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

Gaitbinom.mlm {VGAM} | R Documentation

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

### Description

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

### Usage

    dgaitbinom.mlm(x, size, prob, alter = NULL, inflate = NULL,
                     truncate = NULL, pobs.a = 0, pstr.i = 0,
                     byrow.arg = FALSE, log.arg = FALSE, .errorcheck = TRUE)
    pgaitbinom.mlm(q, size, prob, alter = NULL, inflate = NULL,
                     truncate = NULL, pobs.a = 0, pstr.i = 0,
                     byrow.arg = FALSE, .errorcheck = TRUE)
    qgaitbinom.mlm(p, size, prob, alter = NULL, inflate = NULL,
                 truncate = NULL, pobs.a = 0, pstr.i = 0, byrow.arg = FALSE)
    rgaitbinom.mlm(n, size, prob, alter = NULL, inflate = NULL,
                 truncate = NULL, pobs.a = 0, pstr.i = 0, byrow.arg = FALSE)

### Arguments

`x, q, p, n, log.arg` | Same meaning as in `rbinom`.
`size, prob` | Same meaning as in `rbinom`, i.e., for an ordinary binomial distribution. Short vectors are recycled.
`alter, inflate, truncate` | Vectors of nonnegative integers; the altered, inflated and truncated values. Each argument must have unique values only. The default value of `NULL` means an empty set.
`pstr.i, byrow.arg` | The first argument can be a `length(inflate)`-vector of probabilities; else a matrix of dimension `n x length(inflate)` of probabilities. If a vector then this matrix is constructed from the vector using `byrow.arg` to determine the enumeration of the elements (similar to `matrix`). These arguments are not used unless `inflate` is assigned.
`pobs.a` | This argument is similar to `pstr.i` but is used when `alter` is assigned a vector. The argument `byrow.arg` is used similarly to construct a matrix of dimension `n x length(alter)` of probabilities. This argument is not used unless `alter` is assigned.
`.errorcheck` | Logical. Should be ignored by the user.

### Details

See `Gaitpois` for generic details applying to both distributions.

These functions do what `dgabinom`, `dgibinom`, `dgtbinom`, `pgabinom`, `pgibinom`, `pgtbinom`, `qgabinom`, `qgibinom`, `qgtbinom`, `rgabinom`, `rgibinom`, `rgtbinom` collectively did because the arguments `alter`, `inflate` and `truncate` have been combined.

### Value

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

### Author(s)

T. W. Yee.

### See Also

`Gaitnbinom.mlm`, `Posbinom`, `Binomial`.

### Examples

    avec <- 5:6   # Alter these (special) values
    ivec <- 9:10  # Inflate these (special) values
    tvec <- 2:4   # Truncate these (special) values
    pobs.a <- c(0.1, 0.2)
    pstr.i <- (1:2)/10
    size <- 10; prob <- 0.5; xx <- 0:11
    y <- rgaitbinom.mlm(1000, size, prob, alter = avec, inflate = ivec,
           truncate = tvec, pstr.i = pstr.i, pobs.a = pobs.a, byrow = TRUE)
    table(y)
    (ii <- dgaitbinom.mlm(xx, size, prob, alter = avec, inflate = ivec,
           truncate = tvec, pstr.i = pstr.i, pobs.a = pobs.a, byrow = TRUE))

[Package VGAM version 1.1-3 Index]