Maximum Likelihood Estimation of Translation Parameter of Truncated Distribution II

Abstract

Let $f$ be a density which vanishes for negative values of its argument and varies regularly with exponent $\alpha - 1$ at zero, where $1 < \alpha < 2$. Further, let $f_\theta$ denote $f$ translated by $\theta$. We find and study the asymptotic distribution of the MLE $\hat{\theta}_n$ based on a sample size $n$ as $n \rightarrow \infty$.