% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/log_likelihood.R
\name{nlogL}
\alias{nlogL}
\alias{nlogL_pois}
\alias{nlogL_nb}
\alias{nlogL_del}
\alias{nlogL_pig}
\alias{nlogL_pb}
\alias{nlogL_pois2}
\alias{nlogL_nb2}
\alias{nlogL_del2}
\alias{nlogL_pig2}
\alias{nlogL_pb2}
\alias{nlogL_zipois}
\alias{nlogL_zinb}
\alias{nlogL_zidel}
\alias{nlogL_zipig}
\alias{nlogL_zipb}
\alias{nlogL_zipois2}
\alias{nlogL_zinb2}
\alias{nlogL_zidel2}
\alias{nlogL_zipig2}
\alias{nlogL_zipb2}
\title{Negative log Likelihood functions for Poisson, negative binomial,
Delaporte, Poisson-inverse Gaussian and Poisson-beta distributions}
\usage{
nlogL_pois(data, par.pois)

nlogL_nb(data, par.nb)

nlogL_del(data, par.del)

nlogL_pig(data, par.pig)

nlogL_pb(data, par.pb)

nlogL_pois2(data, par.pois2)

nlogL_nb2(data, par.nb2)

nlogL_del2(data, par.del2)

nlogL_pig2(data, par.pig2)

nlogL_pb2(data, par.pb2)

nlogL_zipois(data, par.zipois)

nlogL_zinb(data, par.zinb)

nlogL_zidel(data, par.zidel)

nlogL_zipig(data, par.zipig)

nlogL_zipb(data, par.zipb)

nlogL_zipois2(data, par.zipois2)

nlogL_zinb2(data, par.zinb2)

nlogL_zidel2(data, par.zidel2)

nlogL_zipig2(data, par.zipig2)

nlogL_zipb2(data, par.zipb2)
}
\arguments{
\item{data}{Vector containing the discrete observations}

\item{par.pois}{Scalar containing the lambda parameter
of the Poisson distribution}

\item{par.nb}{Vector of length 2, containing the size and the mu
parameter of the negative binomial distribution}

\item{par.del}{Vector of length 3, containing the mu, sigma and the nu
parameter of the Delaporte distribution}

\item{par.pig}{Vector of length 2, containing the mu and the sigma
parameter of the Poisson-inverse Gaussian distribution}

\item{par.pb}{Vector of length 3, containing the alpha, beta
and c parameter of the Poisson-beta distribution}

\item{par.pois2, par.nb2, par.del2, par.pig2, par.pb2}{Vector containing the parameters
of the two mixing distributions. First entry represents the
fraction of the first distribution, followed by all parameters
of the first, then all of the second distribution.}

\item{par.zipois, par.zinb, par.zidel, par.zipig, par.zipb}{Vector containing the respective
zero-inflated distribution parameters. The additional first
entry is the inflation parameter for all cases.}

\item{par.zipois2, par.zinb2, par.zidel2, par.zipig2, par.zipb2}{Parameters for the zero-inflated
two population model.}
}
\description{
The negative log Likelihood functions for Poisson, negative binomial,
Delaporte, Poisson-inverse Gaussian and Poisson-beta distributions.
Mixing two distributions of the same kind and/or adding zero-inflation
allows to take characteristics of real data into account.
Additionally, one population and two population mixtures - with and
without zero-inflation - allow distribution fitting of the Poisson,
negative binomial, Delaporte, Poisson-inverse Gaussian and the
Poisson-beta distribution.
}
\details{
Functions nlogL_pois, nlogL_nb, nlogL_del, nlogL_pig, nlogL_pb compute the negative
log-likelihood of Poisson, negative binomial, Poisson-inverse Gaussian and
the Poisson-beta distributions given the data.
Functions nlogL_pois2, nlogL_nb2, nlogL_del2, nlogL_pig2 and nlogL_pb2 compute the negative
log-likelihood values for a two population mixture of distributions whereas
nlogL_zipois, nlogL_zinb, nlogL_zidel, nlogL_zipig, nlogL_zipb compute the same for the
zero-inflated distributions. Furthermore, nlogL_zipois2, nlogL_zinb2, nlogL_zidel2,
nlogL_zipig2 and nlogL_zipb2 are for two population mixtures with zero-inflation.
}
\examples{
x <- rpois(100, 11)
nl1 <- nlogL_pois(x, 11)
nl2 <- nlogL_pois(x, 13)
x <- rnbinom(100, size = 13, mu = 9)
nl <- nlogL_nb(x, c(13, 9))
x <- gamlss.dist::rDEL(100, mu = 5, sigma = 0.2, nu= 0.5)
nl <- nlogL_del(x, c(5, 0.2, 0.5))
x <- gamlss.dist::rPIG(100, mu = 5, sigma = 0.2)
nl <- nlogL_pig(x, c(5, 0.2))
x <- rpb(n = 1000, alpha=5, beta= 3, c=20)
nl <- nlogL_pb(x, c(5, 3, 20))
s <- sample(x = c(0,1), size = 100, replace = TRUE, prob = c(0.3,0.7))
x <- s*rpois(100, 7) + (1-s)*rpois(100, 13)
nl <- nlogL_pois2(x, c(0.3, 13, 7))
s <- sample(x = c(0,1), size = 100, replace = TRUE, prob = c(0.3,0.7))
x <- s*rnbinom(100, size = 13, mu = 9) + (1-s)*rnbinom(100, size = 17, mu = 29)
nl <- nlogL_nb2(x, c(0.3, 17, 29, 13, 9))
s <- sample(x = c(0,1), size = 100, replace = TRUE, prob = c(0.3,0.7))
x <- s * gamlss.dist::rDEL(100, mu = 5, sigma = 0.2, nu = 0.5) +
     (1 - s) * gamlss.dist::rDEL(100, mu = 20, sigma = 2, nu = 0.1)
nl <- nlogL_del2(x, c(0.7,5, 0.2, 20, 2))
s <- sample(x = c(0,1), size = 100, replace = TRUE, prob = c(0.3,0.7))
x <- s * gamlss.dist::rPIG(100, mu = 5, sigma = 0.2) +
     (1 - s) * gamlss.dist::rPIG(100, mu = 20, sigma = 2)
nl <- nlogL_pig2(x, c(0.7, 5, 0.2, 20, 2))
s <- sample(x = c(0,1), size = 100, replace = TRUE, prob = c(0.3,0.7))
x <- s*rpb(100, 5, 3, 20) + (1-s)*rpb(100, 7, 13, 53)
nl <- nlogL_pb2(x, c(0.7, 7, 13, 53, 5, 3, 20))
x <- c(rep(0, 10), rpois(90, 7))
nl <- nlogL_zipois(x, c(0.1, 7))
x <- c(rep(0,10), rnbinom(90, size = 13, mu = 9))
nl <- nlogL_zinb(x, c(0.1, 13, 9))
x <- c(rep(0,10), gamlss.dist::rDEL(90, mu = 13, sigma = 2, nu = 0.5))
nl <- nlogL_zidel(x, c(0.1, 13, 2, 0.5))
x <- c(rep(0,10), gamlss.dist::rPIG(90, mu = 13, sigma = 2))
nl <- nlogL_zipig(x, c(0.1, 13, 2))
x <- c(rep(0, 10), rpb(n = 90, alpha=5, beta= 3, c=20))
nl <- nlogL_zipb(x, c(0.1, 5, 3, 20))
s <- sample(x = c(0, 1), size = 90, replace = TRUE, prob = c(0.3, 0.7))
x <- c(rep(0, 10), s * rpois(90, 7) + (1 - s) * rpois(90, 13))
nl1 <- nlogL_zipois2(x, c(0.1, 0.63, 7, 13))
s <- sample(x = c(0, 1), size = 90, replace = TRUE, prob = c(0.3, 0.7))
x <- c(rep(0, 10), s * rnbinom(90, size = 13, mu = 9) + (1 - s) * rnbinom(90, size = 17, mu = 29))
nl <- nlogL_zinb2(x, c(0.1, 0.63, 13, 9, 17, 29))
s <- sample(x = c(0, 1), size = 90, replace = TRUE, prob = c(0.3, 0.7))
x <- c(rep(0, 10), s * gamlss.dist::rDEL(90, mu = 13, sigma = 9, nu = 0.5) +
             (1 - s) * gamlss.dist::rDEL(90, mu = 17, sigma = 29, nu = 0.1))
nl <- nlogL_zidel2(x, c(0.1, 0.63, 13, 9, 0.5, 17, 29, 0.1))
s <- sample(x = c(0,1), size = 90, replace = TRUE, prob = c(0.3, 0.7))
x <- c(rep(0, 10), s * gamlss.dist::rPIG(90, mu = 13, sigma = 0.2) +
               (1-s) * gamlss.dist::rPIG(90, mu = 17, sigma = 2))
nl <- nlogL_zipig2(x, c(0.1, 0.63, 13, 0.2, 17, 2))
s <- sample(x = c(0,1), size = 90, replace = TRUE, prob = c(0.3,0.7))
x <- c(rep(0,10), s*rpb(90, 5, 3, 20) + (1-s)*rpb(90, 7, 13, 53))
nl <- nlogL_zipb2(x, c(0.1, 0.63, 7, 13, 53, 5, 3, 20))
}
\keyword{Poisson-beta}
\keyword{binomial}
\keyword{likelihood}
\keyword{negative}