dbivgeocure {BivGeo}

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 \theta_1, \theta_2 and \theta_{3} of the Basu-Dhar bivariate Geometric distribution. The parameters are restricted to 0 < \theta_i < 1, i = 1,2 and 0 < \theta_{3} \le 1.

phi11

real number containing the value of the cure fraction incidence parameter \phi_{11} restricted to 0 < \phi_{11} < 1 and \phi_{11} + \phi_{10} + \phi_{01} + \phi_{00}= 1 where \phi_{10}, \phi_{01} and \phi_{00} are the complementary cure fraction incidence parameters for the joint cdf and sf functions.

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 [e-mail]

Jorge Alberto Achcar [e-mail]

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). 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.

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