Description Usage Arguments Value Author(s) References Examples

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.

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. “ |

`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 function `pnpmle`

returns a list of: `Nhat`

, `CI`

(if “`C`

=1”).

`Nhat` |
Point estimate of |

`CI` |
bootstrap confidence interval |

Ji-Ping Wang,Department of Statistics, Northwestern University

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

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)
``` |

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