Penalized conditional NPML estimator for species richness

Description

This function calculate the penalized conditional NPML estimator of the species number by Wang and Lindsay 2005. This estimator was based on the conditional likelihood of a Poisson mixture model. A penalty term was introduced into the model to prevent the boundary problem discussed in Wang and Lindsay 2008. The confidence interval is calculated based on a bootstrap procedure. A Fortran function is called to for the computing.

Usage

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pnpmle(n,t=15,C=0,b=200,seed=NULL,conf=0.95,dis=1)

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…; 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 to define the relatively less abundant species to be used in estimation of the Poisson mixture. The default value is t=15. The recommendation is to use \code{t} ≥ 10.

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”.

conf

a positive number ≤ 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.

Value

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

Nhat

Point estimate of N

CI

bootstrap confidence interval

Author(s)

Ji-Ping Wang,Department of Statistics, Northwestern University

References

Wang, J.-P. Z. and Lindsay, B. G. ,2005, A penalized nonparametric maximum likelihood approach to species richness estimation. Journal of American Statistical Association, 2005,100(471):942-959

Wang, J.-P., and Lindsay, B.G., 2008, An exponential partial prior for improving NPML estimation for mixtures, Statistical Methodology, 2008,5:30-45

Examples

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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
#pnpmle(butterfly,t=15,C=0)

##output estimate with confidence interval using cutoff t=15
#pnpmle(butterfly,t=15,C=1, b=200)