# Generally Altered, Inflated, Truncated and Deflated Negative Binomial Distribution Density, distribution function, quantile function and random generation for the generally altered, inflated, truncated and deflated negative binomial (GAITD-NB) 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. ```r dgaitdnbinom(x, size.p, munb.p, a.mix = NULL, a.mlm = NULL, i.mix = NULL, i.mlm = NULL, d.mix = NULL, d.mlm = NULL, truncate = NULL, max.support = Inf, pobs.mix = 0, pobs.mlm = 0, pstr.mix = 0, pstr.mlm = 0, pdip.mix = 0, pdip.mlm = 0, byrow.aid = FALSE, size.a = size.p, size.i = size.p, size.d = size.p, munb.a = munb.p, munb.i = munb.p, munb.d = munb.p, log = FALSE) pgaitdnbinom(q, size.p, munb.p, a.mix = NULL, a.mlm = NULL, i.mix = NULL, i.mlm = NULL, d.mix = NULL, d.mlm = NULL, truncate = NULL, max.support = Inf, pobs.mix = 0, pobs.mlm = 0, pstr.mix = 0, pstr.mlm = 0, pdip.mix = 0, pdip.mlm = 0, byrow.aid = FALSE, size.a = size.p, size.i = size.p, size.d = size.p, munb.a = munb.p, munb.i = munb.p, munb.d = munb.p, lower.tail = TRUE) qgaitdnbinom(p, size.p, munb.p, a.mix = NULL, a.mlm = NULL, i.mix = NULL, i.mlm = NULL, d.mix = NULL, d.mlm = NULL, truncate = NULL, max.support = Inf, pobs.mix = 0, pobs.mlm = 0, pstr.mix = 0, pstr.mlm = 0, pdip.mix = 0, pdip.mlm = 0, byrow.aid = FALSE, size.a = size.p, size.i = size.p, size.d = size.p, munb.a = munb.p, munb.i = munb.p, munb.d = munb.p) rgaitdnbinom(n, size.p, munb.p, a.mix = NULL, a.mlm = NULL, i.mix = NULL, i.mlm = NULL, d.mix = NULL, d.mlm = NULL, truncate = NULL, max.support = Inf, pobs.mix = 0, pobs.mlm = 0, pstr.mix = 0, pstr.mlm = 0, pdip.mix = 0, pdip.mlm = 0, byrow.aid = FALSE, size.a = size.p, size.i = size.p, size.d = size.p, munb.a = munb.p, munb.i = munb.p, munb.d = munb.p) ``` ## Arguments - `x, q, p, n, log, lower.tail`: Same meaning as in `rnbinom`. - `size.p, munb.p`: Same meaning as in `rnbinom`. See `Gaitdpois` for generic information. - `size.a, munb.a`: See `Gaitdpois` for generic information. - `size.i, munb.i`: See `Gaitdpois` for generic information. - `size.d, munb.d`: See `Gaitdpois` for generic information. - `truncate, max.support`: See `Gaitdpois` for generic information. - `a.mix, i.mix, d.mix`: See `Gaitdpois` for generic information. - `a.mlm, i.mlm, d.mlm`: See `Gaitdpois` for generic information. - `pobs.mlm, pstr.mlm, byrow.aid`: See `Gaitdpois` for generic information. - `pobs.mix, pstr.mix`: See `Gaitdpois` for generic information. - `pdip.mix, pdip.mlm`: See `Gaitdpois` for generic information. ## Details These functions for the NBD are analogous to the Poisson, hence most details have been put in `Gaitdpois`. The NBD has two possible parameterizations: one involving a probability (argument begins with `prob`) and the other the mean (beginning with `mu`). Only the latter is supported here. For now, arguments such as `prob.p` and `prob.a` are no longer supported. That's because `mu` is more likely to be used by most statisticians than `prob`; see `dnbinom`. ## Warning See `Gaitdpois` about the dangers of too much inflation and/or deflation on GAITD PMFs, and the difficulties detecting such. ## Returns `dgaitdnbinom` gives the density, `pgaitdnbinom` gives the distribution function, `qgaitdnbinom` gives the quantile function, and `rgaitdnbinom` generates random deviates. The default values of the arguments correspond to ordinary `dnbinom`, `pnbinom`, `qnbinom`, `rnbinom` respectively. ## Author(s) T. W. Yee. ## Note Four functions were moved from `VGAM` to `VGAMdata`; they can be seen at `Posnegbin`. It is preferable to use `dgaitdnbinom(x, size, munb.p = munb, truncate = 0)` instead of `dposnbinom(x, size, munb = munb)`, etc. ## See Also `gaitdnbinomial`, `Gaitdpois`, `multinomial`, `Gaitdbinom`, `Gaitdlog`, `Gaitdzeta`. ## Examples ```r size <- 10; xgrid <- 0:25 ivec <- c(5, 6, 10, 14); avec <- c(8, 11); munb <- 10 tvec <- 15; pobs.a <- 0.05; pstr.i <- 0.25 dvec <- 13; pdip.mlm <- 0.03; pobs.mlm <- 0.05 (ddd <- dgaitdnbinom(xgrid, size, munb.p = munb, munb.a = munb + 5, truncate = tvec, pobs.mix = pobs.a, pdip.mlm = pdip.mlm, d.mlm = dvec, pobs.mlm = pobs.a, a.mlm = avec, pstr.mix = pstr.i, i.mix = ivec)) ## Not run: dgaitdplot(c(size, munb), fam = "nbinom", ylab = "Probability", xlab = "x", xlim = c(0, 25), truncate = tvec, pobs.mix = pobs.mix, pobs.mlm = pobs.mlm, a.mlm = avec, all.lwd = 3, pdip.mlm = pdip.mlm, d.mlm = dvec, pstr.mix = pstr.i, i.mix = ivec, deflation = TRUE, main = "GAITD Combo PMF---NB Parent") ## End(Not run) ```

gaitdnbinomUC function