mombivgeo {BivGeo} | R Documentation |
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)
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. |
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}}
mombivgeo
gives the values of the moments estimator.
Invalid arguments will return an error message.
Ricardo P. Oliveira rpuziol.oliveira@gmail.com
Jorge Alberto Achcar achcar@fmrp.usp.br
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.
Geometric
for the univariate geometric distribution.
# 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