mombivgeo {BivGeo}R Documentation

Moments Estimator for the Basu-Dhar Bivariate Geometric Distribution


This function computes the estimators based on the method of the moments for each parameter of the Basu-Dhar bivariate geometric distribution.


mombivgeo(x, y)



matrix or vector containing the data. If x is a matrix then it is considered as x the first column and y the second column (y argument need be setted to NULL). Additional columns and y are ignored.


vector containing the data of y. It is used only if x is also a vector. Vectors x and y should be of equal length.


The moments estimators of \theta_1, \theta_2, \theta_3 of the Basu-Dhar bivariate geometric distribution are given by:

\hat \theta_1 = \frac{\bar{Y}(1 - \bar{W})}{\bar{W}(1 - \bar{Y})}

\hat \theta_2 = \frac{\bar{X}(\bar{W} - 1)}{\bar{W}(\bar{X} - 1)}

\hat \theta_3 = \frac{\bar{X}(\bar{X} - 1)(\bar{Y} - 1)}{(\bar{W} - 1)\bar{X} \bar{Y}}


mombivgeo gives the values of the moments estimator.

Invalid arguments will return an error message.


Ricardo P. Oliveira

Jorge Alberto Achcar


mombivgeo is calculated directly from the definition.


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.

See Also

Geometric for the univariate geometric distribution.


# Generate the data set:

x1 		<- 	rbivgeo1(n = 1000, theta = c(0.5, 0.5, 0.7))
x2 		<- 	rbivgeo2(n = 1000, theta = c(0.5, 0.5, 0.7))

# Compute de moment estimator by:

mombivgeo(x = x1, y = NULL) # For data set x1
#             [,1]
# theta1 0.5053127
# theta2 0.5151873
# theta3 0.6640406

mombivgeo(x = x2, y = NULL) # For data set x2
#             [,1]
# theta1 0.4922327
# theta2 0.5001577
# theta3 0.6993893

[Package BivGeo version 2.0.1 Index]