SPECIES (version 1.2.0)

pcg: Poisson-compound Gamma estimator for the species richness

Description

Function to calculate the Poisson-compound Gamma estimators of the species number by Wang 2010. This method is essentially a conditional NPMLE method. The species abundance here is assumed to follow a compound Gamma model. The confidence interval is obtained based on a bootstrap procedure. A Fortran function is called to for the computing. This function requires Fortran compiler installed.

Usage

pcg(n,t=35,C=0,alpha=c(1:10),b=200,seed=NULL,conf=0.95,dis=1)

Value

The function pcg returns a list of: Nhat, CI (if “C=1”) and AlphaModel.

Nhat

point estimate of N.

CI

bootstrap confidence interval.

AlphaModel

unified shape parameter of compound Gamma selected from cross-validation.

Arguments

n

a matrix or a numerical data frame of two columns. It is also called the “frequency of frequencies” data in literature. The first column is the frequency \(j=1, 2\ldots\); and the second column is \(n_j\), the number of species observed with \(j\) individuals in the sample.

t

a positive integer. t is the cutoff value defining the relatively less abundant species to be used in estimation. The default value for t=35. The estimator is more sensitive to t compared with pnpmle or unpmle estimators. We recommend to use \(t \ge 20\) if the maximum frequency (\(j\)) is greater than 20. Otherwise use the maximum frequency of \(j\) for t.

C

integer either 0 or 1. It specifies whether bootstrap confidence interval should be calculated. “C=1” for YES and “C=0” for NO.The default of C is set as 0.

b

integer. b specifies the number of bootstrap samples to be generated for confidence interval. It is ignored if “C=0”.

alpha

a positive grid for Gamma shape parameter. alpha must be a numerical vector for positive numbers. A cross-validation will be used to select a unified shape parameter value for the compound Gamma from the specified “alpha” grid. The default “alpha” grid is \(1,2,\ldots,10\).

conf

a positive number \(\le 1\). conf specifies the confidence level for confidence interval. The default is 0.95.

seed

a single value, interpreted as an integer. Seed for random number generation

dis

0 or 1. 1 for on-screen display of the mixture output, and 0 for none.

Author

Ji-Ping Wang, Department of Statistics, Northwestern University

Details

The pcg estimator is computing intensive. The computing of bootstrap confidence interval may take up to a few hours.

References

Wang, J.-P. (2010), Estimating the species richness by a Poisson-Compound Gamma model, 97(3): 727-740

Examples

library(SPECIES)
##load data from the package, 
## \dQuote{butterfly} is the famous butterfly data by Fisher 1943.

data(butterfly)

##output estimate without confidence interval using cutoff t=15
##pcg(butterfly,t=20,C=0,alpha=c(1:10))

##output estimate with confidence interval using cutoff t=15
#pcg(butterfly,t=20,C=1,alpha=c(1:10),b=200)