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Heavy or semi-heavy tail, that is the question.

ABSTRACT: While there has been considerable research on the analysis of extreme values and outliers by using heavy-tailed distributions, little is known about the semi-heavy-tailed behaviors of data when there are a few suspicious outliers. To address the situation where data are skewed possessing semi-heavy tails, we introduce two new skewed distribution families of the hyperbolic secant with exciting properties. We extend the semi-heavy-tailedness property of data to a linear regression model. In particular, we investigate the asymptotic properties of the ML estimators of the regression parameters when the error term has a semi-heavy-tailed distribution. We conduct simulation studies comparing the ML estimators of the regression parameters under various assumptions for the distribution of the error term. We also provide three real examples to show the priority of the semi-heavy-tailedness of the error term comparing to heavy-tailedness. Online supplementary materials for this article are available. All the new proposed models in this work are implemented by the shs R package, which can be found on the GitHub webpage.

SUBMITTER: Ownuk J

PROVIDER: S-EPMC9041666 | biostudies-literature | 2021

REPOSITORIES: biostudies-literature

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Heavy or semi-heavy tail, that is the question.

Ownuk Jamil J Baghishani Hossein H Nezakati Ahmad A

Journal of applied statistics 20200310 4

While there has been considerable research on the analysis of extreme values and outliers by using heavy-tailed distributions, little is known about the semi-heavy-tailed behaviors of data when there are a few suspicious outliers. To address the situation where data are skewed possessing semi-heavy tails, we introduce two new skewed distribution families of the hyperbolic secant with exciting properties. We extend the semi-heavy-tailedness property of data to a linear regression model. In partic ...[more]

PMID: 35706985

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Project description:Myosin heavy chain (MyHC) type and muscle fiber size are informative but time-consuming variables of interest for livestock growth, muscle biology, and meat science. The objective of this study was to validate a semi-automated protocol for determining MyHC type and size of muscle fibers. Muscle fibers obtained from the longissimus and semitendinosus of fed beef carcasses were embedded and frozen within 45 min of harvest. Immunohistochemistry was used to distinguish MyHC type I, IIA, and IIX proteins, dystrophin, and nuclei in transverse sections of frozen muscle samples. Stained muscle cross sections were imaged and analyzed using two workflows: 1) Nikon workflow which used Nikon Eclipse inverted microscope and NIS Elements software and 2) Cytation5 workflow consisting of Agilent BioTek Cytation5 imaging reader and Gen5 software. With the Cytation5 workflow, approximately six times more muscle fibers were evaluated compared to the Nikon workflow within both the longissimus (P < 0.01; 768 vs. 129 fibers evaluated) and semitendinosus (P < 0.01; 593 vs. 96 fibers evaluated). Combined imaging and analysis took approximately 1 h per sample with the Nikon workflow and 10 min with the Cytation5 workflow. When muscle fibers were evaluated by the objective thresholds of the Cytation5 workflow, a greater proportion of fibers were classified as glycolytic MyHC types, regardless of muscle (P < 0.01). Overall mean myofiber cross-sectional area was 14% smaller (P < 0.01; 3,248 vs. 3,780) when determined by Cytation5 workflow than when determined by Nikon workflow. Regardless, Pearson correlation of mean muscle fiber cross-sectional areas determined by Nikon and Cytation5 workflows was 0.73 (P < 0.01). In both workflows cross-sectional area of MyHC type I fibers was the smallest and area of MyHC type IIX fibers was the largest. These results validated the Cytation5 workflow as an efficient and biologically relevant tool to expedite data capture of muscle fiber characteristics while using objective thresholds for muscle fiber classification.

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Heavy or semi-heavy tail, that is the question.

Publications

Heavy or semi-heavy tail, that is the question.

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