VGAM (version 1.1-4)

Gaitnbinom: Generally--Altered, --Inflated and --Truncated Negative Binomial Distribution

Description

Density, distribution function, quantile function and random generation for the generally--altered, --inflated and --truncated negative binomial distribution. Both parametric and nonparametric variants are supported; these are based on finite mixtures of the parent with itself and the multinomial logit model (MLM) respectively. Altogether it can be abbreviated as GAAIIT--NB(size.p, munb.p)--NB(size.a, munb.a)--MLM--NB(size.i, munb.i)--MLM, and it is also known as the GAIT-NB PNP combo where PNP stands for parametric and nonparametric.

Usage

dgaitnbinom(x, size.p, prob.p = NULL, munb.p = NULL,
            alt.mix = NULL, alt.mlm = NULL,
            inf.mix = NULL, inf.mlm = NULL, truncate = NULL,
            max.support = Inf, pobs.mix = 0, pobs.mlm = 0,
            pstr.mix = 0, pstr.mlm = 0, byrow.ai = FALSE,
            size.a = size.p, size.i = size.p,
            prob.a = prob.p, prob.i = prob.p,
            munb.a = munb.p, munb.i = munb.p,
            deflation = FALSE, log = FALSE)
pgaitnbinom(q, size.p, prob.p = NULL, munb.p = NULL,
            alt.mix = NULL, alt.mlm = NULL,
            inf.mix = NULL, inf.mlm = NULL, truncate = NULL,
            max.support = Inf, pobs.mix = 0, pobs.mlm = 0,
            pstr.mix = 0, pstr.mlm = 0, byrow.ai = FALSE,
            size.a = size.p, size.i = size.p,
            prob.a = prob.p, prob.i = prob.p,
            munb.a = munb.p, munb.i = munb.p,
            lower.tail = TRUE)
qgaitnbinom(p, size.p, prob.p = NULL, munb.p = NULL,
            alt.mix = NULL, alt.mlm = NULL,
            inf.mix = NULL, inf.mlm = NULL, truncate = NULL,
            max.support = Inf, pobs.mix = 0, pobs.mlm = 0,
            pstr.mix = 0, pstr.mlm = 0, byrow.ai = FALSE,
            size.a = size.p, size.i = size.p,
            prob.a = prob.p, prob.i = prob.p,
            munb.a = munb.p, munb.i = munb.p)
rgaitnbinom(n, size.p, prob.p = NULL, munb.p = NULL,
            alt.mix = NULL, alt.mlm = NULL,
            inf.mix = NULL, inf.mlm = NULL, truncate = NULL,
            max.support = Inf, pobs.mix = 0, pobs.mlm = 0,
            pstr.mix = 0, pstr.mlm = 0, byrow.ai = FALSE,
            size.a = size.p, size.i = size.p,
            prob.a = prob.p, prob.i = prob.p,
            munb.a = munb.p, munb.i = munb.p)

Arguments

x, q, p, n, log, lower.tail

Same meaning as in rnbinom.

size.p, prob.p, munb.p

Same meaning as in rnbinom. See Gaitpois for generic information.

size.a, prob.a, munb.a

See Gaitpois for generic information.

size.i, prob.i, munb.i

See Gaitpois for generic information.

truncate, max.support

See Gaitpois for generic information.

alt.mix, inf.mix

See Gaitpois for generic information.

alt.mlm, inf.mlm

See Gaitpois for generic information.

pobs.mlm, pstr.mlm, byrow.ai

See Gaitpois for generic information.

pobs.mix, pstr.mix

See Gaitpois for generic information.

deflation

See Gaitpois for generic information.

Value

dgaitnbinom gives the density, pgaitnbinom gives the distribution function, qgaitnbinom gives the quantile function, and rgaitnbinom generates random deviates. The default values of the arguments correspond to ordinary dnbinom, pnbinom, qnbinom, rnbinom respectively.

Details

These functions for the NBD are analogous to the Poisson, hence most details have been put in Gaitpois. The NBD has two possible parameterizations: one involving a probability (argument begins with prob) and the other the mean (beginning with mu). Because NegBinomial only allows one of these arguments to be used, the functions here have the same behaviour.

See Also

Gaitpois, multinomial, Gaitbinom, Gaitlog, Gaitzeta.

Examples

# NOT RUN {
size <- 10
ivec <- c(6, 14); avec <- c(8, 11); munb <- 10; xgrid <- 0:25
tvec <- 15; max.support <- 20; pobs.a <- 0.05; pstr.i <- 0.25
(ddd <- dgaitnbinom(xgrid, size, munb.p = munb, munb.a = munb + 5,
   truncate = tvec, max.support = max.support, pobs.mix = pobs.a,
   pobs.mlm = pobs.a, alt.mlm = avec,
   pstr.mix = pstr.i, inf.mix = ivec))
# }
# NOT RUN {
plot(xgrid, ddd, type = "n", ylab = "Probability", xlab = "x",
              main = "GAIT PNP Combo PMF---NB Parent")
mylwd <- 1
abline(v = avec, col = 'blue', lwd = mylwd)
abline(v = ivec, col = 'purple', lwd = mylwd)
abline(v = tvec, col = 'tan', lwd = mylwd)
abline(v = max.support, col = 'magenta', lwd = mylwd)
abline(h = c(pobs.a, pstr.i, 0:1), col = 'gray', lty = "dashed")
lines(xgrid, dnbinom(xgrid, size, mu = munb), col = 'gray', lty = 2)
lines(xgrid, ddd, type = "h", col = "pink", lwd = 7)  # GAIT PNP combo PMF
points(xgrid[ddd == 0], ddd[ddd == 0], pch = 16)  
# }