# mombivgeo: Moments Estimator for the Basu-Dhar Bivariate Geometric... In BivGeo: 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

 1 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 θ_1, θ_2, θ_3 of the Basu-Dhar bivariate geometric distribution are given by:

\hat θ_1 = \frac{\bar{Y}(1 - \bar{W})}{\bar{W}(1 - \bar{Y})}

\hat θ_2 = \frac{\bar{X}(\bar{W} - 1)}{\bar{W}(\bar{X} - 1)}

\hat θ_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). Basu<e2><80><93>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.
  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 # 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