

covbivgeo is calculated directly from the definition.

covbivgeo(theta)

Arguments

  • theta: vector (of length 3) containing values of the parameters θ1,θ2\theta_1, \theta_2 and θ3\theta_{3} of the Basu-Dhar bivariate Geometric distribution. For real data applications, use the maximum likelihood estimates or Bayesian estimates to get the covariance.

Returns

covbivgeo computes the covariance for the Basu-Dhar bivariate geometric distribution for arbitrary parameter values.

Invalid arguments will return an error message.

Details

The covariance between X and Y, assuming the Basu-Dhar bivariate geometric distribution, is given by,

Cov(X,Y)=θ1θ2θ3(1−θ3)(1−θ1θ3)(1−θ2θ3)(1−θ1θ2θ3) Cov(X,Y) = \frac{\theta_1 \theta_2 \theta_{3}(1 - \theta_3)}{(1 - \theta_1\theta_3)(1 - \theta_2\theta_3)(1 - \theta_1 \theta_2 \theta_{3})}

Note that the covariance is always positive.

Examples

covbivgeo(theta = c(0.5, 0.5, 0.7))
# [1] 0.1506186
covbivgeo(theta = c(0.2, 0.5, 0.7))
# [1] 0.04039471
covbivgeo(theta = c(0.8, 0.9, 0.1))
# [1] 0.0834061
covbivgeo(theta = c(0.9, 0.9, 0.9))
# [1] 7.451626

References

Basu, A. P., & Dhar, S. K. (1995). Bivariate geometric distribution. Journal of Applied Statistical Science, 2 , 1, 33-44.

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

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

de Oliveira, R. P., & Achcar, J. A. (2018). Basu-Dhar's bivariate geometric distribution in presence of censored data and covariates: some computational aspects. Electronic Journal of Applied Statistical Analysis, 11 , 1, 108-136.

de Oliveira, R. P., Achcar, J. A., Peralta, D., & Mazucheli, J. (2018). Discrete and continuous bivariate lifetime models in presence of cure rate: a comparative study under Bayesian approach. Journal of Applied Statistics, 1-19.

Author(s)

Ricardo P. Oliveira rpuziol.oliveira@gmail.com

Jorge Alberto Achcar achcar@fmrp.usp.br

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