In this paper we derive second and third order bias-corrected maximum likelihood estimates in general uniparametric models. We compare the corrected estimates and the usual maximum likelihood estimate in terms of their mean squared errors. We also obtain closed-form expressions for bias-corrected estimates in one-parameter exponential family models. Our results cover many important and commonly...

The heavy tailed distributions have mostly been used for modeling the financial data. The kappa distribution has higher peak and heavier tail than the normal distribution. In this paper, we consider the estimation of the three unknown parameters of a Kappa distribution for evaluating the value at risk measure. The value at risk (VaR) as a quantile of a distribution is one of the import...