pcg: Poisson-compound Gamma estimator for the species richness In SPECIES: Statistical package for species richness estimation

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

 `1` ```pcg(n,t=35,C=0,alpha=c(1:10),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 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 ≥ 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,…,10. `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.

Details

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

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.

Author(s)

Ji-Ping Wang, Department of Statistics, Northwestern University

References

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

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 ##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) ```

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