R: Fitting a zero-truncated negative binomial distribution

preseqR.ztnb.em {preseqR} | R Documentation

## Fitting a zero-truncated negative binomial distribution

### Description

`preseqR.ztnb.em` fits a zero-truncated negative binomial (ZTNB) distribution to the initial sample. Since the species with zero observations are missed in the sample, an EM algorithm is used to estimate the parameters assuming the number of individuals for each species follows a Negative Binomial distribution with the zero counts as a missing latent data.

### Usage

    preseqR.ztnb.em(n, size = SIZE.INIT, mu = MU.INIT)

### Arguments

`n` | A two-column matrix. The first column is the frequency j = 1,2,…; and the second column is N_j, the number of species with each species represented exactly j times in the initial sample. The first column must be sorted in an ascending order.
`size` | A positive double setting the initial value of the parameter `size` in a negative binomial distribution for the EM algorithm. Default value is 1.
`mu` | A positive double setting the initial value of the parameter `mu` in a negative binomial distribution for the EM algorithm. Default value is 0.5.

### Details

See the supplement of Daley and Smith (2013).

### Value

`size` | The estimate of the parameter `size` in the negative binomial.
`mu` | The estimate of the parameter `mu` in the negative binomial.
`loglik` | Log-likelihood under estimated ZTNB.

### Author(s)

Chao Deng

### Examples

    ## load library
    library(preseqR)

    ## import data
    data(FisherButterfly)

    ## print the parameters of a fitting negative binomial distribution
    preseqR.ztnb.em(FisherButterfly)

[Package preseqR version 4.0.0 Index]