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When all types in the dataset of interest are equally common, all p i values equal 1 / R, and the Shannon index hence takes the value ln(R). The more unequal the abundances of the types, the larger the weighted geometric mean of the p i values, and the smaller the corresponding Shannon entropy. If practically all abundance is concentrated to ...
There are many ways to measure biodiversity within a given ecosystem. However, the two most popular are Shannon-Weaver diversity index, [4] commonly referred to as Shannon diversity index, and the other is Simpsons diversity index. [5] Although many scientists prefer to use Shannon's diversity index simply because it takes into account species ...
The Shannon index is the most commonly used way to quantitatively determine species diversity, H, as modeled by the following equation: = = The Shannon index factors in both species evenness and species richness, as represented by the variables p i and s, respectively. The lowest possible value of H is zero, and the higher a community’s H ...
The Shannon entropy is restricted to random variables taking discrete values. The corresponding formula for a continuous random variable with probability density function f ( x ) with finite or infinite support X {\displaystyle \mathbb {X} } on the real line is defined by analogy, using the above form of the entropy as an expectation: [ 10 ] : 224
The source for this is a 1989 work by Charles J. Krebs. In a newer work, however (CJ Krebs. Ecology: the experimental analysis of distribution and abundance, 5th edition. p617-618), the same author calls the index the Shannon-Wiener index. Is there other information that could be used to find the "correct" name for the index, if one exists?
The Wiener index is named after Harry Wiener, who introduced it in 1947; at the time, Wiener called it the "path number". [2] It is the oldest topological index related to molecular branching. [ 3 ] Based on its success, many other topological indexes of chemical graphs, based on information in the distance matrix of the graph, have been ...
More colloquially, a first passage time in a stochastic system, is the time taken for a state variable to reach a certain value. Understanding this metric allows one to further understand the physical system under observation, and as such has been the topic of research in very diverse fields, from economics to ecology .
The Shannon information is closely related to entropy, which is the expected value of the self-information of a random variable, quantifying how surprising the random variable is "on average". This is the average amount of self-information an observer would expect to gain about a random variable when measuring it.