rnbinom.inar1: Generate Time Series with Negative Binomial Distribution and...
In spass: Study Planning and Adaptation of Sample Size

Description Usage Arguments Details Value Source References Examples

rnbinom.inar1 generates one or more independent time series following the NB-INAR(1) model. The generated data has negative binomial marginal distribution and an autoregressive covariance structure.

1	rnbinom.inar1(n, size, mu, rho, tp)

`n`	number of observations. If length(n) > 1, the length is taken to be the number required.
`size`	dispersion parameter (the shape parameter of the gamma mixing distribution). Must be strictly positive, need not be integer.
`mu`	parametrization via mean: see 'Details'.
`rho`	correlation coefficient of the underlying autoregressive correlation structure. Must be between 0 and 1.
`tp`	number of observed time points.

The generated marginal negative binomial distribution with mean mu = μ and size = η has density

(μ/(μ+η))^x Γ(x + η)/(Γ(x+1)Γ(η)) (η/(μ+η))^η

for 0 < μ, 0 < η and x=0, 1, 2, ....

Within the NB-INAR(1) model, the correlation between two time points t and s for rho = ρ is given through

ρ^|t-s|

for 0 ≤ ρ ≤ 1.

rnbinom.inar1 returns a matrix of dimension n x tp with marginal negative binomial distribution with mean mu and dispersion parameter size, and an autoregressive correlation structure between time points.

rnbinom.inar1 computes a reparametrization of the NB-INAR(1) model by McKenzie 1986 using code contributed by Thomas Asendorf.

McKenzie Ed (1986), Autoregressive Moving-Average Processes with Negative-Binomial and Geometric Marginal Distributions. Advances in Applied Probability Vol. 18, No. 3, pp. 679-705.

set.seed(8)
random<-rnbinom.inar1(n=1000, size=0.6, mu=2, rho=0.8, tp=6)
cor(random)

#Check the marginal distribution of time point 3
plot(table(random[,3])/1000, xlab="Probability", ylab="Observation")
lines(0:26, dnbinom(0:26, mu=2, size=0.6), col="red")
legend("topright",legend=c("Theoretical Marginal Distribution", "Observed Distribution"), 
col=c("red", "black"), lty=1, lwd=c(1,2))