R/mombivgeo.R

In BivGeo: Basu-Dhar Bivariate Geometric Distribution

#' @importFrom stats runif
#'
#' @name mombivgeo
#' @aliases mombivgeo
#'
#' @title 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.
#'
#' @author Ricardo P. Oliveira \email{rpuziol.oliveira@gmail.com}
#' @author Jorge Alberto Achcar \email{achcar@fmrp.usp.br}
#'
#' @references
#'
#' Basu, A. P., & Dhar, S. K. (1995). Bivariate geometric distribution. \emph{Journal of Applied Statistical Science}, \bold{2}, 1, 33-44.
#'
#' Li, J., & Dhar, S. K. (2013). Modeling with bivariate geometric distributions. \emph{Communications in Statistics-Theory and Methods}, 42, \bold{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. \emph{Journal of Applied Statistics}, \bold{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. \emph{Electronic Journal of Applied Statistical Analysis}, \bold{11}, 1, 108-136.
#'
#' @param 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.
#'
#' @param 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.
#'
#'
#' @return \code{\link[BivGeo]{mombivgeo}} gives the values of the moments estimator.
#'
#' @return Invalid arguments will return an error message.
#'
#' @usage
#'
#' mombivgeo(x, y)
#'
#' @details
#'
#' The moments estimators of \eqn{\theta_1, \theta_2, \theta_3} of the Basu-Dhar bivariate geometric distribution are given by:
#' \deqn{\hat \theta_1 = \frac{\bar{Y}(1 - \bar{W})}{\bar{W}(1 - \bar{Y})}}
#' \deqn{\hat \theta_2 = \frac{\bar{X}(\bar{W} - 1)}{\bar{W}(\bar{X} - 1)}}
#' \deqn{\hat \theta_3 = \frac{\bar{X}(\bar{X} - 1)(\bar{Y} - 1)}{(\bar{W} - 1)\bar{X} \bar{Y}}}
#'
#' @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
#' @source
#'
#' \code{\link[BivGeo]{mombivgeo}} is calculated directly from the definition.
#'
#' @seealso
#'
#' \code{\link[stats]{Geometric}} for the univariate geometric distribution.
#'
#' @rdname mombivgeo
#' @export

mombivgeo <- function(x, y = NULL)
{
	if(is.matrix(x))
	{
		x0	<-	x[,1]
		y0	<-	x[,2]
	}
	else if(is.vector(x) & is.vector(y))
	{
		if(length(x)==length(y))
		{
			x0	<-	x
			y0	<-	y
		}
		else
		{
			stop('lengths of x and y are not equal')
		}
	}
	else
	{
		stop('x is not a matrix or x and y are not vectors')
	}

	## Generating min(Xi,Yi)

	min_xy 	<- 	pmin(x0,y0)

	##  Estimatives: Moments

	xbar 	<- 	mean(x0)
	ybar 	<- 	mean(y0)
	zbar 	<- 	mean(min_xy)

	theta1 	<- 	(ybar * (1 - zbar))/(zbar * (1 - ybar))
	theta2 	<- 	(xbar * (zbar - 1))/(zbar * (xbar - 1))
	theta3 	<- 	(zbar * (xbar - 1) * (ybar - 1))/(xbar * ybar * (zbar - 1))

	est <- rbind(theta1,theta2,theta3)
	return(est)
}