The Hawks process is a point with self-exciting property. It has been used to model earthquakes, social media events, infections, etc., and getting lot of attention. However, as real problem, there are often situations where we can not obtain data sufficient observation time. In such cases, it appropriate approximate the error distribution an estimator by normal distribution. To overcome this p...

The paper studies the properties of a sequential maximum likelihood estimator of the drift parameter in a one dimensional reflected Ornstein-Uhlenbeck process. We observe the process until the observed Fisher information reaches a specified precision level. We derive the explicit formulas for the sequential estimator and its mean squared error. The estimator is shown to be unbiased and uniforml...

In this paper, we present that how much the variances of the classical estimators, namely, maximum likelihood estimator and moment estimator deviate from the minimum variance bound while estimating for the Maxwell distribution. We also sketch this difference for the negative integer moment estimator. We note the poor performance of the negative integer moment estimator in the said consideration...

In a finite mixture of location-scale distributions maximum likelihood estimator does not exist because of the unboundedness of the likelihood function when the scale parameter of some mixture component approaches zero. In order to study the strong consistency of maximum likelihood estimator, we consider the case that the scale parameters of the component distributions are restricted from below...

In finite mixture of location-scale distributions maximum likelihood estimator does not exist because of the unboundedness of the likelihood function when the scale parameter of some mixture component approaches zero. In order to study the strong consistency of maximum likelihood estimator, we consider the case that the scale parameters of the component distributions are restricted from below b...

The finite mixture of normal distributions in both mean and variance parameters have wide applications. It is well known that the likelihood function of this model is unbounded for any given sample size. Hence, the ordinary maximum likelihood estimator is not consistent. At the same time, a local maximum of the likelihood function can often be found to have good statistical properties. In this ...

The paper proposes a new non-parametric density estimator from region-censored observations with application in the context of population studies, where standard maximum likelihood is affected by over-fitting and non-uniqueness problems. It is a maximum entropy estimator that satisfies a set of constraints imposing a close fit to the empirical distributions associated with the set of censoring ...

The Maximum Likelihood Estimator (MLE) and Extended Quasi-Likelihood (EQL) estimator have commonly been used to estimate the unknown parameters within the joint modeling of mean and dispersion framework. However, these estimators can be very sensitive to outliers in the data. In order to overcome this disadvantage, the usage of the maximum Trimmed Likelihood Estimator (TLE) and the maximum Exte...