# Penalized conditional NPML estimator for species richness

### 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 |

### 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 |

`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 |

`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 |

`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)
``` |