mombivgeo function

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.

Source

mombivgeo is calculated directly from the definition.

mombivgeo(x, y)

Arguments

• x: 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.
• y: 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.

Returns

mombivgeo gives the values of the moments estimator.

Invalid arguments will return an error message.

Details

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

Examples

# Generate the data set:

set.seed(123)
x1              <-      rbivgeo1(n = 1000, theta = c(0.5, 0.5, 0.7))
set.seed(123)
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

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.

See Also

Geometric for the univariate geometric distribution.

Author(s)

Ricardo P. Oliveira rpuziol.oliveira@gmail.com

Jorge Alberto Achcar achcar@fmrp.usp.br