tppxg.reg: Estimation of the TPPXG regression coefficients.

In TPXG: Two Parameter Xgamma & Poisson Xgamma: Regression & Distribution Functions

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)

Arguments

y	A numeric vector containg non-negative integer values.
x	A matrix or a data.frame with the predictor variables.

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.

Value

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

Author(s)

Nikolaos Kontemeniotis.

R implementation and documentation: Nikolaos Kontemeniotis [e-mail] and Michail Tsagris [e-mail].

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)

TPXG documentation built on April 3, 2025, 10:37 p.m.