VGAM: gaitbinomUC – R documentation

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gaitbinomUC

Generally–Altered, –Inflated and –Truncated Binomial Distribution

Description

Density, distribution function, quantile function and random generation for the generally–altered, –inflated and –truncated 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–Binom(size.p, prob.p)–Binom(size.a, prob.a)–MLM–Binom(size.i, prob.i)–MLM, and it is also known as the GAIT-Binom PNP combo where PNP stands for parametric and nonparametric.

Usage

dgaitbinom(x, size.p, prob.p,
           alt.mix = NULL, alt.mlm = NULL,
           inf.mix = NULL, inf.mlm = NULL, truncate = NULL,
           max.support = NULL, 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,
           deflation = FALSE, log = FALSE)
pgaitbinom(q, size.p, prob.p,
           alt.mix = NULL, alt.mlm = NULL,
           inf.mix = NULL, inf.mlm = NULL, truncate = NULL,
           max.support = NULL, 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,
           lower.tail = TRUE)
qgaitbinom(p, size.p, prob.p,
           alt.mix = NULL, alt.mlm = NULL,
           inf.mix = NULL, inf.mlm = NULL, truncate = NULL,
           max.support = NULL, 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)
rgaitbinom(n, size.p, prob.p,
           alt.mix = NULL, alt.mlm = NULL,
           inf.mix = NULL, inf.mlm = NULL, truncate = NULL,
           max.support = NULL, 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)

Arguments

`x, q, p, n, log, lower.tail`	Same meaning as in `Binomial`.
`size.p, prob.p`	Same meaning as in `Binomial`. See `Gaitpois` for generic information.
`size.a, prob.a`	See `Gaitpois` for generic information.
`size.i, prob.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 GAIT binomial distribution are analogous to the GAIT Poisson, hence most details have been put in Gaitpois.

Value

dgaitbinom gives the density, pgaitbinom gives the distribution function, qgaitbinom gives the quantile function, and rgaitbinom generates random deviates. The default values of the arguments correspond to ordinary dbinom, pbinom, qbinom, rbinom respectively.

Note

Functions Posbinom have been moved to VGAMdata. It is better to use dgaitbinom(x, size, prob, truncate = 0) instead of dposbinom(x, size, prob), etc.

Author(s)

T. W. Yee.

Examples

size <- 20
ivec <- c(6, 10); avec <- c(8, 11); prob <- 0.5; xgrid <- 0:25
tvec <- 14; pobs.a <- 0.05; pstr.i <- 0.15
(ddd <- dgaitbinom(xgrid, size, prob.p = prob, prob.a = prob + 5,
   truncate = tvec, 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---Binomial 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(h = c(pobs.a, pstr.i, 0:1), col = 'gray', lty = "dashed")
lines(xgrid, dbinom(xgrid, size, prob), 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