covbivgeo {BivGeo} R Documentation

## Covariance for the Basu-Dhar Bivariate Geometric Distribution

### Description

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

### Usage

covbivgeo(theta)


### Arguments

 theta vector (of length 3) containing values of the parameters \theta_1, \theta_2 and \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.

### Details

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

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.

### Value

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

Invalid arguments will return an error message.

### Author(s)

Ricardo P. Oliveira rpuziol.oliveira@gmail.com

Jorge Alberto Achcar achcar@fmrp.usp.br

### Source

covbivgeo is calculated directly from the definition.

### 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.

### Examples


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



[Package BivGeo version 2.0.1 Index]