Mustafa Ç. Korkmaz

A new generalized two-sided class of distributions with an emphasis on two-sided generalized normal distribution

ABSTRACT The ordinary-G class of distributions is defined to have the cumulative distribution function (cdf) as the value of the cdf of the ordinary distribution F whose range is the unit interval at G, that is, F(G), and it generalizes the ordinary distribution. In this work, we consider the standard two-sided power distribution to define other classes like the beta-G and the Kumaraswamy-G classes. We extend the idea of two-sidedness to other ordinary distributions like normal. After studying the basic properties of the new class in general setting, we consider the two-sided generalized normal distribution with maximum likelihood estimation procedure.

Two-Sided Generalized Exponential Distribution

We derive a generalization of the exponential distribution by making log transformation of the standard two-sided power distribution. We show that this new generalization is in fact a mixture of a truncated exponential distribution and truncated generalized exponential distribution introduced by Gupta and Kundu [Generalized exponential distributions. Aust. N. Z. J. Stat. 41(1999):173–188]. The newly defined distribution is more flexible for modeling data than the ordinary exponential distribution. We study its properties, estimate the parameters, and demonstrate it on some well-known real data sets comparing other existing methods.

The Exponential Lindley Odd Log-Logistic-G Family: Properties, Characterizations and Applications

A new family of distributions called the exponential Lindley odd log-logistic G family is introduced and studied. The new generator generalizes three newly defined G families and also defines two new G families. We provide some mathematical properties of the new family. Characterizations based on truncated moments as well as in terms of the hazard function are presented. The maximum likelihood is used for estimating the model parameters. We assess the performance of the maximum likelihood estimators in terms of biases and mean squared errors by means of a simulation study. Finally, the usefulness of the family is illustrated by means of three real data sets. The new model provides consistently better fits than other competitive models for these data sets.

The Weibull Marshall–Olkin family: Regression model and application to censored data

Abstract We introduce a new class of distributions called the Weibull Marshall–Olkin-G family. We obtain some of its mathematical properties. The special models of this family provide bathtub-shaped, decreasing-increasing, increasing-decreasing-increasing, decreasing-increasing-decreasing, monotone, unimodal and bimodal hazard functions. The maximum likelihood method is adopted for estimating the model parameters. We assess the performance of the maximum likelihood estimators by means of two simulation studies. We also propose a new family of linear regression models for censored and uncensored data. The flexibility and importance of the proposed models are illustrated by means of three real data sets.

A Generalized Skew Slash Distribution via Gamma-normal Distribution

ABSTRACT In this article, we introduce a generalization of the slash distribution via the gamma-normal distribution. We define the new slash distribution by relation of a gamma-normal random variable with respect to a power of a uniform random variable. The newly defined distribution generalizes the slash distribution and is more flexible in terms of its kurtosis and skewness than the slash distribution. Basic properties of the new distribution are studied. We derive the maximum likelihood estimators of its parameters and apply the distribution to a real dataset.