This function calculate the unconditional NPML estimator of the species number by Norris and Pollock 1996, 1998. This estimator was obtained from the full likelihood based on a Poisson mixture model. The confidence interval is calculated based on a bootstrap procedure.
unpmle(n,t=15,C=0,method="W-L",b=200,conf=.95,seed=NULL,dis=1)The function unpmle returns a list of: Nhat, CI (if “C=1”)
point estimate of N
bootstrap confidence interval.
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.
a positive integer. t specifies the cutoff value to define the relatively less abundant species to be used in estimation. The default value for t=15. The estimator is fairly insensitive to the choice of t. The recommendation is
to use \(t \ge 10\).
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.
string either “N-P” or “W-L”(default). If method=“N-P”, unconditional NPMLE will be used using an algorithm by Bonhing and Schon (2005).
Sometimes this method can be extremely slow. Alternatively one can use method “W-L”, an approximate method (but with high precision and much faster) by Wang and Lindsay 2005.
integer. b specifies the number of bootstrap samples for confidence interval. It is ignored if “C=0”.
a positive number \(\le 1\). conf specifies the confidence level for confidence interval. The default is 0.95.
a single value, interpreted as an integer. Seed for random number generation
0 or 1. 1 for on-screen display of the mixture output, and 0 for none.
Ji-Ping Wang, Department of Statistics, Northwestern University
The computing is intensive if method=“N-P” is used particularly when extrapolation is large.
It may takes hours to compute the bootstrap confidence interval. If method=“W-L” is used, computing usually
is much much faster. Estimates from both methods are often identical.
Norris, J. L. I., and Pollock, K. H. (1996), Nonparametric MLE Under Two Closed Capture-Recapture Models With Heterogeneity, Biometrics, 52,639-649.
Norris, J. L. I., and Pollock, K. H.(1998), Non-Parametric MLE for Poisson Species Abundance Models Allowing for Heterogeneity Between Species, Environmental and Ecological Statistics, 5, 391-402.
Bonhing, D. and Schon, D., (2005), Nonparametric maximum likelihood estimation of population size based on the counting distribution, Journal of the Royal Statistical Society, Series C: Applied Statistics, 54, 721-737.
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
library(SPECIES)
##load data from the package,
## "butterfly" is the famous butterfly data by Fisher 1943.
data(butterfly)
##output estimate without confidence interval using cutoff t=15
#unpmle(butterfly,t=15,C=0)
##output estimate with confidence interval using cutoff t=15
#unpmle(butterfly,t=15,C=1,b=200)
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