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    Estimating the mean and variance from the five-number summary of a log-normal distribution

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    log-normal_16April2020[1].pdf
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    2.143Mb
    Format:
    PDF
    Description:
    Accepted manuscript
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    Type
    Article
    Authors
    Shi, Jiandong
    Tong, Tiejun
    Wang, Yuedong
    Genton, Marc G. cc
    KAUST Department
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Spatio-Temporal Statistics and Data Analysis Group
    Statistics Program
    Date
    2020-07-31
    Online Publication Date
    2020-07-31
    Print Publication Date
    2020
    Embargo End Date
    2021-04-25
    Submitted Date
    2020-02-14
    Permanent link to this record
    http://hdl.handle.net/10754/664948
    
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    Abstract
    In the past several decades, meta-analysis has been widely used to pool multiple studies for evidence-based practice. To conduct a meta-analysis, the mean and variance from each study are often required; whereas in certain studies, the five-number summary may instead be reported that consists of the median, the first and third quartiles, and/or the minimum and maximum values. To transform the fivenumber summary back to the mean and variance, several popular methods have emerged in the literature. However, we note that most existing methods are developed under the normality assumption; and when this assumption is violated, these methods may not be able to provide a reliable transformation. In this paper, we propose to estimate the mean and variance from the five-number summary of a log-normal distribution. Specifically, we first make the log-transformation of the reported quantiles. With the existing mean estimators and newly proposed variance estimators under the normality assumption, we construct the estimators of the log-scale mean and variance. Finally, we transform them back to the original scale for the final estimators. We also propose a biascorrected method to further improve the estimation of the mean and variance. Simulation studies demonstrate that our new estimators have smaller biases and smaller relative risks in most settings. A real data example is used to illustrate the practical usefulness of our new estimators.
    Citation
    Shi, J., Tong, T., Wang, Y., & Genton, M. G. (2020). Estimating the mean and variance from the five-number summary of a log-normal distribution. Statistics and Its Interface, 13(4), 519–531. doi:10.4310/sii.2020.v13.n4.a9
    Sponsors
    The authors thank the editor, the associate editor, and the reviewer for their helpful comments that have led to a significant improvement of the paper. Tiejun Tong's research was supported by the Initiation Grant for Faculty Niche Research Areas (No. RC-IG-FNRA/17-18/13) and the Century Club Sponsorship Scheme of Hong Kong Baptist University, the General Research Fund (No. HKBU12303918), the Health and Medical Research Fund (No. 04150476), and the National Natural Science Foundation of China (No. 11671338).
    Publisher
    International Press of Boston
    Journal
    Statistics and its Interface
    DOI
    10.4310/SII.2020.V13.N4.A9
    Additional Links
    https://www.intlpress.com/site/pub/pages/journals/items/sii/content/vols/0013/0004/a009/
    ae974a485f413a2113503eed53cd6c53
    10.4310/SII.2020.V13.N4.A9
    Scopus Count
    Collections
    Articles; Statistics Program; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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