# pnpmle: Penalized conditional NPML estimator for species richness In SPECIES: Statistical package for species richness estimation

## 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

 `1` ```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

 ``` 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) ```

SPECIES documentation built on May 30, 2017, 12:31 a.m.