Show simple item record

dc.contributor.authorShi, Jiandong
dc.contributor.authorTong, Tiejun
dc.contributor.authorWang, Yuedong
dc.contributor.authorGenton, Marc G.
dc.date.accessioned2020-09-06T12:07:43Z
dc.date.available2020-09-06T12:07:43Z
dc.date.issued2020-07-31
dc.date.submitted2020-02-14
dc.identifier.citationShi, 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
dc.identifier.issn1938-7997
dc.identifier.issn1938-7989
dc.identifier.doi10.4310/SII.2020.V13.N4.A9
dc.identifier.urihttp://hdl.handle.net/10754/664948
dc.description.abstractIn 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.
dc.description.sponsorshipThe 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).
dc.publisherInternational Press of Boston
dc.relation.urlhttps://www.intlpress.com/site/pub/pages/journals/items/sii/content/vols/0013/0004/a009/
dc.rightsArchived with thanks to Statistics and its Interface
dc.titleEstimating the mean and variance from the five-number summary of a log-normal distribution
dc.typeArticle
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.contributor.departmentSpatio-Temporal Statistics and Data Analysis Group
dc.contributor.departmentStatistics Program
dc.identifier.journalStatistics and its Interface
dc.rights.embargodate2021-04-25
dc.eprint.versionPost-print
dc.contributor.institutionDepartment of Mathematics, Hong Kong Baptist University, Hong Kong
dc.contributor.institutionDepartment of Statistics and Applied Probability, University of California-Santa Barbara, Santa Barbara, USA
dc.identifier.volume13
dc.identifier.issue4
dc.identifier.pages519-531
kaust.personGenton, Marc G.
dc.date.accepted2020-04-25
dc.identifier.eid2-s2.0-85089464942
refterms.dateFOA2020-09-06T12:15:07Z
dc.date.published-online2020-07-31
dc.date.published-print2020


Files in this item

Thumbnail
Name:
log-normal_16April2020[1].pdf
Size:
2.143Mb
Format:
PDF
Description:
Accepted manuscript

This item appears in the following Collection(s)

Show simple item record