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.

[1]  Jurgen A. Doornik,et al.  Ox: an Object-oriented Matrix Programming Language , 1996 .

[2]  Gordon Johnston,et al.  Statistical Models and Methods for Lifetime Data , 2003, Technometrics.

[3]  Kerstin Vogler,et al.  Table Of Integrals Series And Products , 2016 .

[4]  Mahdi Doostparast,et al.  A new family of distributions: the Kumaraswamy odd log-logistic, properties and applications , 2014 .

[5]  M. J. S. Khan,et al.  A Generalized Exponential Distribution , 1987 .

[6]  Morad Alizadeh,et al.  The Zografos-Balakrishnan odd log-logistic family of distributions: Properties and Applications , 2016 .

[7]  P. N. Lee,et al.  Survival Distributions: Reliability Applications in the Biomedical Sciences , 1976 .

[8]  David W. Hosmer,et al.  Applied Survival Analysis: Regression Modeling of Time-to-Event Data , 2008 .

[9]  Peter F. Heil,et al.  Survival Distributions: Reliability Applications in the Biomedical Sciences , 1976 .

[10]  Saralees Nadarajah,et al.  Closed-form expressions for moments of a class of beta generalized distributions , 2011 .

[11]  Deo Kumar Srivastava,et al.  The exponentiated Weibull family: a reanalysis of the bus-motor-failure data , 1995 .

[12]  Samuel Kotz,et al.  The Exponentiated Type Distributions , 2006 .

[13]  M. Alizadeh,et al.  A new generalized odd log-logistic family of distributions , 2017 .

[14]  Narayanaswamy Balakrishnan,et al.  A General Purpose Approximate Goodness-of-Fit Test , 1995 .

[15]  Emrah Altun,et al.  The generalized odd log-logistic family of distributions: properties, regression models and applications , 2017 .

[16]  D. Kundu,et al.  Theory & Methods: Generalized exponential distributions , 1999 .

[17]  J. Lynch,et al.  On the distribution of the breaking strain of a bundle of brittle elastic fibers , 2004, Advances in Applied Probability.

[18]  M. H. Tahir,et al.  The beta odd log-logistic generalized family of distributions , 2016 .

[19]  M. R. Leadbetter,et al.  Extremes and Related Properties of Random Sequences and Processes: Springer Series in Statistics , 1983 .

[20]  P. V. Rao,et al.  Applied Survival Analysis: Regression Modeling of Time to Event Data , 2000 .

[21]  Haiyan Wu,et al.  A Symmetric Component Alpha Normal Slash Distribution: Properties and Inferences , 2013, J. Stat. Theory Appl..