mombivgeo {BivGeo} R Documentation

## Moments Estimator for the Basu-Dhar Bivariate Geometric Distribution

### Description

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

### Usage

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.

### Details

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}}

### Value

mombivgeo gives the values of the moments estimator.

Invalid arguments will return an error message.

### Author(s)

Ricardo P. Oliveira rpuziol.oliveira@gmail.com

Jorge Alberto Achcar achcar@fmrp.usp.br

### Source

mombivgeo 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). Basuâ€“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.

Geometric for the univariate geometric distribution.

### 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


[Package BivGeo version 2.0.1 Index]