TPXG (version 1.0)

Probability Mass Function of the TPPXG Distribution: 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)

Value

A numeric vector containing the probability mass function value of the TPPXG distribution for each of the given values of x.

Arguments

x

A numeric vector containing non-negative integer values.

alpha

A positive real number.

theta

A positive real number.

Author

Nikolaos Kontemeniotis.

R implementation and documentation: Nikolaos Kontemeniotis and Michail Tsagris .

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: $$ P(X=x)=\frac{\theta^2}{(\alpha+\theta)(1+\theta)^{x+3}} \left\{(1+\theta)^2+\frac{\alpha \theta}{2}(x+1)(x+2)\right\}; x = 0, 1, 2, 3, \dots $$

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

ptppxg,qtppxg,rtppxg

Examples

x <- rtppxg(100)
dtppxg(x, 1, 1)