This function computes the joint probability mass function of the Basu-Dhar bivariate geometric distribution assuming arbitrary parameter values in presence of cure fraction.
dbivgeocure(x, y, theta, phi11, log = FALSE)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.
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.
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 \(0 < \theta_{3} \le 1\).
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.
logical argument for calculating the log probability or the probability function. The default value is FALSE.
dbivgeocure gives the values of the probability mass function in presence of cure fraction.
Invalid arguments will return an error message.
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 \(z_1 = \max(x - 1, y - 1),z_2 = \max(x, y - 1), z_3 = \max(x - 1, y), z_4 = \max(x, y)\).
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<U+2013>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.
Geometric for the univariate geometric distribution.
# NOT RUN {
# 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
# }
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