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Öğe The Burr X Pareto distribution: properties, applications and VaR estimation(MDPI, 2018) Korkmaz, Mustafa Çağatay; Altun, Emrah; Yousof, Haitham M.; Afify, Ahmed Z.; Nadarajah, SaraleesIn this paper, a new three-parameter Pareto distribution is introduced and studied. We discuss various mathematical and statistical properties of the new model. Some estimation methods of the model parameters are performed. Moreover, the peaks-over-threshold method is used to estimate Value-at-Risk (VaR) by means of the proposed distribution. We compare the distribution with a few other models to show its versatility in modelling data with heavy tails. VaR estimation with the Burr X Pareto distribution is presented using time series data, and the new model could be considered as an alternative VaR model against the generalized Pareto model for financial institutions.Öğe The extended gamma distribution with regression model and applications(American Institute of Mathematical Sciences, 2021) Altun, Emrah; Korkmaz, Mustafa Çağatay; El-Morshedy, Mahmoud; Eliwa, M. S.This paper introduces a new extension of the gamma distribution, named as a new extended gamma distribution, via mixture representation of xgamma and gamma distributions. The statistical properties of the proposed distribution are derived such as moment generating and characteristic functions, variance, skewness, and kurtosis measures, Lorenz curve, and mean residual life function. The maximum likelihood, parametric bootstrap, method of moments, least squares, and weighted least squares estimation methods are considered to obtain the unknown model parameters. The finite sample performance of estimation methods is discussed via a simulation study. Using the proposed distribution, we propose a new regression model for the right-skewed response variable as an alternative to the gamma regression model. Two real data sets are analyzed to convince the readers for the usefulness of the proposed model.Öğe The hjorth's IDB generator of distributions: properties, characterizations, regression modeling and applications(Atlantis Press, 2020) Korkmaz, Mustafa Çağatay; Altun, Emrah; Yousof, Haitham M.; Hamedani, G. G.We introduce a new flexible class of continuous distributions via the Hjorth’s IDB model. We provide some mathematical prop-erties of the new family. Characterizations based on two truncated moments, conditional expectation as well as in terms of thehazard function are presented. The maximum likelihood method is used for estimating the model parameters. We assess the per-formance of the maximum likelihood estimators in terms of biases and mean squared errors by means of the simulation study.A new regression model as well as residual analysis are presented. Finally, the usefulness of the family is illustrated by means offour real data sets. The new model provides consistently better fits than other competitive models for these data sets.Öğe The log exponential-power distribution: Properties, estimations and quantile regression model(MDPI, 2021) Korkmaz, Mustafa Çağatay; Altun, Emrah; Alizadeh, Morad; El-Morshedy, MahmoudRecently, bounded distributions have attracted attention. These distributions are frequently used in modeling rate and proportion data sets. In this study, a new alternative model is proposed for modeling bounded data sets. Parameter estimations of the proposed distribution are obtained via maximum likelihood method. In addition, a new regression model is defined under the proposed distribution and its residual analysis is examined. As a result of the empirical studies on real data sets, it is observed that the proposed regression model gives better results than the unit-Weibull and Kumaraswamy regression models.Öğe A new extended g family of continuous distributions with mathematical properties, characterizations and regression modeling(Univ Punjab, 2018) Hamedani, G. G.; Altun, Emrah; Korkmaz, Mustafa Çağatay; Yousof, Haitham M.; Butt, Nadeem ShafiqueWe propose a new extended G family of distributions. Some of its structural properties are derived and some useful characterization results are presented. The maximum likelihood method is used to estimate the model parameters by means of graphical and numerical Monte Carlo simulation study. The flexibility of the new family illustrated by means of two real data sets. Moreover, we introduce a new log-location regression model based on the proposed family. The martingale and modified deviance residuals are defined to detect outliers and evaluate the model assumptions. The potentiality of the new regression model is illustrated by means of a real data set.Öğe A new flexible family of continuous distributions: the additive Odd-G family(MDPI AG, 2021) Altun, Emrah; Korkmaz, Mustafa Çağatay; El-Morshedy, Mahmoud; S. Eliwa, MohamedThis paper introduces a new family of distributions based on the additive model structure. Three submodels of the proposed family are studied in detail. Two simulation studies were performed to discuss the maximum likelihood estimators of the model parameters. The log location-scale regression model based on a new generalization of the Weibull distribution is introduced. Three datasets were used to show the importance of the proposed family. Based on the empirical results, we concluded that the proposed family is quite competitive compared to other models.Öğe A new flexible lifetime model with log-location regression modeling, properties and applications(Taru Publication, 2019) Korkmaz, Mustafa Çağatay; Altun, Emrah; Alizadeh, Morad; Yousof, Haitham M.In this paper, we propose a new lifetime model for modeling fatigue lifetime data. Some of its statistical properties are obtained. The method of maximum likelihood is used to estimate the model parameters. Simulation study is given to demonstrate the maximum likelihood estimators of the parameters of proposed model. Moreover, a new log-location-scale regression model is introduced with its residuals analysis. Three applications to real data sets are given to prove the usefulness of proposed model in real data modeling.Öğe On the Unit-Chen distribution with associated quantile regression and applications(De Gruyter Open Ltd, 2022) Korkmaz, Mustafa Çağatay; Altun, Emrah; Chesneau, Christophe; Yousof, Haitham M.In this paper, a new distribution defined on (0, 1) is introduced. It is obtained by the transformation of a positive random variable following the Chen distribution with respect to the inverted exponential function. Basic distributional properties of the newly defined distribution are studied. Then, as a statistical model, we examine different methods of estimation for related parameters. We assess the performance of the obtained estimators by a complete simulation study. Subsequently, the quantile regression model based on the proposed distribution is introduced. Applications of the proposed models to real data sets show that they have better modeling capabilities than fair competitors. © 2022 Mathematical Institute Slovak Academy of Sciences.Öğe The xgamma family: Censored regression modelling and applications(National Statistical Institute, 2020) Cordeiro, Gauss M.; Altun, Emrah; Korkmaz, Mustafa Çağatay; Pescim, Rodrigo R.; Afify, Ahmed Z.; Yousof, Haitham M.In this paper, a new family of distributions with one extra shape parameter, called the xgamma-G, is proposed. comprehensive treatment of some of its mathematical properties including ordinary and incomplete moments and quantile and generating functions are derived. The unknown model parameters are estimated by the maximum likelihood method and the performance of the maximum likelihood estimators are assessed via two extensive simulation studies. Additionally, the log-location-scale regression model for censored data based on a special member of the family is introduced. The usefulness of the proposed models is illustrated utilizing three real data sets.
