An Extension of the Kumaraswamy Distribution

Carrasco, Jalmar M. F.; Cordeiro, Gauss M.

doi:10.5539/ijsp.v6n3p61

Cited by 4 publications

(5 citation statements)

References 17 publications

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“…The limitation of current research remains on the classicity of the statistical framework considered. Directions for future research include the estimation of the entropy of the Kumaraswamy distribution in more sophisticated statistical schemes with physical motivations, such as the progressive type II censoring scheme, generalized progressively hybrid censoring scheme, etc., or taking into account generalized versions of the Kumaraswamy distribution, such as the one proposed by [40].…”

Section: Plos Onementioning

confidence: 99%

Estimation of different types of entropies for the Kumaraswamy distribution

et al. 2021

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The estimation of the entropy of a random system or process is of interest in many scientific applications. The aim of this article is the analysis of the entropy of the famous Kumaraswamy distribution, an aspect which has not been the subject of particular attention previously as surprising as it may seem. With this in mind, six different entropy measures are considered and expressed analytically via the beta function. A numerical study is performed to discuss the behavior of these measures. Subsequently, we investigate their estimation through a semi-parametric approach combining the obtained expressions and the maximum likelihood estimation approach. Maximum likelihood estimates for the considered entropy measures are thus derived. The convergence properties of these estimates are proved through a simulated data, showing their numerical efficiency. Concrete applications to two real data sets are provided.

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Section: Plos Onementioning

confidence: 99%

Estimation of different types of entropies for the Kumaraswamy distribution

et al. 2021

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“…Then, its cf Φ X ( t ) is defined as [52, p. 342]:

Φ_{X} (t) = E (e^{i t X}) = \int_{- \infty}^{\infty} e^{i t x} d F (x), t \in ℝ,

where

normali = \sqrt{- 1}

. However, the cf can be not analytically tractable, as noticed in the BW, 4,42,43 BF, 44 BKw, 45 BLL, 46 beta‐Gumbel, 53 and beta log‐normal 54 models. To address this issue, Colombo 55 has suggested the MT as an alternative.…”

Section: Mellin Transform As a Special Probability Weighted Moment: S...mentioning

confidence: 99%

“…Because of analytical tractability and suitability for beta-generalization, we separate the following baseline distributions for investigation: Weibull, 37 Fréchet, 38,39 Kumaraswamy, 40 and log-logistic (LL). 41 Their corresponding beta-generalizations are the beta-Weibull (BW), 4,42,43 the beta-Fréchet (BF), 44 the beta-Kumaraswamy (BKw), 45 and the beta-LL (BLL) 46 distributions. We introduce closed-form expressions for the Fréchet and Kumaraswamy PWM functions.…”

Section: Introductionmentioning

confidence: 99%

Goodness‐of‐fit measures based on the Mellin transform for beta generalized lifetime data

Vasconcelos

Cintra

Nascimento

2021

Math Methods in App Sciences

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In recent years various probability models have been proposed for describing lifetime data. Increasing model flexibility is often sought as a means to better describe asymmetric and heavy tail distributions. Such extensions were pioneered by the beta-G family. However, efficient (GoF) measures for the beta-G distributions are sought. In this paper, we combine probability weighted moments (PWMs) and the Mellin transform (MT) in order to furnish new qualitative and quantitative GoF tools for model selection within the beta-G class. We derive PWMs for the Fréchet and Kumaraswamy distributions, and we provide expressions for the MT, and for the log-cumulants (LC) of the beta-Weibull, beta-Fréchet, beta-Kumaraswamy, and beta-log-logistic distributions. Subsequently, we construct LC diagrams and, based on the Hotelling's T 2 statistic, we derive confidence ellipses for the LCs. Finally, the proposed GoF measures are applied on five real data sets in order to demonstrate their applicability.

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“…Furthermore, the development of generalized distributions with support on the interval (0,1) seems very rare in the literature, although the importance of such generalized distributions cannot be over-emphasized. Examples of such few generalized distribution on (0,1) include the generalized beta distribution of the first kind (McDonald, 1984), the generalized Kumaraswamy distribution (Carrasco et al 2010), the Kumaraswamy -Kumaraswamy distribution (El Sherpieny and Ahmad 2014), and the exponentiated generalized Kumaraswamy distribution (Elgarhy et al 2018). For random processes that assume values on the interval (0,1), there is a great need to develop flexible and highly adaptive distributions to model such processes.…”

Section: Introductionmentioning

confidence: 99%

A New Family of Generalized Distributions on the Unit Interval: The T− kumasatwamy Family of Distributions

Osatohanmwen¹,

Oyegue²,

Ewere³

et al. 2021

Journal of Data Science

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The so-called Kumaraswamy distribution is a special probability distribution developed to model doubled bounded random processes for which the mode do not necessarily have to be within the bounds. In this article, a generalization of the Kumaraswamy distribution called the T-Kumaraswamy family is defined using the T-R {Y} family of distributions framework. The resulting T-Kumaraswamy family is obtained using the quantile functions of some standardized distributions. Some general mathematical properties of the new family are studied. Five new generalized Kumaraswamy distributions are proposed using the T-Kumaraswamy method. Real data sets are further used to test the applicability of the new family.

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An Extension of the Kumaraswamy Distribution

Cited by 4 publications

References 17 publications

Estimation of different types of entropies for the Kumaraswamy distribution

Estimation of different types of entropies for the Kumaraswamy distribution

Goodness‐of‐fit measures based on the Mellin transform for beta generalized lifetime data

A New Family of Generalized Distributions on the Unit Interval: The T− kumasatwamy Family of Distributions

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