The Marshall-Olkin Additive Weibull Distribution with Variable Shapes for the Hazard Rate

Afify, Ahmed Z.; Cordeiro, Gauss M.; Yousof, Haitham M.; Saboor, Abdus; Ortega, Edwin M. M.

doi:10.15672/hjms.201612618532

Cited by 27 publications

(19 citation statements)

References 24 publications

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“…The second data set contains 346 observations and refers to nicotine measurements, made from several brands of cigarettes in 1998, collected by the Federal Trade. These data have been analyzed by Afify et al [5]. Table 5 lists the competitive models of the MOGBXII distribution which will be compared with it.…”

Section: Two Applicationsmentioning

confidence: 99%

The extended Burr XII distribution: properties and applications

Afify¹,

Abdellatif²

2019

J. Nonlinear Sci. Appl.

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This paper introduces a new four-parameter lifetime model called the Marshall-Olkin generalized Burr XII (MOGBXII) distribution. We derive some of its mathematical properties, including quantile and generating functions, ordinary and incomplete moments, mean residual life, and mean waiting time and order statistics. The MOGBXII density can be expressed as a linear mixture of Burr XII densities. The maximum likelihood and least squares methods are used to estimate the MOGBXII parameters. Simulation results are obtained to compare the performances of the two estimation methods for both small and large samples. We empirically illustrate the flexibility and importance of the MOGBXII distribution in modeling various types of lifetime data.

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Section: Two Applicationsmentioning

confidence: 99%

The extended Burr XII distribution: properties and applications

Afify¹,

Abdellatif²

2019

J. Nonlinear Sci. Appl.

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“…where G(x, ψ) is the baseline cumulative distribution function(cdf) which may depend on the vector parameter ψ. Many famous MO-G families and its special distributions are available in literature such as Marshall-Olkin-G (Marshall and Olkin;1997), the MO extended Lomax (Ghitany et al;2007), MO semi-Burr and MO Burr (Jayakumar and Mathew;2008), MO q-Weibull (Jose et al;2010), MO extended Lindley (Ghitany et al;2012), the generalized MO-G (Nadarajah et al (2013), the MO Fréchet (Krishna et al;, the MO family (Cordeiro and Lemonte;, MO extended Weibull (Santos-Neto et al;, the beta MO-G (Alizadeh et al 2015), the MO generalized exponential (Ristić, & Kundu;, MO gamma-Weibull (Saboor and Pogány;, MO generalized-G (Yousof et al;, MO additive Weibull (Afify et al; and Weibull MO family (Korkmaz et al;2019). This paper is sketched into the following sections.…”

Section: Introductionmentioning

confidence: 99%

On Burr III Marshal Olkin family: development, properties, characterizations and applications

et al. 2019

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In this paper, a flexible family of distributions with unimodel, bimodal, increasing, increasing and decreasing, inverted bathtub and modified bathtub hazard rate called Burr III-Marshal Olkin-G (BIIIMO-G) family is developed on the basis of the T-X family technique. The density function of the BIIIMO-G family is arc, exponential, left-skewed, right-skewed and symmetrical shaped. Descriptive measures such as quantiles, moments, incomplete moments, inequality measures and reliability measures are theoretically established. The BIIIMO-G family is characterized via different techniques. Parameters of the BIIIMO-G family are estimated using maximum likelihood method. A simulation study is performed to illustrate the performance of the maximum likelihood estimates (MLEs). The potentiality of BIIIMO-G family is demonstrated by its application to real data sets.

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“…respectively, where β > 0 is a shape parameter. Some useful generalization of the Weibull distribution studied in the literature includes, but are not limited to, Mudholkar and Srivastava (1993), Mudholkar et al (1995), Mudholkar et al (1996), Xie and Lai (1995), Ghitany et al (2005), Famoye et al (2005), Sarhan and Zaindin (2009), Silva et al (2010), Aryal and Tsokos (2011), Xie et al (2002), Lai et al (2003), Cordeiro et al (2010), Provost et al (2011), Cordeiro et al (2012), Shahbaz et al (2012), Khan and King (2013), Cordeiro et al (2013), Merovci and Elbatal (2013), Hanook et al (2013), Yousof et al (2015), Cordeiro et al (2014), Lee et al (2007), Elbatal and Aryal (2013), Aryal and Elbatl (2015), Afify et al (2016), Nofal et al (2016), El-Bassiouny et al (2016), Yousof et al (2017a,b,c,d), Aryal et al (2017a,b), Korkmaz et al (2017), El-Bassiouny et al (2017), Alizadeh et al (2017a,b), Brito et al (2015). , Yousof et al (2018), , Hamedani et al (2018), among others.…”

Section: Introductionmentioning

confidence: 99%

The Two-Parameter Odd Lindley Weibull Lifetime Model with Properties and Applications

Almamy¹,

Ibrahim²,

Eliwa³

et al. 2018

IJSP

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In this work, we study the two-parameter Odd Lindley Weibull lifetime model. This distribution is motivated by the wide use of the Weibull model in many applied areas and also for the fact that this new generalization provides more flexibility to analyze real data. The Odd Lindley Weibull density function can be written as a linear combination of the exponentiated Weibull densities. We derive explicit expressions for the ordinary and incomplete moments, moments of the (reversed) residual life, generating functions and order statistics. We discuss the maximum likelihood estimation of the model parameters. We assess the performance of the maximum likelihood estimators in terms of biases, variances, mean squared of errors by means of a simulation study. The usefulness of the new model is illustrated by means of two real data sets. The new model provides consistently better fits than other competitive models for these data sets. The Odd Lindley Weibull lifetime model is much better than \ Weibull, exponential Weibull, Kumaraswamy Weibull, beta Weibull, and the three parameters odd lindly Weibull with three parameters models so the Odd Lindley Weibull model is a good alternative to these models in modeling glass fibres data as well as the Odd Lindley Weibull model is much better than the Weibull, Lindley Weibull transmuted complementary Weibull geometric and beta Weibull models so it is a good alternative to these models in modeling time-to-failure data.

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The Marshall-Olkin Additive Weibull Distribution with Variable Shapes for the Hazard Rate

Cited by 27 publications

References 24 publications

The extended Burr XII distribution: properties and applications

The extended Burr XII distribution: properties and applications

On Burr III Marshal Olkin family: development, properties, characterizations and applications

The Two-Parameter Odd Lindley Weibull Lifetime Model with Properties and Applications

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