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

Alizadeh, Morad; Altun, Emrah; Cordeiro, Gauss M.; Rasekhi, Mahdi

doi:10.1080/00949655.2017.1406938

Cited by 31 publications

(23 citation statements)

References 8 publications

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“…In the special case of the half-Cauchy distribution, this is performed by [ 24 ] which introduced the generalized odd half-Cauchy-G (GOHC-G) family defined by the following cdf:

where

and

denotes the cdf of a univariate continuous distributions with parameter vector denoted by

. A twin family is given by the odd power Cauchy-G (OPC-G) introduced by [ 25 ] and defined by the following cdf:

…”

Section: Introductionmentioning

confidence: 99%

The Truncated Cauchy Power Family of Distributions with Inference and Applications

Aldahlan

Jamal²,

Chesneau

et al. 2020

Entropy

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As a matter of fact, the statistical literature lacks of general family of distributions based on the truncated Cauchy distribution. In this paper, such a family is proposed, called the truncated Cauchy power-G family. It stands out for the originality of the involved functions, its overall simplicity and its desirable properties for modelling purposes. In particular, (i) only one parameter is added to the baseline distribution avoiding the over-parametrization phenomenon, (ii) the related probability functions (cumulative distribution, probability density, hazard rate, and quantile functions) have tractable expressions, and (iii) thanks to the combined action of the arctangent and power functions, the flexible properties of the baseline distribution (symmetry, skewness, kurtosis, etc.) can be really enhanced. These aspects are discussed in detail, with the support of comprehensive numerical and graphical results. Furthermore, important mathematical features of the new family are derived, such as the moments, skewness and kurtosis, two kinds of entropy and order statistics. For the applied side, new models can be created in view of fitting data sets with simple or complex structure. This last point is illustrated by the consideration of the Weibull distribution as baseline, the maximum likelihood method of estimation and two practical data sets wit different skewness properties. The obtained results show that the truncated Cauchy power-G family is very competitive in comparison to other well implanted general families.

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“…In the special case of the half-Cauchy distribution, this is performed by [ 24 ] which introduced the generalized odd half-Cauchy-G (GOHC-G) family defined by the following cdf:

where

and

denotes the cdf of a univariate continuous distributions with parameter vector denoted by

. A twin family is given by the odd power Cauchy-G (OPC-G) introduced by [ 25 ] and defined by the following cdf:

…”

Section: Introductionmentioning

confidence: 99%

The Truncated Cauchy Power Family of Distributions with Inference and Applications

Aldahlan

Jamal²,

Chesneau

et al. 2020

Entropy

View full text Add to dashboard Cite

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“…This interesting method attracted the attention of some researchers. We refer the reader to [1,4]. Generating new model based on this method resulted in creating very flexible statistical model.…”

Section: Introductionmentioning

confidence: 99%

Odd Hyperbolic Cosine Exponential-Exponential (OHC-EE) Distribution

2019

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In the present paper, we introduce a new lifetime distribution based on the general odd hyperbolic cosine-FG model. Some important properties of proposed model including survival function, quantile function, hazard function, order statistic are obtained. In addition estimating unknown parameters of this model will be examined from the perspective of classic and Bayesian statistics. Moreover, an example of real data set is studied; point and interval estimations of all parameters are obtained by maximum likelihood, bootstrap (parametric and non-parametric) and Bayesian procedures. Finally, the superiority of proposed model in terms of parent exponential distribution over other fundamental statistical distributions is shown via the example of real observations.

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“…The most notorious of these families are the exponentiated-G family [1], the beta-G family [2], and the gamma-G family [3]. Recent promising families include the Kumaraswamy-G family [4], the type I half-logistic-G family [5], the generalized odd log-logistic family [6], the odd power Cauchy family [7], the exponentiated generalized Topp-Leone-G family [8], and the type II general inverse exponential-G family [9].…”

Section: Introductionmentioning

confidence: 99%

Different Estimation Methods for Type I Half-Logistic Topp–Leone Distribution

ZeinEldin

Chesneau

Jamal³

et al. 2019

Mathematics

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In this study, we propose a new flexible two-parameter continuous distribution with support on the unit interval. It can be identified as a special member of the so-called type I half-logistic-G family of distributions, defined with the Topp-Leone distribution as baseline. Among its features, the corresponding probability density function can be left skewed, right-skewed, approximately symmetric, J-shaped, as well as reverse J-shaped, making it suitable for modeling a wide variety of data sets. It thus provides an alternative to the so-called beta and Kumaraswamy distributions. The mathematical properties of the new distribution are determined, deriving the asymptotes, shapes, quantile function, skewness, kurtosis, some power series expansions, ordinary moments, incomplete moments, moment-generating function, stress strength parameter, and order statistics. Then, a statistical treatment of the related model is proposed. The estimation of the unknown parameters is performed by a simulation study exploring seven methods, all described in detail. Two practical data sets are analyzed, showing the usefulness of the new proposed model.

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

Cited by 31 publications

References 8 publications

The Truncated Cauchy Power Family of Distributions with Inference and Applications

The Truncated Cauchy Power Family of Distributions with Inference and Applications

Odd Hyperbolic Cosine Exponential-Exponential (OHC-EE) Distribution

Different Estimation Methods for Type I Half-Logistic Topp–Leone Distribution

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