TPXG (version 1.0)

Maximum Likelihood Estimation of TPPXG Distribution: Maximum likelihood estimation of the TPPXG distribution parameters.

Description

Estimation of \(\alpha\) and \(\theta\) parameters of Two Parameter Poisson Xgamma distribution using maximum likelihood.

Usage

tppxg.mle(x)

Value

A named numeric vector containing the estimated values for \(\alpha\), \(\theta\) and maximum likelihood.

Arguments

x

A numeric vector containg non-negative integer values.

Author

Nikolaos Kontemeniotis.

R implementation and documentation: Nikolaos Kontemeniotis and Michail Tsagris .

Details

The log-likelihood function of the TPPXG distribution is given by: $$ \ln L(\alpha,\theta)=2n\ln \theta-n\ln(\alpha+\theta)-\left(3n+\sum_{i=1}^n x_i\right)\ln(1+\theta)+ \sum_{i=1}^n\ln \left((1+\theta)^2+\frac{\alpha \theta}{2}(x_i+1)(x_i+2)\right) $$

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.reg

Examples

x <- rtppxg(1000)
tppxg.mle(x)