Abstract
Zipf's law describes the empirical size distribution of the components of many systems in natural and social sciences and humanities. We show, by solving a statistical model, that Zipf's law co-occurs with the maximization of the diversity of the component sizes. The law ruling the increase of such diversity with the total dimension of the system is derived and its relation with Heaps's law is discussed. As an example, we show that our analytical results compare very well with linguistics and population datasets.
Highlights
We show that our analytical results compare very well with linguistics and population datasets
Diversity is a central concept in ecology, economics, information theory, and other natural and social sciences
It can be quantified by diversity indices [1,2], such as richness, the Gini-Simpson index, or BoltzmannShannon entropy, which characterize the system under study from different angles
Summary
Diversity is a central concept in ecology, economics, information theory, and other natural and social sciences. Zipf’s law describes the empirical size distribution of the components of many systems in natural and social sciences and humanities.
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