The RichitRichards family of distributions and its use in forestry
Wang, Mingliang, Ramesh, Nadarajah I. and Rennolls, Keith (2007) The RichitRichards family of distributions and its use in forestry. Canadian Journal of Forest Research, 37 (10). pp. 20522062. ISSN 00455067 (doi:10.1139/X07023)

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Abstract
Johnson's SB and the logitlogistic are fourparameter distribution models that may be obtained from the standard normal and logistic distributions by a fourparameter transformation. For relatively small data sets, such as diameter at breast height measurements obtained from typical sample plots, distribution models with four or less parameters have been found to be empirically adequate. However, in situations in which the distributions are complex, for example in mixed stands or when the stand has been thinned or when working with aggregated data, then distribution models with more shape parameters may prove to be necessary. By replacing the symmetric standard logistic distribution of the logitlogistic with a oneparameter “standard Richards” distribution and transforming by a fiveparameter Richards function, we obtain a new sixparameter distribution model, the “RichitRichards”. The RichitRichards includes the “logitRichards”, the “Richitlogistic”, and the logitlogistic as submodels. Maximum likelihood estimation is used to fit the model, and some problems in the maximum likelihood estimation of bounding parameters are discussed. An empirical case study of the RichitRichards and its submodels is conducted on pooled diameter at breast height data from 107 sample plots of Chinese fir (Cunninghamia lanceolata (Lamb.) Hook.). It is found that the new models provide significantly better fits than the fourparameter logitlogistic for large data sets.
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