VGAM: gaitnbinomUC – R documentation

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gaitnbinomUC

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.

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.

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.

Note

Four functions were moved from VGAM to VGAMdata; they can be seen at Posnegbin. It is better to use dgaitnbinom(x, size, munb.p = munb, truncate = 0) instead of dposnbinom(x, size, munb = munb), etc.

Author(s)

T. W. Yee.

Examples

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)  
## End(Not run)

VGAM

Vector Generalized Linear and Additive Models

v1.1-5

GPL-3

Authors

Thomas Yee [aut, cre], Cleve Moler [ctb] (author of several LINPACK routines)

Initial release

2021-01-13