R: Generally-Altered, -Inflated and -Truncated Negative Binomial...

Gaitnbinom.mlm {VGAM} | R Documentation

## Generally–Altered, –Inflated and –Truncated Negative Binomial Distribution (GAIT–NB–MLM–MLM)

### Description

Density, distribution function, quantile function and random generation for the generally–altered, –inflated and –truncated negative binomial distribution, based on the multinomial logit model (MLM). This distribution is sometimes abbreviated as GAIT–NB–MLM–MLM.

### Usage

    dgaitnbinom.mlm(x, size, prob = NULL, munb = NULL, alter = NULL,
                    inflate = NULL, truncate = NULL, max.support = Inf,
                    pobs.a = 0, pstr.i = 0, byrow.arg = FALSE,
                    log.arg = FALSE)
    pgaitnbinom.mlm(q, size, prob = NULL, munb = NULL, alter = NULL,
                    inflate = NULL, truncate = NULL, max.support = Inf,
                    pobs.a = 0, pstr.i = 0, byrow.arg = FALSE)
    qgaitnbinom.mlm(p, size, prob = NULL, munb = NULL, alter = NULL,
                    inflate = NULL, truncate = NULL, max.support = Inf,
                    pobs.a = 0, pstr.i = 0, byrow.arg = FALSE)
    rgaitnbinom.mlm(n, size, prob = NULL, munb = NULL, alter = NULL,
                    inflate = NULL, truncate = NULL, max.support = Inf,
                    pobs.a = 0, pstr.i = 0, byrow.arg = FALSE)

### Arguments

`x, q, p, n, log.arg` | Same meaning as in `NegBinomial`.
`size, prob, munb` | Same meaning as in `NegBinomial`, i.e., for an ordinary negative binomial distribution. Argument `mu` has been renamed to `munb` to emphasize that it refers to the negative binomial mean. Only one of `prob` and `munb` should be specified. Short vectors are recycled.
`alter, inflate, truncate` | Se `Gaitpois`.
`pstr.i, byrow.arg` | See `Gaitpois`.
`pobs.a, max.support` | See `Gaitpois`.

### Details

Largely similar to `Gaitpois` except a negative binomial distribution replaces the Poisson distribution. Special cases of these functions include `dposnegbin`, `dzanegbin`, `dzinegbin`, `pposnegbin`, `pzanegbin`, `pzinegbin`, `qposnegbin`, `qzanegbin`, `qzinegbin`, `rposnegbin`, `rzanegbin`, `rzinegbin` corresponding to the special value 0. However, now arguments `alter`, `inflate` and `truncate` have been supplied in one function.

### Value

`dgaitnbinom.mlm` gives the density (PMF), `pgaitnbinom.mlm` gives the distribution function, `qgaitnbinom.mlm` gives the quantile function, and `rgaitnbinom.mlm` generates random deviates. The default values of the arguments correspond to ordinary `dnegbin`, `pnegbin`, `qnegbin`, `rnegbin` respectively.

### Author(s)

T. W. Yee.

### See Also

`gatnbinomial.mlm`, `Gaitpois`, `NegBinomial`.

### Examples

    avec <- c(5, 10)   # Alter these (special) values
    ivec <- c(15, 20)  # Inflate these (special) values
    tvec <- 0          # Truncate this (special) value
    pobs.a <- c(0.1, 0.2)
    pstr.i <- c(0.1, 0.1); size <- 3; munb <- 15; x <- 0:22
    y <- rgaitnbinom.mlm(1000, size, munb = munb, alter = avec,
                         inflate = ivec, truncate = tvec, max.support = 20,
                         pstr.i = pstr.i, pobs.a = pobs.a, byrow = TRUE)
    table(y)
    (pmf <- dgaitnbinom.mlm(x, size, munb = munb, alter = avec,
                            inflate = ivec, truncate = tvec, max.support = 20,
                            pstr.i = pstr.i, pobs.a = pobs.a, byrow = TRUE))
    ## Not run:  plot(x, pmf, type = "h", col = "blue", las = 1,
                   main = "Heaped data that is also upper-truncated")
    ## End(Not run)

[Package VGAM version 1.1-3 Index]