Several Results Of Simpson Diversity Indices And
Exploratory Data Analysis In The Pielou Model
Author(s)
D. Almorza Gomar & M. H. García Nieto
Abstract
The Pielou model is a model of the abundance of species in a habitat. In this
paper, we apply Simpson diversity indices to the Pielou model and obtain a
result that may be useful for testing the goodness of fit of the Pielou model. To
obtain our results, we describe the broken stick model as a probability
distribution and we present some results from exploratory data analysis of this
model. The inequalities we present are useful in ecological studies that apply the
Pielou model.
Keywords: Pielou model, probability distribution, diversity, Simpson index,
exploratory data analysis.
1 Introduction
In the Pielou model the probability of finding an individual of the specie i in the
habitat is ∑ −=
−i S
i k S p
k=0S
1 1 where 0 ≤pi ≤1, ∀i = 1, 2,...., S and ∑
s
i= i p
1
= 1, pi
≥pj ,∀i ≤j , with i, j =1,…, S.
1.1 Pielou model as a probability distribution
The probability density function (pdf) given by
++ −+= i S S S pi 1 ... 1
1 1 1 with
S >1, provides a probability distribution that arises from the Pielou model.
Proof
The pdf is consistent with 0 ≤pi ≤1, ∀i = 1,2,...., S and pi ≥pj , ∀i ≤j,
with i, j =1, 2,…, S. Therefore, it is sufficient to prove that ∑
=
s
i i p
1
= 1.
Keywords
Pielou model, probability distribution, diversity, Simpson index,
exploratory data analysis.
Related Book
Other papers in this volume
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