negbin.gc {gcKrig}

The Negative Binomial Marginal of Class marginal.gc

Description

The negative binomial marginal parameterized in terms of its mean and overdispersion.

By default, this function is used for likelihood inference and spatial prediction in functions mlegc and predgc of the package gcKrig. When all marginal parameters are given, the function is used for simulation and computing correlation in a trans-Gaussian random field in functions simgc and corrTG.

Usage

negbin.gc(link = "log", mu = NULL, od = NULL)

Arguments

link

the model link function.

mu

a non-negative scalar of the mean parameter.

od

a non-negative scalar of the overdispersion parameter.

Details

The negative binomial distribution with parameters mu = a and od = 1/b has density

\frac{\Gamma(y+b)}{\Gamma(b)y!} \Big(\frac{b}{b+a}\Big)^b \Big(1 - \frac{b}{b+a}\Big)^y

which is called NB2 by Cameron and Trivedi (2013). Under this parameterization, var(Y)= mu + od*mu^2, where mu is the mean parameter and od is the overdispersion parameter. For more details see Han and De Oliveira (2016).

Value

An object of class marginal.gc representing the marginal component.

Author(s)

Zifei Han [e-mail]

References

Cameron,A.C. and Trivedi,P.K. (2013) Regression Analysis of Count Data. Cambridge University Press, 2nd Edition.

Han, Z. and De Oliveira, V. (2016) On the correlation structure of Gaussian copula models for geostatistical count data. Australian and New Zealand Journal of Statistics, 58:47-69.

See Also

marginal.gc, beta.gc, binomial.gc, gm.gc, gaussian.gc, poisson.gc, weibull.gc, zip.gc