# On Tukey's gh family of distributions

Cardinal Scholar
 dc.contributor.advisor Ali, Mir M. en_US dc.contributor.author Majumder, M. Mahbubul A. en_US dc.date.accessioned 2011-06-03T19:41:26Z dc.date.available 2011-06-03T19:41:26Z dc.date.created 2007 en_US dc.date.issued 2007 dc.identifier LD2489.Z72 2007 .M35 en_US dc.identifier.uri http://cardinalscholar.bsu.edu/handle/handle/188332 dc.description.abstract Skewness and elongation are two factors that directly determine the shape of a probability distribution. Thus, to obtain a flexible distribution it is always desirable that the parameters of the distribution directly determine the skewness and elongation. To meet this purpose, Tukey (1977) introduced a family of distributions called g-and-h family (gh family) based on a transformation of the standard normal variable where g and h determine the skewness and the elongation, respectively. The gh family of distributions was extensively studied by Hoaglin (1985) and Martinez and Iglewicz (1984). For its flexibility in shape He and Raghunathan (2006) have used this distribution for multiple imputations. Because of the complex nature of this family of distributions, it is not possible to have an explicit mathematical form of the density function and the estimates of the parameters g and h fully depend on extensive numerical computations.In this study, we have developed algorithms to numerically compute the density functions. We present algorithms to obtain the estimates of g and h using method of moments, quantile method and maximum likelihood method. We analyze the performance of each method and compare them using simulation technique. Finally, we study some special cases of gh family and their properties. dc.description.sponsorship Department of Mathematical Sciences dc.format.extent vi, 49 leaves : ill. ; 28 cm. en_US dc.source Virtual Press en_US dc.subject.lcsh Distribution (Probability theory) -- Computer simulation. en_US dc.title On Tukey's gh family of distributions en_US dc.description.degree Thesis (M.A.) dc.identifier.cardcat-url http://liblink.bsu.edu/catkey/1371472 en_US
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• Master's Theses [5510]
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