Bivariate inverse Weibull distribution

Muhammed, Hiba Z.

doi:10.1080/00949655.2015.1110585

Cited by 34 publications

(21 citation statements)

References 17 publications

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“…The bivariate data could be exchange rates in two time periods, strength components, results of two teams in Olympic games etc. Therefore, many bivariate distributions are proposed in literature, for example, bivariate generalised exponential distribution by Kundu and Gupta (2009); bivariate generalised linear failure rate distribution by Sarhan et al (2011) Marshall-Olkin bivariate Weibull distribution by Kundu and Gupta (2013); bivariate Kumaraswamy distribution by Barreto-Souza and Lemonte (2013); bivariate exponential distribution by Balakrishnan and Shiji (2014); bivariate exponentiated generalised Weibull-Gompertz distribution by El-Bassiouny et al (2016); bivariate exponentiated modifi ed Weibull extension distribution by El-Gohary et al (2016); bivariate exponentiated extended Weibull family by Roozegar and Jafari (2016); bivariate inverse Weibull distribution by Hiba (2016); bivariate exponentiated discrete Weibull distribution by El-Morshedy et al (2020c); bivariate exponentiated generalised linear exponential distribution by Ibrahim et al (2019); bivariate Gumbel-G family by Eliwa and El-Morshedy (2019); univarite and multivariate generalized slash student distribution by El-Bassiouny and El-Morshedy (2015), univariate and multivariate double slash distribution by El-Morshedy et al (2020c), bivariate discrete inverse Weibull distribution by , bivariate odd Weibull-G family by Eliwa and El-Morshedy (2020b), bivariate Burr X generator by El-Morshedy et al (2020c), among others. However, in many practical situations, classical bivariate distributions do not provide adequate fi ts to real data.…”

Section: June 2020mentioning

confidence: 99%

Bivariate Gompertz generator of distributions: statistical properties and estimation with application to model football data

Eliwa

Alhussain

Ahmed

et al. 2020

J. Natn. Sci. Foundation Sri Lanka

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In this paper, the bivariate extension of the so called Gompertz-G family was introduced and studied in detail. Marshall and Olkin shock model was used to build the proposed bivariate family. The new family was constructed from three independent Gompertz-H families using a minimisation process. Some of its statistical properties such as joint probability density function, coeffi cient of median correlation, moments, product moment, covariance, conditional probability density function, joint reliability function, stress-strength reliability and joint reversed (hazard) rate function were derived. After introducing the general class, three special models of the new family were discussed. Maximum likelihood method was used to estimate the family parameters. A simulation study was carried out to examine the bias and mean square error of the maximum likelihood estimators. Finally, the importance of the proposed bivariate family was illustrated by means of real dataset, and it was found that the proposed model provides better fi t than other well-known models in the statistical literature such as bivariate Gompertz, bivariate generalized Gompertz, bivariate Gumbel Gompertz, bivariate Burr X Gompertz and bivariate exponentiated Weibull-Gomperz

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Section: June 2020mentioning

confidence: 99%

Bivariate Gompertz generator of distributions: statistical properties and estimation with application to model football data

Eliwa

Alhussain

Ahmed

et al. 2020

J. Natn. Sci. Foundation Sri Lanka

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“…In this Section, we introduce a bivariate extended of the NKw-G family according to Marshall and Olkin shock model (see, Marshall and Olkin, [43]). Several authors used the Marshall and Olkin approach as a method to generate bivariate distributions, see Sarhan and Balakrishnan, [44], Kundu and Dey [45], El-Gohary et al [46], Muhammed [47], El-Bassiouny et al [48], Ghosh and Hamedani [49], El-Morshedy et al [50,51], Eliwa et al [52], Hussain et al [53], and others. The BvNKw-G family is constructed from three independent NKw-G families by utilizing a minimization process.…”

Section: Bivariate New Kumaraswamy (Bvnkw) G-familymentioning

confidence: 99%

A New Kumaraswamy Generalized Family of Distributions with Properties, Applications and Bivariate Extension

Tahir¹,

Hussain²,

Cordeiro³

et al. 2020

Preprint

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For bounded unit interval, we propose a new Kumaraswamy generalized (G) family of distributions from a new generator which could be an alternate to the Kumaraswamy-G family proposed earlier by Cordeiro and de-Castro in 2011. This new generator can also be used to develop alternate G-classes such as beta-G, McDonald-G, Topp-Leone-G, Marshall-Olkin-G and Transmuted-G for bounded unit interval. Some mathematical properties of this new family are obtained and maximum likelihood method is used for estimating the family parameters. We investigate the properties of one special model called a new Kumaraswamy-Weibull (NKwW) distribution. Parameter estimation is dealt and maximum likelihood estimators are assessed through simulation study. Two real life data sets are analyzed to illustrate the importance and flexibility of this distribution. In fact, this model outperforms some generalized Weibull models such as the Kumaraswamy-Weibull, McDonald-Weibull, beta-Weibull, exponentiated-generalized Weibull, gamma-Weibull, odd log-logistic-Weibull, Marshall-Olkin-Weibull, transmuted-Weibull, exponentiated-Weibull and Weibull distributions when applied to these data sets. The bivariate extension of the family is proposed and the estimation of parameters is given. The usefulness of the bivariate NKwW model is illustrated empirically by means of a real-life data set.

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“…Moreover, Sarhan et al [8] presented bivariate generalized linear failure rate distribution. Recently, Muhammed [9] introduced bivariate inverse Weibull (BIW) distribution.…”

Section: Introductionmentioning

confidence: 99%

Multivariate Inverted Kumaraswamy Distribution: Derivation and Estimation

Aly

Abuelamayem

2020

Mathematical Problems in Engineering

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Industrial revolution leads to the manufacturing of multicomponent products; to guarantee the sufficiency of the product and consumer satisfaction, the producer has to study the lifetime of the products. This leads to the use of bivariate and multivariate lifetime distributions in reliability engineering. The most popular and applicable is Marshall–Olkin family of distributions. In this paper, a new bivariate lifetime distribution which is the bivariate inverted Kumaraswamy (BIK) distribution is found and its properties are illustrated. Estimation using both maximum likelihood and Bayesian approaches is accomplished. Using different selection criteria, it is found that BIK provides the best performance compared with other bivariate distributions like bivariate exponential and bivariate inverse Weibull distributions. As a generalization, the multivariate inverted Kumaraswamy (MIK) distribution is derived. Few studies have been conducted on the multivariate Marshall–Olkin lifetime distributions. To the best of our knowledge, none of them handle estimation process. In this paper, we developed an algorithm to show how to estimate the unknown parameters of MIK using both maximum likelihood and Bayesian approaches. This algorithm could be applied in estimating other Marshall–Olkin multivariate lifetime distributions.

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Bivariate inverse Weibull distribution

Cited by 34 publications

References 17 publications

Bivariate Gompertz generator of distributions: statistical properties and estimation with application to model football data

Bivariate Gompertz generator of distributions: statistical properties and estimation with application to model football data

A New Kumaraswamy Generalized Family of Distributions with Properties, Applications and Bivariate Extension

Multivariate Inverted Kumaraswamy Distribution: Derivation and Estimation

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