A Bimodal Extension of the Generalized Gamma Distribution

A bimodal extension of the generalized gamma distribution is proposed by using a mixing approach. Some distributional properties of the new distribution are investigated. The maximum likelihood (ML) estimators for the parameters of the new distribution are obtained. Real data examples are given to show the strength of the new distribution for modeling data.Una extensión bimodal de la distribución gamma generalizada es propuesta a través de un enfoque de mixturas. Algunas propiedades de la nueva distribución son investigadas. Los estimadores máximo verosímiles (ML por sus siglas en inglés) de los parámetros de la nueva distribución son obtenidos. Algunos ejemplos con datos reales son utilizados con el fin de mostrar las fortalezas de la nueva distribución en la modelación de datos

Parameter estimation for mixtures of skew Laplace normal distributions and application in mixture regression modeling

arslan, olcay/0000-0002-7067-4997; dogru, fatma zehra/0000-0001-8220-2375WOS: 000415766400036In this article, we propose mixtures of skew Laplace normal (SLN) distributions to model both skewness and heavy-tailedness in the neous data set as an alternative to mixtures of skew Student-t-normal (STN) distributions. We give the expectation-maximization (EM) algorithm to obtain the maximum likelihood (ML) estimators for the parameters of interest. We also analyze the mixture regression model based on the SLN distribution and provide the ML estimators of the parameters using the EM algorithm. The performance of the proposed mixture model is illustrated by a simulation study and two real data examples

Robust mixture regression modeling using the least trimmed squares (LTS)-estimation method

dogru, fatma zehra/0000-0001-8220-2375; arslan, olcay/0000-0002-7067-4997WOS: 000438753900020Mixture regression models are used to investigate the relationship between variables that come from unknown latent groups and to model heterogenous datasets. In general, the error terms are assumed to be normal in the mixture regression model. However, the estimators under normality assumption are sensitive to the outliers. In this article, we introduce a robust mixture regression procedure based on the LTS-estimation method to combat with the outliers in the data. We give a simulation study and a real data example to illustrate the performance of the proposed estimators over the counterparts in terms of dealing with outliers

Heteroscedastic and heavy-tailed regression with mixtures of skew Laplace normal distributions

arslan, olcay/0000-0002-7067-4997; dogru, fatma zehra/0000-0001-8220-2375; Yu, Keming/0000-0001-6341-8402WOS: 000483398600001Joint modelling skewness and heterogeneity is challenging in data analysis, particularly in regression analysis which allows a random probability distribution to change flexibly with covariates. This paper, based on a skew Laplace normal (SLN) mixture of location, scale, and skewness, introduces a new regression model which provides a flexible modelling of location, scale and skewness parameters simultaneously. The maximum likelihood (ML) estimators of all parameters of the proposed model via the expectation-maximization (EM) algorithm as well as their asymptotic properties are derived. Numerical analyses via a simulation study and a real data example are used to illustrate the performance of the proposed model.'The Scientific and Technological Research Council of Turkey (TUBITAK)' as part of '2219-International Postdoctoral Research Scholarship Programme' [1059B191700233]This study is supported by 'The Scientific and Technological Research Council of Turkey (TUBITAK)' (grant number 1059B191700233) as part of '2219-International Postdoctoral Research Scholarship Programme'

Doubly reweighted estimators for the parameters of the multivariate t-distribution

BULUT, Y. Murat/0000-0002-0545-7339; arslan, olcay/0000-0002-7067-4997; dogru, fatma zehra/0000-0001-8220-2375WOS: 000444437300008The t-distribution (univariate and multivariate) has many useful applications in robust statistical analysis. The parameter estimation of the t-distribution is carried out using maximum likelihood (ML) estimation method, and the ML estimates are obtained via the Expectation-Maximization (EM) algorithm. In this article, we will use the maximum Lq-likelihood (MLq) estimation method introduced by Ferrari and Yang (2010) to estimate all the parameters of the multivariate t-distribution. We modify the EM algorithm to obtain the MLq estimates. We provide a simulation study and a real data example to illustrate the performance of the MLq estimators over the ML estimators

Optimal B-Robust Estimators For the Parameters of the Generalized Half-Normal Distribution

arslan, olcay/0000-0002-7067-4997; dogru, fatma zehra/0000-0001-8220-2375; BULUT, Y. Murat/0000-0002-0545-7339WOS: 000407456900008The purpose of this study is to propose robust estimators by using optimal B-robust (OBR) estimation method (Hampel et al. [5]) for the parameters of the generalized half-normal (GHN) distribution. After given the robust estimators, we provide a small simulation study to compare its performance with the estimators obtained from maximum likelihood (ML) estimation method. We also give a real data example to illustrate the performance of the proposed estimators

Finite Mixtures of Matrix Variate t Distributions

BULUT, Y. Murat/0000-0002-0545-7339; dogru, fatma zehra/0000-0001-8220-2375; arslan, olcay/0000-0002-7067-4997WOS: 000378738800014Finite mixtures of multivariate t distributions (Peel and McLachlan (2000)) were introduced as an alternative to the finite mixtures of multivariate normal distributions to model data sets with heavy tails. In this study, we define the finite mixtures of matrix variate t distributions as an extension of finite mixtures of multivariate t distributions. Mixtures of matrix variate t distributions can provide an alternative robust model to the mixtures of matrix variate normal distributions (Viroli (2011)) for modeling matrix variate data sets with heavy tails. We give an Expectation Maximization (EM) algorithm to find the maximum likelihood (ML) estimators for the parameters of interest. We also provide a small simulation study to illustrate the performance of the proposed EM algorithm for finding estimates

The generalized half-t distribution

dogru, fatma zehra/0000-0001-8220-2375; dogru, fatma zehra/0000-0001-8220-2375; BULUT, Y. Murat/0000-0002-0545-7339; arslan, olcay/0000-0002-7067-4997;WOS: 000402401300014In this paper, we introduce a new distribution as a scale mixture of the generalized half normal (GHN) distribution proposed by [3] and the generalized gamma (GG) distribution. Since the half-t (HT) distribution given in [10] is a special case of the new distribution, we call the new distribution as "generalized half-t (GHT)" distribution. We derive the probability density function (pdf) of the GHT distribution and study some of its properties. We give maximum likelihood (ML) estimators for its parameters based on the Expectation-Maximization (EM) algorithm. We provide a small simulation study to show the performances of the ML estimators for GHT distribution. Also, we give a real data example to illustrate the modeling performance of the proposed distribution over the GHN and HT distributions

Assessment of the New 2012 EULAR/ACR Clinical Classification Criteria for Polymyalgia Rheumatica: A Prospective Multicenter Study

WOS: 000380854200011PubMed ID: 26834222Objective. To assess the performance of the new 2012 provisional European League Against Rheumatism (EULAR)/ American College of Rheumatology (ACR) polymyalgia rheumatica (PMR) clinical classification criteria in discriminating PMR from other mimicking conditions compared with the previous 5 diagnostic criteria in a multicenter prospective study. Methods. Patients older than 50 years, presenting with new-onset bilateral shoulder pain with elevated acute-phase reactants (APR), were assessed for the fulfillment of the new and old classification/diagnostic criteria sets for PMR. At the end of the 1-year followup, 133 patients were diagnosed with PMR (expert opinion) and 142 with non-PMR conditions [69 rheumatoid arthritis (RA)]. Discriminating capacity, sensitivity, and specificity of the criteria sets were estimated. Results. Discriminating capacity of the new clinical criteria for PMR from non-PMR conditions and RA as estimated by area under the curve (AUC) were good with AUC of 0.736 and 0.781, respectively. The new criteria had a sensitivity of 89.5% and a specificity of 57.7% when tested against all non-PMR cases. When tested against all RA, seropositive RA, seronegative RA, and non-RA control patients, specificity changed to 66.7%, 100%, 20.7%, and 49.3%, respectively. Except for the Bird criteria, the 4 previous criteria had lower sensitivity and higher specificity (ranging from 83%-93%) compared with the new clinical criteria in discriminating PMR from all other controls. Conclusion. The new 2012 EULAR/ ACR clinical classification criteria for PMR is highly sensitive; however, its ability to discriminate PMR from other inflammatory/noninflammatory shoulder conditions, especially from seronegative RA, is not adequate. Imaging and other modifications such as cutoff values for APR might increase the specificity of the criteria