Parameter Estimation of Incomplete Gamma Subordinators

In this paper, we estimate the parameters of InG, InG-$\epsilon$ and TInG subordinators which have been studied by Babulal $\mathit{\text{et}}\mathit{\text{al}}$ (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.