Emrah Altun

The generalized odd log-logistic family of distributions: properties, regression models and applications

ABSTRACT We propose a new class of continuous distributions with two extra shape parameters named the generalized odd log-logistic family of distributions. The proposed family contains as special cases the proportional reversed hazard rate and odd log-logistic classes. Its density function can be expressed as a linear combination of exponentiated densities based on the same baseline distribution. Some of its mathematical properties including ordinary moments, quantile and generating functions, two entropy measures and order statistics are obtained. We derive a power series for the quantile function. We discuss the method of maximum likelihood to estimate the model parameters. We study the behaviour of the estimators by means of Monte Carlo simulations. We introduce the log-odd log-logistic Weibull regression model with censored data based on the odd log-logistic-Weibull distribution. The importance of the new family is illustrated using three real data sets. These applications indicate that this family can provide better fits than other well-known classes of distributions. The beauty and importance of the proposed family lies in its ability to model different types of real data.

The odd log-logistic Marshall-Olkin power Lindley Distribution: Properties and applications

Abstract In this paper, we introduce a new extension of the power Lindley distribution, called the odd log-logistic Marshall-Olkin power Lindley distribution. We discuss some of its properties such as the shapes of the density, hazard rate functions, quantile function, mixture representation, moments, and order statistics. We also obtain the estimators of the parameters through maximum likelihood approach. A simulation study is performed to evaluate the performance of the maximum likelihood estimators. Finally, two real data sets are applied to illustrating of the usefulness of the new model and to comparing the fit of the new distribution with those attained by some other extensions of the Lindley and power Lindley distributions.

A new family of distributions with properties, regression models and applications

Abstract In this study, we introduce a new family of continuous distributions with one extra shape parameter, called the Burr-Hatke-G family, based on the Burr-Hatke differential equation. Some of its mathematical properties are derived. The maximum likelihood method is used to estimate the model parameters. Moreover, the log-Burr-Hatke-Weibull regression model based on new the generated family is introduced. The usefulness of the proposed family is demonstrated by means of the three real data applications. Empirical results indicate that the proposed family provides more realistic fits than other well-known family of distributions.

The odd power cauchy family of distributions: properties, regression models and applications

ABSTRACT We study some mathematical properties of a new generator of continuous distributions with one extra parameter called the odd power Cauchy family including asymptotics, linear representation, moments, quantile and generating functions, entropies, order statistics and extreme values. We introduce two bivariate extensions of the new family. The maximum likelihood method is discussed to estimate the model parameters by means of a Monte Carlo simulation study. We define a new log-odd power Cauchy–Weibull regression model. The usefulness of the proposed models is proved empirically by means of three real data sets.

A new generalization of skew-T distribution with volatility models

ABSTRACT In this paper, we propose a new generalized alpha-skew-T (GAST) distribution for generalized autoregressive conditional heteroskedasticity (GARCH) models in modelling daily Value-at-Risk (VaR). Some mathematical properties of the proposed distribution are derived including density function, moments and stochastic representation. The maximum likelihood estimation method is discussed to estimate parameters via a simulation study. Then, the real data application on S&P-500 index is performed to investigate the performance of GARCH models specified under GAST innovation distribution with respect to normal, Students-t and Skew-T models in terms of the VaR accuracy. Backtesting methodology is used to compare the out-of-sample performance of the VaR models. The results show that GARCH models with GAST innovation distribution outperforms among others and generates the most conservative VaR forecasts for all confidence levels and for both long and short positions.

A New Log-location Regression Model with Influence Diagnostics and Residual Analysis

A new four-parameter lifetime model called Odd Log-Logistic Burr XII distribution, is defined and investigated. Some of its mathematical properties are derived. Some useful characterization results based on \ the ratio of two truncated moments, based on the hazard function as well as on the conditional expectation of certain functions of the random variable are presented. The maximum likelihood method is used to estimate the model parameters by means of a graphical Monte Carlo simulation study. Moreover, we introduce a new log-location regression model based on the proposed distribution. The Jackknife estimation method as an alternative method is used to estimate the unknown parameters of new regression model. The generalized cook distance and likelihood distance measures are used to detect the possible influential observations. 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.

A new lifetime model with regression models, characterizations and applications

ABSTRACT In this article, we introduce a new extension of Burr XII distribution called Topp Leone Generated Burr XII distribution. We derive some of its properties. Useful characterizations are presented. Simulation study is performed to assess the performance of the maximum likelihood estimators. Censored maximum likelihood estimation is presented in the general case of multi-censored data. The new location-scale regression model based on the proposed distribution is introduced. The usefulness of the proposed models is illustrated empirically by means of three real datasets.