Here and below, \ propto means proportional; a pdf is always scaled so that its integral over the whole space is one.
2.
The denominator equals mean proportional species abundance in the dataset as calculated with the weighted generalized mean with exponent " q "-1.
3.
Barbour then described a generalized construction using the easily obtained mean proportional for the length of " MB " that avoids most of the specific angles and lengths required in the original.
4.
The denominator hence equals mean proportional species abundance within the subunits ( mean p _ { i | j } ) as calculated with the weighted generalized mean with exponent " q "-1.
5.
Since mean proportional abundance of the types increases with decreasing number of types and increasing abundance of the most abundant type, ? obtains small values in datasets of high diversity and large values in datasets of low diversity.
6.
The effective number of species is the number of equally abundant species needed to obtain the same mean proportional species abundance as that observed in the dataset of interest ( where all species may not be equally abundant ).
7.
The effective number of species is the number of equally-abundant species needed to obtain the same mean proportional species abundance as that observed in the dataset of interest ( where all species may not be equally abundant ).
8.
He instructed to first draw the line " MR " corresponding to the larger of the two numbers with " MP " the smaller, and to construct their mean proportional at " MB ".
9.
Archytas provided a rigorous proof that the basic musical intervals cannot be divided in half, or in other words, that there is no mean proportional between numbers in super-particular ratio ( octave 2 : 1, fourth 4 : 3, fifth 3 : 2, 9 : 8 ) (; ).
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