Probability Mass Function of the TPPXG Distribution {TPXG} | R Documentation |
Probability Mass Function of the TPPXG Distribution
Description
Computes the probability mass function of the Two Parameter Poisson Xgamma distribution for a given set of non-negative integer values.
Usage
dtppxg(x, alpha = 1, theta = 1)
Arguments
x |
A numeric vector containing non-negative integer values. |
alpha |
A positive real number. |
theta |
A positive real number. |
Details
Assume a random variable X follows the two-parameter Poisson-Xgamma distribution, which has the following stochastic representation:
X|\lambda \sim \text{Poisson}(\lambda)
\lambda|\alpha,\theta \sim \text{TPXG}(\alpha,\theta)
Then the probability mass function of X is given by:
P(X=x)=\frac{\theta^2}{(\alpha+\theta)(1+\theta)^{x+3}}
\left\{(1+\theta)^2+\frac{\alpha \theta}{2}(x+1)(x+2)\right\}; x = 0, 1, 2, 3, \dots
Value
A numeric vector containing the probability mass function value of the TPPXG distribution for each of the given values of x.
Author(s)
Nikolaos Kontemeniotis.
R implementation and documentation: Nikolaos Kontemeniotis kontemeniotisn@gmail.com and Michail Tsagris mtsagris@uoc.gr.
References
"Wani, M. A., Ahmad, P. B., Para, B. A. and Elah, N. (2023). A new regression model for count data with applications to health care data. International Journal of Data Science and Analytics."
See Also
Examples
x <- rtppxg(100)
dtppxg(x, 1, 1)