TPXG (version 1.0)

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

Description

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

Usage

tpxg.mle(x)

Value

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

Arguments

x

A numeric vector containg strictly positive values.

Author

Nikolaos Kontemeniotis.

R implementation and documentation: Nikolaos Kontemeniotis and Michail Tsagris .

Details

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

References

"Sen, S., Chandra, N. and Maiti, S. S. (2018). On properties and applications of a two-parameter XGamma distribution. Journal of Statistical Theory and Applications, 17(4): 674--685."

See Also

tpxg.reg

Examples

x <- rtpxg(1000)
tpxg.mle(x)