rbivgeo function

Generates Random Deviates from the Basu-Dhar Bivariate Geometric Distribution

Generates Random Deviates from the Basu-Dhar Bivariate Geometric Distribution

This function generates random values from the Basu-Dhar bivariate geometric distribution assuming arbitrary parameter values.

Source

rbivgeo1 generates random deviates using the inverse transformation method. Returns a matrix that the first column corresponds to X generated random values and the second column corresponds to Y generated random values.

rbivgeo2 generates random deviates using the shock model. Returns a matrix that the first column corresponds to X generated random values and the second column corresponds to Y generated random values. See Marshall and Olkin (1967) for more details.

rbivgeo1(n, theta)
rbivgeo2(n, theta)

Arguments

  • n: number of observations. If length(n) >1> 1, the length is taken to be the number required.
  • theta: vector (of length 3) containing values of the parameters θ1,θ2\theta_1, \theta_2 and θ3\theta_{3} of the Basu-Dhar bivariate Geometric distribution. The parameters are restricted to 0<θi<1,i=1,20 < \theta_i < 1, i = 1,2 and 0<θ3≤10 < \theta_{3} \le 1.

Returns

rbivgeo1 and rbivgeo2 generate random deviates from the Bash-Dhar bivariate geometric distribution. The length of the result is determined by n, and is the maximum of the lengths of the numerical arguments for the other functions.

Invalid arguments will return an error message.

Details

The conditional distribution of X given Y is given by:

If X < Y, then

P(X=x∣Y=y)=θ1x−1(1−θ1) P(X = x | Y = y) = \theta_1^{x - 1}(1 - \theta_1)

If X = Y, then

P(X=x∣Y=y)=θ1x−1(1−θ1θ3−θ2θ3+θ1θ2θ3)1−θ2θ3 P(X = x | Y = y) = \frac{\theta_1^{x - 1}(1 - \theta_1 \theta_{3} - \theta_2 \theta_{3} + \theta_1 \theta_2 \theta_{3})}{1 - \theta_2 \theta_{3}}

If X > Y, then

P(X=x∣Y=y)=θ1x−1θ3x−y(1−θ1θ3)(1−θ2)1−θ2θ3 P(X = x | Y = y) = \frac{\theta_1^{x - 1} \theta_{3}^{x - y}(1 - \theta_{1} \theta_{3}) (1 - \theta_2)}{1 - \theta_2 \theta_{3}}

Examples

rbivgeo1(n = 10, theta = c(0.5, 0.5, 0.7))
#       [,1] [,2]
#  [1,]    2    1
#  [2,]    3    1
#  [3,]    1    1
#  [4,]    1    1
#  [5,]    2    2
#  [6,]    1    3
#  [7,]    2    2
#  [8,]    1    1
#  [9,]    1    1
# [10,]    2    2

rbivgeo2(n = 10, theta = c(0.5, 0.5, 0.7))
#       [,1] [,2]
#  [1,]    1    1
#  [2,]    2    1
#  [3,]    2    1
#  [4,]    4    1
#  [5,]    1    1
#  [6,]    2    2
#  [7,]    3    2
#  [8,]    3    1
#  [9,]    3    2
# [10,]    1    1

References

Marshall, A. W., & Olkin, I. (1967). A multivariate exponential distribution. Journal of the American Statistical Association, 62 , 317, 30-44.

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–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.

Author(s)

Ricardo P. Oliveira rpuziol.oliveira@gmail.com

Jorge Alberto Achcar achcar@fmrp.usp.br

BivGeo packageRead PDF manual