maximum likelihood estimator

This study focuses on estimating the stress-strength parameter R‎, ‎utilizing two independent Type-I progressively hybrid censored samples derived from populations governed by the proportional hazard rate model‎. ‎The maximum likelihood and Bayes estimators are obtained under some well-known loss functions and the assumption that the priors are independently gamma-distributed‎. ‎The asymptotic confidence interval and Bayesian and highest posterior density credible intervals are also presented‎. ‎A Monte Carlo simulation study is used to evaluate the performances of the obtained point estimators and confidence and credible intervals‎. ‎Finally‎, ‎a pair of real data sets is analyzed for illustrative purposes.

In this paper‎, ‎the problem of inferencing the stress-strength reliability under the ranked set sampling and the simple random sampling from the levy distribution function is investigated‎. ‎The maximum likelihood estimators‎, ‎their asymptotic distributions‎, ‎and Bayes estimators are provided for the stress-strength reliability parameter‎. ‎Furthermore‎, ‎using a Monte Carlo simulation‎, ‎for both sampling methods‎, ‎namely‎, ‎simple random sampling and ranked set sampling‎, ‎the Bayes risk estimators and the efficiency of the obtained estimators are computed and compared.

This paper considers parameter estimations in Lomax distribution under progressive type-II censoring with random removals, assuming that the number of units removed at each failure time has a binomial distribution. The maximum likelihood estimators (MLEs) are derived using the expectation-maximization (EM) algorithm. The Bayes estimates of the parameters are obtained using both the squared error and the asymmetric loss functions based on the Lindley approximation. We compare the performance of our procedures using a simulation study and real data.

The article addresses different estimators of the probability density function and the cumulative distribution function for the two-parameter exponential distribution for type-II censored sample. Following estimation methods are considered: maximum likelihood estimator, uniformly minimum variance unbiased estimator and plug-in uniformly minimum variance unbiased estimator. Analysis of real data sets are performed to compare the performances of the proposed methods of estimation. The maximum likelihood estimators of the PDF and the CDF are performing better in mean squared error sense. In case of unknown location and known scale parameter, plug-in uniformly minimum variance unbiased estimator is performing better.

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.

In this paper we focus on two topics. Firstly, we propose $U$-statistics for the Weibull distribution parameters. The consistency and asymptotically normality of the introduced $U$-statistics are proved theoretically and by simulations. Several of methods have been proposed for estimating the parameters of Weibull distribution in the literature. These methods include: the generalized least square type 1, the generalized least square type 2, the $L$-moments, the Logarithmic moments, the maximum likelihood estimation, the method of moments, the percentile method, the weighted least square, and weighted maximum likelihood estimation. Secondly, due to lack of a comprehensive comparison between the Weibull distribution parameters estimators, a comprehensive comparison study is made between our proposed $U$-statistics and above nine estimators. In our knowledge, this work is the most comprehensive comparison study for the estimators for the Weibull distribution. Based on simulations, it turns out that different estimators may appeal for different range of the parameters. So, practitioners are allowed to chose the best estimator that is suggested by the goodness-of-fit criteria.

In this article, we study parameter estimation of the logarithmic series distribution. A well-known method of estimation is the maximum likelihood estimate (MLE) and this method for this distribution resulted in a biased estimator for the small sample size datasets. The goal here is to reduce the bias and root mean square error of MLE of the unknown parameter. Employing the Cox and Snell method, a closed-form expression for the bias-reduction of the maximum likelihood estimator of the parameter is obtained. Moreover, the parametric Bootstrap bias correction of the maximum likelihood estimator is studied. The performance of the proposed estimators is investigated via Monte Carlo simulation studies. The numerical results show that the analytical bias-corrected estimator performs better than bootstrapped-based estimator and MLE for small sample sizes. Also, certain useful characterizations of this distribution are presented. An example via a real dataset is presented for the illustrative purposes.

This paper considers a first-order autoregressive model   with skew-normal innovations from a parametric point of view.   We develop an essential theory for computing the maximum likelihood estimation of model parameters via   an Expectation- Maximization (EM) algorithm.  Also, a Bayesian  method  is   proposed to estimate  the unknown parameters of the model.   The efficiency  and applicability  of the proposed model are   assessed  via  a simulation study and a real-world example.

In this paper, we study the performance of estimators of parametersof two-parameter exponential distribution based on upper records.The generalized likelihood ratio (GLR) test was used to generate preliminary test estimator (PTE) for both parameters. We have compared the proposed estimator with maximum likelihood (ML) and unbiased estimators (UE) under mean-squared error (MSE) and Pitman measure of closeness (PMC). Analytical as well as graphical methods are used to show the range of parameter in which PTE performs better than ML and UE. Results demonstrate that in the case of that prior information is not too far from its real value, the PTE is superior in compare with ML and UE based on both MSE and PMC criteria. The results of the paper will be useful in estimation with record data in life testing experiments.