Genipois {VGAM} | R Documentation

## Generally-Inflated Poisson Distribution

### Description

Density, distribution function, and random generation for the generally-inflated Poisson distribution.

### Usage

    dgenipois(x, lambda, inflate = 0, pstr.i = 0, byrow.arg = FALSE,
              log.arg = FALSE)
    pgenipois(q, lambda, inflate = 0, pstr.i = 0, byrow.arg = FALSE)
    rgenipois(n, lambda, inflate = 0, pstr.i = 0, byrow.arg = FALSE)

### Arguments

`x, q, n, log.arg` | Same type of argument as in `rpois`.
`lambda` | vector of positive means (of an ordinary Poisson distribution). Short vectors are recycled.
`inflate` | vector of nonnegative integers; the inflated values. Must have unique values only. A `NULL` is acceptable and 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`). One can think of this matrix as comprising of structural probabilities. Then the matrix augmented with one more column on the RHS so it has dimension `n x (length(inflate) + 1)` and whose `rowSums` is a vector of 1s. Finally, for `rgenipois`, a multinomial sample is taken and if it belongs to the final column then Poisson random variates are drawn.

### Details

The generally-inflated Poisson distribution is a mixture of an ordinary Poisson distribution with a multinomial distribution. Certain (inflated) values having some prespecified multinomial probabilities can have structural values. Since `inflate = 0` and `pstr.i = 0` then the default is an ordinary Poisson distribution.

### Value

`dgenipois` gives the density, `pgenipois` gives the distribution function, `rgenipois` generates random deviates.

### Author(s)

T. W. Yee.

### See Also

`genipoisson`, `Gentpois`, `Genapois`, `dpospois`, `rpois`.

### Examples

    ivec <- 2:4  # Inflate these values
    pstr.i <- (1:3)/10; lambda <- 2;
    y <- rgenipois(1000, lambda, inflate = ivec, pstr.i = pstr.i, byrow = TRUE)
    table(y)
    (ii <- dgenipois(0:7, lambda, inflate = ivec, pstr.i = pstr.i, byrow=TRUE))
    table(rgenipois(1000, lambda, inflate = ivec, pstr.i = pstr.i, byrow=TRUE))

    ## Not run:  x <- 0:7
    barplot(rbind(dgenipois(x, lambda, inflate = ivec, pstr.i = pstr.i,
                            byrow = TRUE),
                  dpois(x, lambda)),
            beside = TRUE, col = c("blue", "orange"),
            main = paste("Gen-inf Pois(lambda = ", lambda, ", ",
                         "inflate = c(", paste(ivec, collapse = ","),
                         "), pstr.i = c(", paste(pstr.i, collapse = ","),
                         "), byrow = TRUE) vs",
            " Pois(", lambda, ")", sep = ""),
            sub = "Generally-inflated Poisson is blue; Poisson is orange",
            names.arg = as.character(x), las = 1, lwd = 2)
    ## End(Not run)

[Package VGAM version 1.1-1 Index]