{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,7]],"date-time":"2026-02-07T13:00:40Z","timestamp":1770469240575,"version":"3.49.0"},"reference-count":0,"publisher":"Informa UK Limited","issue":"1","license":[{"start":{"date-parts":[[1999,1,1]],"date-time":"1999-01-01T00:00:00Z","timestamp":915148800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics and Decision Sciences"],"published-print":{"date-parts":[[1999,1,1]]},"abstract":"<jats:p>The sample correlation coefficient <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>R<\/mml:mi><\/mml:math> is almost universally used to estimate the\npopulation correlation coefficient <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>\u03c1<\/mml:mi><\/mml:math>. If the pair <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mrow><mml:mrow><mml:mo>(<\/mml:mo><mml:mrow><mml:mi>X<\/mml:mi><mml:mo>,<\/mml:mo><mml:mi>Y<\/mml:mi><\/mml:mrow><mml:mo>)<\/mml:mo><\/mml:mrow><\/mml:mrow><\/mml:math>\nhas a bivariate normal distribution, this\nwould not cause any trouble. However, if the marginals are nonnormal, particularly if they\nhave high skewness and kurtosis, the estimated value from a sample may be quite different from\nthe population correlation coefficient <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>\u03c1<\/mml:mi><\/mml:math>.<\/jats:p><jats:p>The bivariate lognormal is chosen as our case study for this robustness study. Two approaches\nare used: (i) by simulation and (ii) numerical computations.<\/jats:p><jats:p>Our simulation analysis indicates that for the bivariate lognormal, the bias in estimating <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>\u03c1<\/mml:mi><\/mml:math> can\nbe very large if <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mrow><mml:mi>\u03c1<\/mml:mi><mml:mo>\u2260<\/mml:mo><mml:mn>0<\/mml:mn><\/mml:mrow><\/mml:math>, and it can be substantially reduced only after a large number (three to four\nmillion) of observations. This phenomenon, though unexpected at first, was found to be\nconsistent to our findings by our numerical analysis.<\/jats:p>","DOI":"10.1155\/s1173912699000012","type":"journal-article","created":{"date-parts":[[2007,3,8]],"date-time":"2007-03-08T07:44:28Z","timestamp":1173339868000},"page":"7-19","source":"Crossref","is-referenced-by-count":20,"title":["Robustness of the sample correlation - the bivariate lognormal case"],"prefix":"10.1080","volume":"3","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4328-8599","authenticated-orcid":true,"given":"C. D.","family":"Lai","sequence":"first","affiliation":[{"name":"Statistics, IIST, Massey University, New Zealand"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"J. C. W.","family":"Rayner","sequence":"additional","affiliation":[{"name":"School of Mathematics and Applied Statistics, University of Wollongong, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"T. P.","family":"Hutchinson","sequence":"additional","affiliation":[{"name":"School of Behavioural Sciences, Macquarie University, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"301","container-title":["Journal of Applied Mathematics and Decision Sciences"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/archive\/1999\/472545.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/archive\/1999\/472545.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,8]],"date-time":"2024-08-08T14:22:57Z","timestamp":1723126977000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.hindawi.com\/journals\/ads\/1999\/472545\/abs\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1999,1,1]]},"references-count":0,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1999,1,1]]}},"alternative-id":["472545"],"URL":"https:\/\/doi.org\/10.1155\/s1173912699000012","relation":{},"ISSN":["1173-9126"],"issn-type":[{"value":"1173-9126","type":"print"}],"subject":[],"published":{"date-parts":[[1999,1,1]]}}}