R: MLE of count data

MLE of count data (univariate discrete distributions) {Rfast} | R Documentation

## MLE of count data

### Description

MLE of count data.

### Usage

    zip.mle(x, tol = 1e-09)
    ztp.mle(x, tol = 1e-09)
    negbin.mle(x, type = 1, tol = 1e-09)
    binom.mle(x, N = NULL, tol = 1e-07)
    borel.mle(x)
    geom.mle(x, type = 1)
    logseries.mle(x, tol = 1e-09)
    poisson.mle(x)
    betageom.mle(x, tol = 1e-07)
    betabinom.mle(x, N, tol = 1e-07)

### Arguments

`x` | A vector with discrete valued data.
`type` | This argument is for the negative binomial and the geometric distribution. In the negative binomial you can choose which way your prefer. Type 1 is for smal sample sizes, whereas type 2 is for larger ones as is faster. For the geometric it is related to its two forms. Type 1 refers to the case where the minimum is zero and type 2 for the case of the minimum being 1.
`N` | This is for the binomial distribution only, specifying the total number of successes. If NULL, it is sestimated by the data. It can also be a vector of successes.
`tol` | The tolerance level up to which the maximisation stops set to 1e-09 by default.

### Details

Instead of maximising the log-likelihood via a numerical optimiser we used a Newton-Raphson algorithm which is faster.

See wikipedia for the equation to be solved in the case of the zero inflated distribution. https://en.wikipedia.org/wiki/Zero-inflated_model. In order to avoid negative values we have used link functions, log for the lambda and logit for the π as suggested by Lambert (1992). As for the zero truncated Poisson see https://en.wikipedia.org/wiki/Zero-truncated_Poisson_distribution.

zip.mle is for the zero inflated Poisson, whereas ztp.mle is for the zero truncated Poisson distribution.

### Value

The following list is not inclusive of all cases. Different functions have different names. In general a list including:

`mess` | This is for the negbin.mle only. If there is no reason to use the negative binomial distribution a message will appear, otherwise this is NULL.
`iters` | The number of iterations required for the Newton-Raphson to converge.
`loglik` | The value of the maximised log-likelihood.
`prob` | The probability parameter of the distribution. In some distributions this argument might have a different name. For example, param in the zero inflated Poisson.

### Author(s)

Michail Tsagris

R implementation and documentation: Michail Tsagris <mtsagris@uoc.gr> and Manos Papadakis <papadakm95@gmail.com>.

### References

Lambert Diane (1992). Zero-Inflated Poisson Regression, with an Application to Defects in Manufacturing. Technometrics. 34 (1): 1-14

Johnson Norman L., Kotz Samuel and Kemp Adrienne W. (1992). Univariate Discrete Distributions (2nd ed.). Wiley

### See Also

`poisson_only, colrange`

### Examples

    x <- rpois(100, 2)
    res<-zip.mle(x)
    res<-poisson.mle(x)
    ## small difference in the two log-likelihoods as expected.

    x <- rpois(100, 10)
    x[x == 0 ] <- 1
    res<-ztp.mle(x)
    res<-poisson.mle(x)
    ## significant difference in the two log-likelihoods.

    x <- rnbinom(100, 10, 0.6)
    res<-poisson.mle(x)
    res<-negbin.mle(x)

[Package Rfast version 2.0.4 Index]