The transmuted odd log-logistic-G family of distributions

International Journal of Statistical Distributions and Applications, 2019

In this article we transmute the half logistic distribution using quadratic rank transmutation map to develop a transmuted half logistic distribution. The quadratic rank transmutation map enables the introduction of extra parameter into its baseline distribution to enhance more flexibility in the analysis of data in various disciplines such as reliability analysis in engineering, survival analysis, medicine, biological sciences, actuarial science, finance and insurance. The mathematical properties such as moments, quantile, mean, median, variance, skewness and kurtosis of this distribution are discussed. The reliability and hazard functions of the transmuted half logistic distribution are obtained. The probability density functions of the minimum and maximum order statistics of the transmuted half logistic distribution are established and the relationships between the probability density functions of the minimum and maximum order statistics of the parent model and the probability density function of the transmuted half logistic distribution are considered. The parameter estimation is done by the method of maximum likelihood estimation. The flexibility of the model in statistical data analysis and its applicability is demonstrated by using it to fit relevant data. The study is concluded by demonstrating that the transmuted half logistic distribution has a better goodness of fit than its parent model. We hope this model will serve as an alternative to the existing ones in the literature in fitting positive real data.

Journal of Statistical Distributions and Applications, 2017

We introduce and study general mathematical properties of a new generator of continuous distributions with three extra parameters called the odd log-logistic logarithmic generated family of distributions. We present some special models and investigate the asymptotes and shapes. The new density function can be expressed as a linear combination of exponentiated densities based on the same baseline distribution. Explicit expressions for the ordinary and incomplete moments, quantile and generating functions, Shannon and Rényi entropies and order statistics, which hold for any baseline model, are determined. We discuss the estimation of the model parameters by maximum likelihood. Further, we introduce the new family in long-term survival models. We illustrate the potentiality of the proposed models by means of four applications to real data.

2020

We propose a new generalized family of distributions called the odd generalized half logistic Weibull-G family of distributions. We also considered some special cases when the baseline distribution are uniform, Weibull and normal distributions. Structural properties of the new family of distributions including expansion of density, distribution of order statistics, Renyi entropy, moments, probability weighted moments, quantile and generating functions, and maximum likelihood estimates were derived. A characterization based on conditional expectation is presented. A simulation study to examine efficiency of the maximum likelihood estimates is also conducted. Finally, a real data example is presented to illustrate the applicability and usefulness of the proposed model.

Austrian Journal of Statistics, 2018

Recently, new continuous distributions have been proposed to apply in statistical analysis in a way that each one solves a particular part of the classical distribution problems. In this paper, the Generalized Odd Gamma-G distribution is introduced. In particular, G has been considered as the Uniform distribution and some statistical properties such as quantile function, asymptotics, moments, entropy and order statistics have been calculated. We survey the theoretical outcomes with numerical computation by using R software.The fitness capability of this model has been investigated by fitting this model and others based on real data sets. The maximum likelihood estimators are assessed with simulated real data from proposed model. We present the simulation in order to test validity of maximum likelihood estimators .

Statistics, Optimization & Information Computing

We develop a new family of distributions, referred to as the Marshall-Olkin odd exponential half logistic-G, which is a linear combination of the exponential-G family of distributions. The family of distributions can handle heavy-tailed data and has non-monotonic hazard rate functions. We also conducted a simulation study to assess the performance of the proposed model. Real data examples are provided to demonstrate the usefulness of the proposed model in comparison with several other existing models.

Hacettepe Journal of Mathematics and Statistics, 2015

We study some mathematical properties of a new generator of continuous distributions with two additional shape parameters called the Zografos-Balakrishnan odd log-logistic family. We present some special models and investigate the asymptotes and shapes. The density function of the new family can be expressed as a mixture of exponentiated densities based on the same baseline distribution. We derive a power series for its quantile function. Explicit expressions for the ordinary and incomplete moments, quantile and generating functions, Shannon and Rényi entropies and order statistics, which hold for any baseline model, are determined. We estimate the model parameters by maximum likelihood. Two real data sets are used to illustrate the potentiality of the proposed family.

2021

We developed a new generalized distribution referred to as the Topp-Leone Odd Exponential Half Logistic-G (TL-OEHL-G) distribution. The proposed distribution is an infinite linear combination of the exponentiated-G distribution. Some special cases from the TL-OEHL-G distribution are presented. The special cases of the TL-OEHL-G distribution apply to high skewed data and different forms of the hazard rate. Simulation study results for a selected special case are presented. Real data examples to demonstrate flexibility of the new model compared to other models are also provided.

Statistica, 2020

In this paper, a general class of two-sided lifetime distributions is introduced via odd ratio function, the well-known concept in survival analysis and reliability engineering. Some statistical and reliability properties including survival function, quantiles, moments function, asymptotic and maximum likelihood estimation are provided in a general setting. A special case of this new family is taken up by considering the exponential model as the parent distribution. Some characteristics of this specialized model and also a discussion associated with survival regression are provided.A simulation study is presented to investigate the bias and mean square error of the maximum likelihood estimators. Moreover, two examples of real data sets are studied; point and interval estimations of all parameters are obtained by maximum likelihood and bootstrap (parametric and non-parametric) procedures. Finally, the superiority of the proposed model over some common statistical distributions is sho...

Journal of Data Science

We introduce a new class of distributions called the generalized odd generalized exponential family. Some of its mathematical properties including explicit expressions for the ordinary and incomplete moments, quantile and generating functions, Ŕnyi, Shannon and q-entropies, order statistics and probability weighted moments are derived. We also propose bivariate generalizations. We constructed a simple type Copula and introduced a useful stochastic property. The maximum likelihood method is used for estimating the model parameters. The importance and flexibility of the new family are illustrated by means of two applications to real data sets. We assess the performance of the maximum likelihood estimators in terms of biases and mean squared errors via a simulation study.

In this paper we discuss different properties of the two generalizations of the logistic distributions, which can be used to model the data exhibiting a unimodal density having some skewness present. The first generalization is carried out using the basic idea of Azzalini [2] and we call it as the skew logistic distribution. It is observed that the density function of the skew logistic distribution is always unimodal and log-concave in nature. But the distribution function, failure rate function and different moments can not be obtained in explicit forms and therefore it becomes quite difficult to use it in practice. The second generalization we propose as a proportional reversed hazard family with the base line distribution as the logistic distribution. It is also known in the literature as the Type-I generalized logistic distribution. The density function of the proportional reversed hazard logistic distribution may be asymmetric but it is always unimodal and log-concave. The distribution function, hazard function are in compact forms and the different moments can be obtained in terms of the ψ function and its derivatives. We have proposed different estimators and performed one data analysis for illustrative purposes.

Adalzemir da Silva Braga, for the friendship, love and support. To them, I dedicate this work. To my parents, Sebastião da Silva Braga and Maria Lucy, for love, teaching and for showing me that the work is a virtue that can make our dreams come true. To my advisor, Prof. Dr. Edwin Moises Marcos Ortega, for the continuous support of my Doctorate, motivation and knowledge to develop new methods that contribute to the development of the Statistics. To Prof. Dr. Gauss Moutinho Cordeiro by scientific contributions and support that are always helping to develop new theories in the area of Statistics. To the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior-CAPES, the Fundação de Amparo a Pesquisas do Estado do Acre-FAPAC and Universidade Federal do Acre-UFAC for the financial support that contributed for that I could dedicate exclusively to the activities of the doctorate.

Anais da Academia Brasileira de Ciências, 2019

The normal distribution has a central place in distribution theory and statistics. We propose the log-odd normal generalized (LONG) family of distributions based on log-odds and obtain some of its mathematical properties including a useful linear representation for the new family. We investigate, as a special model, the log-odd normal power-Cauchy (LONPC) distribution. Some structural properties of LONPC distribution are obtained including quantile function, ordinary and incomplete moments, generating function and some asymptotics. We estimate the model parameters using the maximum likelihood method. The usefulness of the proposed family is proved empirically by means of a real air pollution data set.

Mathematical and computational applications, 2022

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Journal of Statistical Computation and Simulation, 2017

We introduce a new class of continuous distributions named the Topp-Leone odd log-logistic family, which extends the one-parameter distribution pioneered by Topp and Leone [A family of J-shaped frequency functions. J Amer Statist Assoc. 1955;50:209-219]. We study some of its mathematical properties and describe two special cases. Further, we propose a regression model based on the new Topp-Leone odd log-logistic Weibull distribution. The usefulness and flexibility of the proposed family are illustrated by means of three real data sets.

Symmetry

In this paper, we present a new univariate flexible generator of distributions, namely, the odd Perks-G class. Some special models in this class are introduced. The quantile function (QFUN), ordinary and incomplete moments (MOMs), generating function (GFUN), moments of residual and reversed residual lifetimes (RLT), and four different types of entropy are all structural aspects of the proposed family that hold for any baseline model. Maximum likelihood (ML) and maximum product spacing (MPS) estimates of the model parameters are given. Bayesian estimates of the model parameters are obtained. We also present a novel log-location-scale regression model based on the odd Perks–Weibull distribution. Due to the significance of the odd Perks-G family and the survival discretization method, both are used to introduce the discrete odd Perks-G family, a novel discrete distribution class. Real-world data sets are used to emphasize the importance and applicability of the proposed models.