Marshall–Olkin distribution: parameter estimation and application to cancer data

Güney, Yeşim; Tuaç, Yetkin; Arslan, Olçay

doi:10.1080/02664763.2016.1252730

Cited by 5 publications

(4 citation statements)

References 21 publications

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“…The work by Duarte-López et al (2015) shows the suitability of the MOEZipf distribution when it is used to fit this type of data. Moreover, the work by Güney et al (2017) has also used the MOEZipf distribution for modeling the frequency of cancer types in Turkey during the period 2007-2011. Other bi-parametric models have also been considered, such as the Discrete Gaussian Exponential (DGX) (Bi et al, 2001), the Zipf-Polylog (Valero et al, 2020) and the positive version of the Zipf-PSS (Duarte-López et al, 2020); and their fits have been compared to those associated with the proposed distributions.…”

Section: Applicationsmentioning

confidence: 99%

Randomly stopped extreme Zipf extensions

Duarte-López¹,

Pérez-Casany²,

Valero

2021

Extremes

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In this paper, we extend the Zipf distribution by means of the Randomly Stopped Extreme mechanism; we establish the conditions under which the maximum and minimum families of distributions intersect in the original family; and we demonstrate how to generate data from the extended family using any Zipf random number generator. We study in detail the particular cases of geometric and positive Poisson stopping distributions, showing that, in log-log scale, the extended models allow for top-concavity (top-convexity) while maintaining linearity in the tail. We prove the suitability of the models presented, by fitting the degree sequences in a collaboration and a protein-protein interaction networks. The proposed models not only give a good fit, but they also allow for extracting interesting insights related to the data generation mechanism.

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Section: Applicationsmentioning

confidence: 99%

Randomly stopped extreme Zipf extensions

Duarte-López¹,

Pérez-Casany²,

Valero

2021

Extremes

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“…The total number of degree sequences fitted is 16, which is obtained by 1) The initial value for α is set to be equal to the α estimate obtained for the Zipf distribution proposed by Güney et al (2017).…”

Section: Application Examplesmentioning

confidence: 99%

The Zipf–Poisson-stopped-sum distribution with an application for modeling the degree sequence of social networks

Duarte-López

Pérez-Casany

Valero

2020

Computational Statistics & Data Analysis

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“…Applications to real data sets for some of those extensions include remission times in bladder cancer patients [7] and cancers in general [24], reliability analyses of electronic devices [15] and mechanical components [20], stress-rupture life of kevlar 49/epoxy strands [25], strengths of glass fibers [25], solid epoxy electrical-insulation in an accelerated voltage life test [25], flood peaks in a river [21], lifetimes of front disk brake pads [21], annual salaries of baseball players in Major League Baseball [26], stream flow amounts [20], etc.…”

Section: Introductionmentioning

confidence: 99%

Bias Reduction for the Marshall-Olkin Extended Family of Distributions with Application to an Airplane’s Air Conditioning System and Precipitation Data

et al. 2020

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The Marshall-Olkin extended family of distributions is an alternative for modeling lifetimes, and considers more or less asymmetry than its parent model, achieved by incorporating just one extra parameter. We investigate the bias of maximum likelihood estimators and use it to develop an estimator with less bias than traditional estimators, by a modification of the score function. Unlike other proposals, in this paper, we consider a bias reduction methodology that can be applied to any member of the family and not necessarily to any particular distribution. We conduct a Monte Carlo simulation in order to study the performance of the corrected estimators in finite samples. This simulation shows that the maximum likelihood estimator is quite biased and the proposed estimator is much less biased; in small sample sizes, the bias is reduced by around 50 percent. Two applications, related to the air conditioning system of an airplane and precipitations, are presented to illustrate the results. In those applications, the bias reduction for the shape parameters is close to 25% and the bias reduction also reduces, among others things, the width of the 95% confidence intervals for quantiles lower than 0.594.

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Marshall–Olkin distribution: parameter estimation and application to cancer data

Cited by 5 publications

References 21 publications

Randomly stopped extreme Zipf extensions

Randomly stopped extreme Zipf extensions

The Zipf–Poisson-stopped-sum distribution with an application for modeling the degree sequence of social networks

Bias Reduction for the Marshall-Olkin Extended Family of Distributions with Application to an Airplane’s Air Conditioning System and Precipitation Data

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