TPXG (version 1.0)

Maximum Likelihood Estimation of TPPXG Regression Coefficients: Estimation of the TPPXG regression coefficients.

Description

This function estimates the Two Parameter Poisson Xgamma regression coefficients as well as the \(\alpha\) parameter of the Two Parameter Poisson Xgamma distribution using the maximum likelihood method.

Usage

tppxg.reg(y, x)

Value

A named list containing \(\alpha\) parameter, a vector containing the \(\beta\) coefficients and the maximum likelihood value.

Arguments

y

A numeric vector containg non-negative integer values.

x

A matrix or a data.frame with the predictor variables.

Author

Nikolaos Kontemeniotis.

R implementation and documentation: Nikolaos Kontemeniotis and Michail Tsagris .

Details

The \(\theta\) parameter has been transformed as a function of the expected value of the response variable Y in the following manner: $$ \theta=\frac{1-\alpha \mu +\sqrt{(\alpha \mu -1)^2+12\alpha \mu}}{2\mu}$$ Given that the response variable satisfies \(Y_i \sim \text{TPPXG}(\alpha, \mu_i)\), then the \(i^{\text{th}}\) mean of Y is related to the predictor variables using the log link function: $$ \mu_i=e^{x_i^T \beta} \quad i=1,2,3,\dots n $$ For more details, see the paper referenced below.

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

tppxg.mle

Examples

x <- matrix( rnorm(100 * 2), ncol = 2 )
y <- rtppxg(100)
tppxg.reg(y, x)