Ülkü Erişoğlu

Modeling Heterogeneous Survival Data Using Mixture of Extended Exponential-Geometric Distributions

In this article, we propose a mixture of extended exponential-geometric distributions to model heterogeneous survival data. Various properties of the proposed mixture of extended exponential-geometric distributions are discussed. Maximum likelihood estimations of the parameters are obtained by using the EM algorithm. Illustrative examples based on real data are also given.

A comparison of the parameter estimation methods for bimodal mixture Weibull distribution with complete data

Bimodal mixture Weibull distribution being a special case of mixture Weibull distribution has been used recently as a suitable model for heterogeneous data sets in many practical applications. The bimodal mixture Weibull term represents a mixture of two Weibull distributions. Although many estimation methods have been proposed for the bimodal mixture Weibull distribution, there is not a comprehensive comparison. This paper presents a detailed comparison of five kinds of numerical methods, such as maximum likelihood estimation, least-squares method, method of moments, method of logarithmic moments and percentile method (PM) in terms of several criteria by simulation study. Also parameter estimation methods are applied to real data.

L-Moments Estimations for Mixture of Weibull Distributions

Mixture of Weibull distributions has wide application in modeling of heterogeneous data sets. The parameter estimation is one of the most important problems related to mixture of Weibull distributions. In this paper, we propose a L-moment estimation method for mixture of two Weibull distributions. The proposed method is compared with maximum likelihood estimation (MLE) method according to the bias, the mean absolute error, the mean total error and completion time of the algorithm (time) by simulation study. Also, applications to real data sets are given to show the flexibility and potentiality of the proposed estimation method. The comparison shows that, the proposed method is better than MLE method.

Heterogeneous data modeling with two-component Weibull–Poisson distribution

The mixture distribution models are more useful than pure distributions in modeling of heterogeneous data sets. The aim of this paper is to propose mixture of Weibull–Poisson (WP) distributions to model heterogeneous data sets for the first time. So, a powerful alternative mixture distribution is created for modeling of the heterogeneous data sets. In the study, many features of the proposed mixture of WP distributions are examined. Also, the expectation maximization (EM) algorithm is used to determine the maximum-likelihood estimates of the parameters, and the simulation study is conducted for evaluating the performance of the proposed EM scheme. Applications for two real heterogeneous data sets are given to show the flexibility and potentiality of the new mixture distribution.

Effect of dimension reduction by principal component analysis on clustering

Abstract In this empirical study, our goal is to investigate the effectiveness of clustering high dimensional data using principle components (PCs) instead of original variables. Effects of PCs instead original variables on clustering of simulated data sets which have different features are investigated by two different criteria. Moreover in this study we also showed that the effectiveness of clustering high dimensional data using standardized variables instead of original variables.