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Parameter Estimation of Incomplete Gamma Subordinators

Meena Sanjay Babulal, Sunil Kumar Gauttam, Aditya Maheshwari

Abstract

In this paper, we estimate the parameters of InG, InG-$ε$ 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-$ε$ 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 $α$ of the InG and InG-$ε$ subordinators using jump distribution of the process. We also discussed the asymptotic normality of MLE.

Parameter Estimation of Incomplete Gamma Subordinators

Abstract

In this paper, we estimate the parameters of InG, InG- 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- 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 of the InG and InG- subordinators using jump distribution of the process. We also discussed the asymptotic normality of MLE.

Paper Structure

This paper contains 6 sections, 32 equations.

Table of Contents

  1. Introduction
  2. preliminaries
  3. Maximum likelihood estimation
  4. Asymptotic normality of MLE
  5. Method of moments Estimation
  6. $\mathbf{Acknowledgment}$

Theorems & Definitions (1)

  • Definition 4.1