Control charts are the most popular monitoring tools used to distinguish between special (assignable) and common causes of variation and to detect any changes in processes. The time that a control chart gives an out of control signal is not the real time of change. The actual time of the change is called the change point. Knowing the real time of the change will help and simplify finding the as...

We study maximum likelihood estimation in log-linear models under conditional Poisson sampling schemes. We derive necessary and sufficient conditions for existence of the maximum likelihood estimator (MLE) of the model parameters and investigate estimability of the natural and mean-value parameters under a nonexistent MLE. Our conditions focus on the role of sampling zeros in the observed table...

this article examines statistical inference for  where and are independent but not identically distributed pareto of the first kind (pareto (i)) random variables with same scale parameter but different shape parameters. the maximum likelihood, uniformly minimum variance unbiased and bayes estimators with gamma prior are used for this purpose. simulation studies which compare the estimators are ...

Control charts are used to detect changes in a process. Once a change is detected, knowledge of the change point would simplify the search for and identification of the special cause. Consequently, having an estimate of the process change point following a control chart signal would be useful to process analysts. Change point methods for the uncorrelated process have been studied extensively in...

In this paper, a remedial measure is first proposed to eliminate the effect of autocorrelation in phase-ІІ monitoring of autocorrelated polynomial profiles, where there is a first order autoregressive (AR(1)) relation between the error terms in each profile. Then, a control chart based on the generalized linear test (GLT) is proposed to monitor the coefficients of polynomial profiles and an R-c...

Stein’s result has transformed common belief in statistical world that the maximum likelihood estimator, which is in common use for more than a century, is optimal. Charles Stein showed in 1955 that it is possible to uniformly improve the maximum likelihood estimator (MLE) for the Gaussian model in terms of total squared error risk when several parameters are estimated simultaneously from indep...

In this paper a Maximum Likelihood Estimator is derived in the Generalized Linear Model-based regression profiles under the monotonic change in Phase II. The performance of proposed estimator is comprehensively investigated through some special cases and compared to estimators under step change and drift. The results show that the proposed estimator has better performance in small and medium sh...

For the regression parameter β0 in the Cox model, there have been several estimators constructed based on various types of approximated likelihood, but none of them has demonstrated small-sample advantage over Cox’s partial likelihood estimator. In this article, we derive the full likelihood function for (β0, F0), where F0 is the baseline distribution in the Cox model. Using the empirical likel...

Diffusion models have been used extensively in many applications. These models, such as those used in the financial engineering, usually contain unknown parameters which we wish to determine. One way is to use the maximum likelihood method with discrete samplings to devise statistics for unknown parameters. In general, the maximum likelihood functions for diffusion models are not available, hen...

It is well known that the normal mixture with unequal variance has unbounded likelihood and thus the corresponding global maximum likelihood estimator (MLE) is undefined. One of the commonly used solutions is to put a constraint on the parameter space so that the likelihood is bounded and then one can run the EM algorithm on this constrained parameter space to find the constrained global MLE. H...