The generalized Cauchy family of distributions with applications

Alzaatreh, Ayman; Lee, Carl; Famoye, Felix; Ghosh, İndranil

doi:10.1186/s40488-016-0050-3

Cited by 33 publications

(42 citation statements)

References 15 publications

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“…This data set has been analyzed by Cordeiro et al [14]. Using this data set, we fit the ELOLL-N, Lindley-normal (L-N) (Ç akmakyapan and Ozel, [9]), exponential-normal (E-N) or Lehmann type II exponentiated-normal (Alzaatreh et al, [5]; Cordeiro et al [15]), McDonaldnormal (McN) (Alexander et al [3]), normal-normal{exponential} (NNE) (Alzaatreh et al [6]), normal-Cauchy{log-logistic} (NCLL) (Alzaatreh, et al [7]), logistic-normal (LN) (Tahir et al [32]), generelized Kumaraswamy-normal (GKw-N) (Cordeiro et al [11]) and generalized odd log-logistic normal (GOLLN) (Cordeiro, et al [10]) distributions models. The results of this application are listed in Table 3.…”

Section: Discussionmentioning

confidence: 99%

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

Korkmaz¹,

Yousof²,

Hamedani³

2018

JSTA

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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.

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Section: Discussionmentioning

confidence: 99%

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

Korkmaz¹,

Yousof²,

Hamedani³

2018

JSTA

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“…In the literature, many authors have used this T-R{Y} framework to develop probability distributions, such as Aljarrah et al [16]; Alzatraah et al [19,20]; Nasir et al [25,26]; Jamal et al [27,28]; Zubair et al [21]; Famoye et al [22]; and Jamal and Nasir [29]. None of these authors has generalized Dagum distribution using this framework.…”

Section: Proposed T-dagum{y} Classmentioning

confidence: 99%

“…One major importance of providing new distribution through the quantile function of an existing distribution is that the newly formed distribution has the tendency of having higher flexibility in handling bimodality in datasets and it is a weighted hazard function of the baseline distribution (Dagum distribution in this case). For more detailed informations on the importance of using this method, T-R {Y}, see Aljarrah et al [16]; Alzaatreh et al [19,20]; Zubair et al [21]; and Famoye et al [22]. Also, for detailed knowledge of Dagum distribution, see Bandourian et al [4]; Kleiber and Kotz [2]; Kleiber [3]; Domma and Condino [5]; Oluyede and Rajasooriya [6]; Oluyede and Ye [7]; Oluyede et al [8]; Huang and Oluyede [9]; Silva et al [10]; Shahzad and Asghar [11]; Oluyede et al [12]; Nasiru et al [13]; and Bakouch et al [14].…”

Section: Introductionmentioning

confidence: 99%

T-Dagum: A Way of Generalizing Dagum Distribution Using Lomax Quantile Function

Ekum

Adamu

Akarawak

2020

Journal of Probability and Statistics

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Recently, different distributions have been generalized using the T-R {Y} framework but the possibility of using Dagum distribution has not been assessed. The T-R {Y} combines three distributions, with one as a baseline distribution, with the strength of each distribution combined to produce greater effect on the new generated distribution. The new generated distributions would have more parameters but would have high flexibility in handling bimodality in datasets and it is a weighted hazard function of the baseline distribution. This paper therefore generalized the Dagum distribution using the quantile function of Lomax distribution. A member of T-Dagum class of distribution called exponentiated-exponential-Dagum {Lomax} (EEDL) distribution was proposed. The distribution will be useful in survival analysis and reliability studies. Different characterizations of the distribution are derived, such as the asymptotes, stochastic ordering, stress-strength analysis, moment, Shannon entropy, and quantile function. Simulated and real data are used and compared favourably with existing distributions in the literature.

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“…The q -normal model is also studied in the literature on the generalized Cauchy distribution. For example, see [ 10 , 11 , 12 , 13 ].…”

Section: Introductionmentioning

confidence: 99%

Regularization Methods Based on the Lq-Likelihood for Linear Models with Heavy-Tailed Errors

Hirose

2020

Entropy

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We propose regularization methods for linear models based on the Lq-likelihood, which is a generalization of the log-likelihood using a power function. Regularization methods are popular for the estimation in the normal linear model. However, heavy-tailed errors are also important in statistics and machine learning. We assume q-normal distributions as the errors in linear models. A q-normal distribution is heavy-tailed, which is defined using a power function, not the exponential function. We find that the proposed methods for linear models with q-normal errors coincide with the ordinary regularization methods that are applied to the normal linear model. The proposed methods can be computed using existing packages because they are penalized least squares methods. We examine the proposed methods using numerical experiments, showing that the methods perform well, even when the error is heavy-tailed. The numerical experiments also illustrate that our methods work well in model selection and generalization, especially when the error is slightly heavy-tailed.

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The generalized Cauchy family of distributions with applications

Cited by 33 publications

References 15 publications

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

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

T-Dagum: A Way of Generalizing Dagum Distribution Using Lomax Quantile Function

Regularization Methods Based on the Lq-Likelihood for Linear Models with Heavy-Tailed Errors

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