FHUBdiscrete {gcKrig}

Compute the Frechet Hoeffding Upper Bound for Given Discrete Marginal Distributions

Description

This function implemented the method of computing the Frechet Hoeffding upper bound for discrete marginals described in Nelsen (1987), which can only be applied to discrete marginals. Four commonly used marginal distributions were implemented. The distribution "nb" (negative binomial) and "zip" (zero-inflated Poisson) are parameterized in terms of the mean and overdispersion, see Han and De Oliveira (2016).

Usage

FHUBdiscrete(marg1, marg2, mu1, mu2, od1 = 0, od2 = 0, binomial.size1 = 1,
  binomial.size2 = 1)

Arguments

marg1

name of the first discrete marginal distribution. Should be one of the "poisson", "zip", "nb" or "binomial".

marg2

name of the second discrete marginal distribution. Should be one of the "poisson", "zip", "nb" or "binomial".

mu1

mean of the first marginal distribution. If binomial then it is n_1 p_1.

mu2

mean of the second marginal distribution. If binomial then it is n_2 p_2.

od1

the overdispersion parameter of the first marginal. Only used when marginal distribution is either "zip" or "nb".

od2

the overdispersion parameter of the second marginal. Only used when marginal distribution is either "zip" or "nb".

binomial.size1

the size parameter (number of trials) when marg1 = "binomial".

binomial.size2

the size parameter (number of trials) when marg2 = "binomial".

Value

A scalar denoting the Frechet Hoeffding upper bound of the two specified marginal.

Author(s)

Zifei Han [e-mail]

References

Nelsen, R. (1987) Discrete bivariate distributions with given marginals and correlation. Communications in Statistics Simulation and Computation, 16:199-208.

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.

Han, Z. and De Oliveira, V. (2018) gcKrig: An R Package for the Analysis of Geostatistical Count Data Using Gaussian Copulas. Journal of Statistical Software, 87(13), 1–32. doi: 10.18637/jss.v087.i13.

Examples

## Not run: 

FHUBdiscrete(marg1 = 'nb', marg2 = 'zip',mu1 = 10, mu2 = 2, od1 = 2, od2 = 0.2)
FHUBdiscrete(marg1 = 'binomial', marg2 = 'zip', mu1 = 10, mu2 = 4, binomial.size1 = 25, od2 = 2)
FHUBdiscrete(marg1 = 'binomial', marg2 = 'poisson', mu1 = 0.3, mu2 = 20, binomial.size1 = 1)

NBmu = seq(0.01, 30, by = 0.02)
 fhub <- c()
 for(i in 1:length(NBmu)){
  fhub[i] = FHUBdiscrete(marg1 = 'nb', marg2 = 'nb',mu1 = 10, mu2 = NBmu[i], od1 = 0.2, od2 = 0.2)
}
plot(NBmu, fhub, type='l')

## End(Not run)