Description Usage Arguments Details Value Note Author(s) References Examples

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.

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 |

`t` |
a positive integer. |

`C` |
integer either 0 or 1. It specifies whether bootstrap confidence interval should be calculated. “ |

`method` |
string either “N-P” or “W-L”(default). If |

`b` |
integer. |

`conf` |
a positive number |

`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. |

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.

The function `unpmle`

returns a list of: `Nhat`

, `CI`

(if “`C`

=1”)

`Nhat` |
point estimate of N |

`CI` |
bootstrap confidence interval. |

The unconditional NPML estimator is unstable from either `method='N-P'`

or `method='W-L'`

. Extremely large estimates may occur.
This is also reflected in that the upper confidence bound often greatly vary from different runs of bootstrap procedure. In contrast the penalized NPMLE by `pnpmle`

function is much more stable.

Ji-Ping Wang, Department of Statistics, Northwestern University

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

1 2 3 4 5 6 7 8 9 10 11 12 13 | ```
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)
``` |

Embedding an R snippet on your website

Add the following code to your website.

For more information on customizing the embed code, read Embedding Snippets.