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Raymond K. W. Wong and Norman Chidambaram

Abstract

A maximum likelihood approach to the application of the gamma size distribution is described and compared with the method of moments approach suggested by Ulbrich. Estimation of distribution parameters based on the maximum likelihood principle and Ulbrich's estimation method have different weighting characteristics, which are illustrated through the use of quantile-quantile plots. The ability of the gamma size distribution to describe curvature on a semilogarithmic diagram, and the mathematical simplicity of incorporating it in the sampling error model based on the Poisson process make it possible to derive a sampling error model with consideration given to changes in size distribution shape. It is also shown that variations in size distribution shape can have significant effects on the estimation of sampling errors.

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Raymond K. W. Wong, Norman Chidambaram, Lawrence Cheng, and Marianne English

Abstract

The use of a shifted gamma size distribution for hailstone samples is proposed. This is shown to provide a better fit than the usual exponential form, using time-resolved Alberta data. It is also concluded that there is a dependence of the shape of hailstone size distributions on the duration of sampling time. Such shape variations are associated with the sampling efficiency of the smaller size categories. The importance of the smaller sizes to the common hail integral estimates is also investigated. The minimum sizes required for sampling accuracy of these integral estimates are also obtained.

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