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 ...

The Liu estimator has consistently been demonstrated to be an attractive shrinkage method for reducing the effects of multicollinearity. The Poisson regression model is a well-known model in applications when the response variable consists of count data. However, it is known that multicollinearity negatively affects the variance of the maximum likelihood estimator (MLE) of the Poisson regressio...

identification of a real time of a change in a process, when an out-of-control signal is present is significant. this may reduce costs of defective products as well as the time of exploring and fixing the cause of defects. another popular topic in the statistical process control (spc) is profile monitoring, where knowing the distribution of one or more quality characteristics may not be appropr...

The maximum likelihood estimator of the Weibull shape parameter can be very biased. An estimator based on the modified profile likelihood is proposed and its properties are studied. It is shown that the new estimator is almost unbiased with relative bias being less than 1% in most of situations, and it is much more efficient than the regular MLE. The smaller the sample or the heavier of the cen...

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...

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...

Assuming a first-order auto-regressive model for the auto-correlation structure between observations, in this paper, a transformation method is first employed to eliminate the effect of auto-correlation. Then, a maximum likelihood estimator (MLE) of a step change in the parameters of the transformed model is derived and three separate EWMA control charts are used to monitor the parameters of th...

In optical coherence tomography (OCT), unbiased and low variance Doppler frequency estimators are desirable for blood velocity estimation. Hardware improvements in OCT mean that ever higher acquisition rates are possible. However, it is known that the Kasai autocorrelation estimator, unexpectedly, performs worse as acquisition rates increase. Here we suggest that maximum likelihood estimators (...

♦ parameter space-Ω = {all θ} ♦ estimator-a random variable (or vector) ♦ estimate-a value (vector) derived from a realization ♦ (log)-likelihood function-n i=1 f (x i ; θ). ♦ maximum likelihood estimator (estimate)[mle]) is called an unbiased estimator of θ. Otherwise, it is said to be biased. ♦ parameter estimation by method of moments. Example 1: mle for the mean and variance of a random sam...

We study a class of quadratic stochastic programs where the distribution of random variables has unknown parameters. A traditional approach is to estimate the parameters using a maximum likelihood estimator (MLE) and to use this as input in the optimization problem. For the unconstrained case, we show that an estimator that shrinks the MLE towards an arbitrary vector yields a uniformly better r...