Parameter Estimation of Incomplete Gamma Subordinators

TL;DR

This paper develops parameter estimation methods for InG, InG-ε, and TInG subordinators, utilizing fractional moments and maximum likelihood estimation, and discusses their asymptotic properties.

Contribution

It introduces modified moment methods for InG and InG-ε subordinators and applies MLE to estimate parameters, including analysis of asymptotic normality.

Findings

Fractional moments enable parameter estimation for InG and InG-ε due to infinite moments.

Maximum likelihood estimation is used for the parameter α of InG and InG-ε.

Asymptotic normality of the MLE is discussed.

Abstract

In this paper, we estimate the parameters of InG, InG-$\epsilon$ and TInG subordinators which have been studied by Babulal \textit{et al} (see \cite{babulal}). We have modified the method of moments technique to use fractional moments of the InG and InG-$\epsilon$ subordinator due to their infinite moments. For the TInG subordinator's parameter estimation, we have used the method of moments. We also compute the maximum likelihood estimator(MLE) for the parameter $\alpha$ of the InG and InG-$\epsilon$ subordinators using jump distribution of the process. We also discussed the asymptotic normality of MLE.