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Multimodal distribution
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==== Sambrook Smith's index ==== A further index (''B'') has been proposed by Sambrook Smith ''et al''<ref name=SambrookSmith1997>{{cite journal | last1 = Sambrook Smith | first1 = GH | last2 = Nicholas | first2 = AP | last3 = Ferguson | first3 = RI | year = 1997 | title = Measuring and defining bimodal sediments: Problems and implications | journal = Water Resources Research | volume = 33 | issue = 5| pages = 1179β1185 | doi=10.1029/97wr00365 | bibcode=1997WRR....33.1179S| doi-access = free }}</ref> <math display="block"> B = | \phi_2 - \phi_1 | \frac{ p_2 }{ p_1 } </math> where ''p''<sub>1</sub> and ''p''<sub>2</sub> are the proportion contained in the primary (that with the greater amplitude) and secondary (that with the lesser amplitude) mode and ''Ο''<sub>1</sub> and ''Ο''<sub>2</sub> are the ''Ο''-sizes of the primary and secondary mode. The ''Ο''-size is defined as minus one times the log of the data size taken to the base 2. This transformation is commonly used in the study of sediments. The authors recommended a cut off value of 1.5 with B being greater than 1.5 for a bimodal distribution and less than 1.5 for a unimodal distribution. No statistical justification for this value was given.
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