The Intrinsic Distribution and Selection Bias of Long-Period Cometary Orbits

• Published in: Journal of the American Statistical Association Vol. 98; no. 463; pp. 515 - 521
• Main Authors: Jupp, Peter E, Kim, Peter T, Koo, Ja-Yong, Wiegert, Paul
• Format: Journal Article
• Language: English
• Published: Alexandria, VA Taylor & Francis 01.09.2003; American Statistical Association; Taylor & Francis Ltd
• Subjects: Applications and Case Studies; Astronomy; Comets; Directed normal; Ecliptic coordinate system; Ecliptic plane; Exact sciences and technology; Mathematical foundations; Mathematical methods; Mathematics; Observational astronomy; Orbits; Parametric inference; Probability and statistics; Quantile-quantile plot; Sciences and techniques of general use; Sine function; Solar orbits; Space based observatories; Spheres; Spherical data; Spherical uniform distribution; Statistical methods; Statistics; Uniformity; Rank statistic; Data analysis; Bias; Statistical theory; Standardization; Selection effect; Confidence interval; Parametric method; Philosophical aspect; Selection problem; Spatial distribution; Distribution function; Bootstrap; Quantile; Biased estimation
• ISSN: 0162-1459; 1537-274X
• DOI: 10.1198/016214503000000305

A question that arises in the study of cometary orbits is whether or not the directed normals to the orbits are uniformly distributed on the celestial sphere. Previous studies by statisticians have not taken selection effects into account and have tended to reject uniformity. Here a plausible selection mechanism is proposed that gives rise to a one-parameter family of distributions on the sphere. Data on long-period comets are analyzed using this one-parameter family. A nonzero selection effect is detected, and its size is estimated. Subject to this selection effect, uniformity of the directed normals can no longer be ruled out.