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.
1 
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. 
C 
integer either 0 or 1. It specifies whether bootstrap confidence interval should be calculated. “ 
b 
integer. 
conf 
a positive number ≤ 1. 
seed 
a single value, interpreted as an integer. Seed for random number generation 
dis 
0 or 1. 1 for onscreen display of the mixture output, and 0 for none. 
The function pnpmle
returns a list of: Nhat
, CI
(if “C
=1”).
Nhat 
Point estimate of 
CI 
bootstrap confidence interval 
JiPing Wang,Department of Statistics, Northwestern University
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):942959
Wang, J.P., and Lindsay, B.G., 2008, An exponential partial prior for improving NPML estimation for mixtures, Statistical Methodology, 2008,5:3045
1 2 3 4 5 6 7 8 9 10 11  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)

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