dbivgeocure {BivGeo} | R Documentation |

## Joint Probability Mass Function for the Basu-Dhar Bivariate Geometric Distribution in Presence of Cure Fraction

### Description

This function computes the joint probability mass function of the Basu-Dhar bivariate geometric distribution assuming arbitrary parameter values in presence of cure fraction.

### Usage

```
dbivgeocure(x, y, theta, phi11, log = FALSE)
```

### 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 |

`phi11` |
real number containing the value of the cure fraction incidence parameter |

`log` |
logical argument for calculating the log probability or the probability function. The default value is FALSE. |

### Details

The joint probability mass function for a random vector (`X`

, `Y`

) following a Basu-Dhar bivariate geometric distribution in presence of cure fraction could be written as:

`P(X = x, Y = y) = \phi_{11}(\theta_{1}^{x - 1} \theta_{2}^{y - 1} \theta_{3}^{z_1} - \theta_{1}^{x} \theta_{2}^{y - 1} \theta_{3}^{z_2} - \theta_{1}^{x - 1} \theta_{2}^{y} \theta_{2}^{z_3} + \theta_{1}^{x} \theta_{2}^{y} \theta_{3}^{z_4})`

where `x,y > 0`

are positive integers and `z_1 = \max(x - 1, y - 1),z_2 = \max(x, y - 1), z_3 = \max(x - 1, y), z_4 = \max(x, y)`

.

### Value

`dbivgeocure`

gives the values of the probability mass function in presence of cure fraction.

Invalid arguments will return an error message.

### Author(s)

Ricardo P. Oliveira rpuziol.oliveira@gmail.com

Jorge Alberto Achcar achcar@fmrp.usp.br

### Source

`dbivgeocure`

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.

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.

de Oliveira, R. P., Achcar, J. A., Peralta, D., & Mazucheli, J. (2018). Discrete and continuous bivariate lifetime models in presence of cure rate: a comparative study under Bayesian approach. *Journal of Applied Statistics*, 1-19.

### See Also

`Geometric`

for the univariate geometric distribution.

### Examples

```
# If log = FALSE:
dbivgeocure(x = 1, y = 2, theta = c(0.2, 0.4, 0.7), phi11 = 0.4, log = FALSE)
# [1] 0.064512
# If log = TRUE:
dbivgeocure(x = 1, y = 2, theta = c(0.2, 0.4, 0.7), phi11 = 0.4, log = TRUE)
# [1] -2.740904
```

*BivGeo*version 2.0.1 Index]