A Study on The Mixture of Exponentiated-Weibull Distribution PART I (The Method of Maximum Likelihood Estimation) (Published)
Mixtures of measures or distributions occur frequently in the theory and applications of probability and statistics. In the simplest case it may, for example, be reasonable to assume that one is dealing with the mixture in given proportions of a finite number of normal populations with different means or variances. The mixture parameter may also be denumerable infinite, as in the theory of sums of a random number of random variables, or continuous, as in the compound Poisson distribution. The use of finite mixture distributions, to control for unobserved heterogeneity, has become increasingly popular among those estimating dynamic discrete choice models. One of the barriers to using mixture models is that parameters that could previously be estimated in stages must now be estimated jointly: using mixture distributions destroys any additive reparability of the log likelihood function. In this thesis, the maximum likelihood estimators have been obtained for the parameters of the mixture of exponentiated Weibull distribution when sample is available from censoring scheme.The maximum likelihood estimators of the parameters and the asymptotic variance covariance matrix have been obtained. A numerical illustration for these new results is given.
Keywords: Exponentiated Weibull Distributiom (EW), Maximum Likelihood Estimation, Mixture Distribution, Mixture of two Exponentiated Weibull Distribution(MTEW), Moment Estimation, Monte-Carlo Simulation
The observed data from various fields are frequently characterized by measurement error and this has been challenging problem to construct consistent estimators of the parameters in a nonlinear regression model.This study uses simulated data under three (3) sample sizes (i.e 32,256 and 1024) applying Kernel, Wavelet and Polynomial Spline on noisy data in two approaches (i.e denoising only the explanatory variables and denoising both dependent and explanatory variables). The study reveals the performance of denoised nonlinear estimators under different sample sizes for each denoising approach and comparison was made using the mean squared error criterion. The result of the studies shows that the denoised nonlinear least squares estimator (DNLS) is the best under each sample size considered.
PARAMETERS ESTIMATION FOR THE RAYLEIGH DISTRIBUTION BASED ON A SIMPLE STEP-STRESSES MODEL WITH TYPE-II HYBRID CENSORED DATA (Published)
In this paper, we consider a simple step-Stress model under the Rayleigh distribution when the available data are type-II hybrid censored. The maximum likelihood and Bayes estimators as well as, approximate confidence intervals for the parameters are constructed. Bayes estimators are obtained using the symmetric squared error loss functions and asymmetric LINEX and General Entropy (GE) loss functions using non informative priors, a numerical illustration for these new results are also given.MSC: Primary 62N05; 62N01: secondary 62F40; 62F30.
Keywords: Accelerated life testing, Monte-Carlo Simulation, Non-informative prior, Rayleigh distribution, Symmetric and Asymmetries loss function, cumulative exposure model, hybrid censored samples, maximum likelihood estimation(MLE), step stress model, type.