# zigeomUC: Zero-Inflated Geometric Distribution

Description Usage Arguments Details Value Note Author(s) See Also Examples

### Description

Density, and random generation for the zero-inflated geometric distribution with parameter `pstr0`.

### Usage

 ```1 2 3 4``` ```dzigeom(x, prob, pstr0 = 0, log = FALSE) pzigeom(q, prob, pstr0 = 0) qzigeom(p, prob, pstr0 = 0) rzigeom(n, prob, pstr0 = 0) ```

### Arguments

 `x, q` vector of quantiles. `p` vector of probabilities. `prob` see `dgeom`. `n` Same as in `runif`. `pstr0` Probability of structural zero (ignoring the geometric distribution), called phi. The default value corresponds to the response having an ordinary geometric distribution. `log` Logical. Return the logarithm of the answer?

### Details

The probability function of Y is 0 with probability phi, and geometric(prob) with probability 1-phi. Thus

P(Y=0) = phi + (1-phi) * P(W=0)

where W is distributed geometric(prob).

### Value

`dzigeom` gives the density, `pzigeom` gives the distribution function, `qzigeom` gives the quantile function, and `rzigeom` generates random deviates.

### Note

The argument `pstr0` is recycled to the required length, and must have values which lie in the interval [0,1].

These functions actually allow for zero-deflation. That is, the resulting probability of a zero count is less than the nominal value of the parent distribution. See `Zipois` for more information.

T. W. Yee

### See Also

`zigeometric`, `dgeom`.

### Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14``` ```prob <- 0.5; pstr0 <- 0.2; x <- (-1):20 (ii <- dzigeom(x, prob, pstr0)) max(abs(cumsum(ii) - pzigeom(x, prob, pstr0))) # Should be 0 table(rzigeom(1000, prob, pstr0)) ## Not run: x <- 0:10 barplot(rbind(dzigeom(x, prob, pstr0), dgeom(x, prob)), beside = TRUE, col = c("blue","orange"), ylab = "P[Y = y]", xlab = "y", las = 1, main = paste("zigeometric(", prob, ", pstr0 = ", pstr0, ") (blue) vs", " geometric(", prob, ") (orange)", sep = ""), names.arg = as.character(x)) ## End(Not run) ```

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