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. / Department of Mathematical Sciences
| Identifer | oai:union.ndltd.org:BSU/oai:cardinalscholar.bsu.edu:handle/188332 |
| Date | January 2007 |
| Creators | Majumder, M. Mahbubul A. |
| Contributors | Ali, Mir Masoom |
| Source Sets | Ball State University |
| Detected Language | English |
| Format | vi, 49 leaves : ill. ; 28 cm. |
| Source | Virtual Press |
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