On the Marshall–Olkin transformation as a skewing mechanism

Rubio, Francisco J.; Steel, Mark F. J.

doi:10.1016/j.csda.2012.01.003

Cited by 19 publications

(7 citation statements)

References 13 publications

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“…where = (a, θ ) is the parameter space, a > 0 is the new shape parameter, and θ is the parameter space of G. Rubio & Steel (2012) studied Marshall and Olkin's approach as a skewing mechanism. Properties and applications of the mog family have been studied by many, among them we refer to Jose, Naik & Ristić (2010) (for q-Weibull) and Krishna et al (2013) (for Fréchet).…”

Section: Appendix Imentioning

confidence: 99%

MPS: An R package for modelling shifted families of distributions

Teimouri

Nadarajah²

2022

Aus NZ J of Statistics

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Generalised statistical distributions have been widely used over the last decades for modelling phenomena in different fields. The generalisations have been made to produce distributions with more flexibility and lead to more accurate modelling in practice. Statistical analysis of the generalised distributions requires new statistical packages. The Newdistns package due to Nadarajah and Rocha provides R routines with functionality to compute probability density function (PDF), cumulative distribution function (CDF), quantile function, random numbers and parameter estimates of 19 families of distributions with applications in survival analysis. Here, we introduce an R package, called MPS, for computing PDF, CDF, quantile function, random numbers, Q-Q plots and parameter estimates for 24 shifted new families of distributions. By considering an extra location parameter, each family will be defined on the whole real line and so covers a broader range of applicability. We adopt the well-known maximum product spacing approach to estimate parameters of the families because under some situations the maximum likelihood (ML) estimators fail to exist. We demonstrate MPS by analysing two well-known real data sets. For the first data set, the ML estimators break down, but MPS works well. For the second set, adding a location parameter results in a reasonable model while the absence of the location parameter makes the model quite inappropriate. The MPS is available from CRAN at https://cran.r-project.org/package=MPS.

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Section: Appendix Imentioning

confidence: 99%

MPS: An R package for modelling shifted families of distributions

Teimouri

Nadarajah²

2022

Aus NZ J of Statistics

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“…The proportional odds family of Marshall & Olkin corresponds to w ( v ) = w P O ( v ) = v /{ γ + (1 − γ ) v },0 < v < 1, γ > 0. I must stress that, as their names suggest, these families are largely intended to be used in a lifetime distribution context—and work on them by Marshall & Olkin is well motivated and, of course, first class—but they have also been suggested for use as skewing mechanisms on

double-struckR

; Rubio & Steel show the choice w P O to be poor in this regard in general.…”

Section: The Menu: Four (Or Five) Main Familiesmentioning

confidence: 99%

On Families of Distributions with Shape Parameters

Jones

2014

Int Statistical Rev

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Univariate continuous distributions are one of the fundamental components on which statistical modelling, ancient and modern, frequentist and Bayesian, multi-dimensional and complex, is based. In this article, I review and compare some of the main general techniques for providing families of typically unimodal distributions on R with one or two, or possibly even three, shape parameters, controlling skewness and/or tailweight, in addition to their all-important location and scale parameters. One important and useful family is comprised of the 'skew-symmetric' distributions brought to prominence by Azzalini. As these are covered in considerable detail elsewhere in the literature, I focus more on their complements and competitors. Principal among these are distributions formed by transforming random variables, by what I call 'transformation of scale'-including two-piece distributions-and by probability integral transformation of nonuniform random variables. I also treat briefly the issues of multi-variate extension, of distributions on subsets of R and of distributions on the circle. The review and comparison is not comprehensive, necessarily being selective and therefore somewhat personal.

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“…The resulting new models are known to give more versatility to model numerous types of data sets. The early researches employing this technique by Lam and Leung (2001), Economou and Caroni (2007), Rao et al (2009), Nanda and Das (2012), Rubio and Steel (2012), Cordeiro et al (2014) and Castellares and Lemonte (2016). According to Marshall and Olkin (1997), "the sf and pdf of the MOE class are defined, bȳ…”

Section: Introductionmentioning

confidence: 99%

The Marshall-Olkin Modified Lindley Distribution: Properties and Applications

Gillariose¹,

Tomy²,

Jamal

et al. 2020

JRSS

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This article is devoted to a new Marshall-Olkin distribution by using a recent modification of the Lindley distribution. Mathematical features of the new model are described. Utilizing maximum likelihood method, the parameters of the new model are estimated. Performance of the estimation approach is discussed by means of a simulation procedure. Moreover, applications of the new distribution are presented which reveal its superiority over other three competing Marshall-Olkin extended distributions of the literature.

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On the Marshall–Olkin transformation as a skewing mechanism

Cited by 19 publications

References 13 publications

MPS: An R package for modelling shifted families of distributions

MPS: An R package for modelling shifted families of distributions

On Families of Distributions with Shape Parameters

The Marshall-Olkin Modified Lindley Distribution: Properties and Applications

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