Improved maximum likelihood estimation of parameters in the Maxwell distribution

Maximum likelihood estimators are usually biased. The first order bias term of the maximum likelihood estimators can be large for a small or medium sample size, and this bias may have a significant effect on distribution performance. Different methods may be used to reduce this bias. These methods have inspired many scholars to study this field over the past years, but the use of Bartlett’s method requires the expected value of third power derivatives of the likelihood function. Consequently, because this quantity (the expected value of third power derivatives of the likelihood function) is not necessarily calculable in some distributions, in this paper we propose a new method based on algebraic approximation of the maximum likelihood estimator bias which needless the expected value of third power derivatives of the likelihood function. In addition, as an application of this method, we will consider a bias correction for estimating parameters of Maxwell distribution.