The beta log-normal distribution

“…The mathematical tractability of the BLN error model allows three results. Note that we use a three‐parameter version of this distribution, defined as the distribution of the product of independent Beta(α,1) and Log Normal(μ,σ 2 ) random variates, rather than the four parameter version given in .…”

Section: Appendixmentioning

confidence: 99%

Error model for reduction of cardiac and respiratory motion effects in quantitative liver DW‐MRI

Murphy

Wolfson

Gamst

et al. 2012

Magnetic Resonance in Med

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Diffusion-weighted images of the liver exhibit signal dropout from cardiac and respiratory motion, particularly in the left lobe. These artifacts cause bias and variance in derived parameters that quantify intra-voxel incoherent motion (IVIM). Many models of diffusion have been proposed, but few separate attenuation from diffusion or perfusion from that of bulk motion. The error model proposed here (Beta*LogNormal) is intended to accomplish that separation by modeling stochastic attenuation from bulk motion as multiplication by a Beta-distributed random variate. Maximum likelihood estimation with this error model can be used to derive IVIM parameters separate from signal dropout, and does not require a priori specification of parameters to do so. Liver IVIM parameters were derived for six healthy subjects under this error model and compared with least-squares estimates. Least-squares estimates exhibited bias due to cardiac and respiratory gating and due to location within the liver. Bias from these factors was significantly reduced under the Beta*LogNormal model, as was within-organ parameter variance. Similar effects were appreciable in diffusivity maps in two patients with focal liver lesions. These results suggest that, relative to least-squares estimation, the Beta*LogNormal model accomplishes the intended reduction of bias and variance from bulk motion in liver diffusion imaging.

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“…We compare the GEW model with some of its sub-models and we also compare it with some competitor models: the Burr XII geometric (BXIIG) (Silva and Cordeiro 2015), the beta log-normal (BLN) (Castellares et al 2013) and the exponentiated Weibull-Poisson (EWP) (Mahmoudi and Sepahdar 2013) distributions. The MLEs of the models parameters and the Akaike Information Criterion (AIC) statistic for some models fitted to the data are listed in Table 1.…”

Section: The Gew Model Its Sub-models and Some Competitorsmentioning

confidence: 99%

The gamma extended Weibull distribution

et al. 2016

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The two-parameter Weibull has been the most popular distribution for modeling lifetime data. We propose a four-parameter gamma extended Weibull model, which generalizes the Weibull and extended Weibull distributions, among several other models. We obtain explicit expressions for the ordinary and incomplete moments, generating and quantile functions and mean deviations. We employ the method of maximum likelihood for estimating the model parameters. We propose a log-gamma extended Weibull regression model with censored data. The applicability of the new models is well justified by means of two real data sets.

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The beta log-normal distribution

Cited by 24 publications

References 26 publications

The log‐power‐normal distribution is the exponentiated lognormal distribution

The log‐power‐normal distribution is the exponentiated lognormal distribution

Error model for reduction of cardiac and respiratory motion effects in quantitative liver DW‐MRI

The gamma extended Weibull distribution

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