# pbivgeo: Joint Cumulative Function for the Basu-Dhar Bivariate... In BivGeo: Basu-Dhar Bivariate Geometric Distribution

## Description

This function computes the joint cumulative function of the Basu-Dhar bivariate geometric distribution assuming arbitrary parameter values.

## Usage

 `1` ```pbivgeo(x, y, theta, lower.tail = TRUE) ```

## 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. `theta` vector (of length 3) containing values of the parameters θ_1, θ_2 and θ_3 of the Basu-Dhar bivariate Geometric distribution. The parameters are restricted to 0 < θ_i < 1, i = 1,2 and 0 < θ_3 ≤ 1. `lower.tail` logical; If TRUE (default), probabilities are P(X ≤ x, Y ≤ y) otherwise P(X > x, Y > y).

## Details

The joint cumulative function for a random vector (X, Y) following a Basu-Dhar bivariate geometric distribution could be written as:

P(X ≤ x, Y ≤ y) = 1 - (θ_{1}θ_3)^{x} - (θ_{2}θ_3)^{y} + θ_{1}^{x}θ_{2}^{y} θ_{3}^{\max(x,y)}

and the joint survival function is given by:

P(X > x, Y > y) = θ_{1}^{x}θ_{2}^{y} θ_{3}^{\max(x,y)}

## Value

`pbivgeo` gives the values of the cumulative function.

Invalid arguments will return an error message.

## Author(s)

Ricardo P. Oliveira rpuziol.oliveira@gmail.com

Jorge Alberto Achcar achcar@fmrp.usp.br

## Source

`pbivgeo` 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.

## See Also

`Geometric` for the univariate geometric distribution.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19``` ```# If x and y are integer numbers: pbivgeo(x = 1, y = 2, theta = c(0.2, 0.4, 0.7), lower.tail = TRUE) #  0.79728 # If x is a matrix: matr <- matrix(c(1,2,3,5), ncol = 2) pbivgeo(x = matr, y = NULL, theta = c(0.2,0.4,0.7), lower.tail = TRUE) #  0.8424384 0.9787478 # If lower.tail = FALSE: pbivgeo(x = 1, y = 2, theta = c(0.2, 0.4, 0.7), lower.tail = FALSE) #  0.01568 matr <- matrix(c(1,2,3,5), ncol = 2) pbivgeo(x = matr, y = NULL, theta = c(0.9,0.4,0.7), lower.tail = FALSE) #  0.01975680 0.00139404 ```

BivGeo documentation built on May 2, 2019, 6:12 a.m.