Zero-Inflated Binomial Distribution

Density, distribution function, quantile function and random generation for the zero-inflated binomial distribution with parameter pstr0.

dzibinom(x, size, prob, pstr0 = 0, log = FALSE)
pzibinom(q, size, prob, pstr0 = 0)
qzibinom(p, size, prob, pstr0 = 0)
rzibinom(n, size, prob, pstr0 = 0)

Arguments

x, q: vector of quantiles.
p: vector of probabilities.
size: number of trials. It is the $N$ symbol in the formula given in zibinomial.
prob: probability of success on each trial.
n: Same as in runif.

log

Same as pbinom.

pstr0

Probability of a structural zero (i.e., ignoring the binomial distribution), called $\phi$. The default value of $\phi=0$ corresponds to the response having an ordinary binomial distribution.

Details

The probability function of $Y$ is 0 with probability $\phi$, and $Binomial(size, prob)$ with probability $1-\phi$. Thus $$P(Y=0) =\phi + (1-\phi) P(W=0)$$ where $W$ is distributed $Binomial(size, prob)$.

Value

dzibinom gives the density, pzibinom gives the distribution function, qzibinom gives the quantile function, and rzibinom generates random deviates.

Author

T. W. Yee

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.

Examples

prob <- 0.2; size <- 10; pstr0 <- 0.5
(ii <- dzibinom(0:size, size, prob, pstr0 = pstr0))
#>  [1] 0.5536870912 0.1342177280 0.1509949440 0.1006632960 0.0440401920
#>  [6] 0.0132120576 0.0027525120 0.0003932160 0.0000368640 0.0000020480
#> [11] 0.0000000512
max(abs(cumsum(ii) - pzibinom(0:size, size, prob, pstr0 = pstr0)))  # 0?
#> [1] 1.110223e-16
table(rzibinom(100, size, prob, pstr0 = pstr0))
#> 
#>  0  1  2  3  4 
#> 54 20 10 10  6 

table(qzibinom(runif(100), size, prob, pstr0 = pstr0))
#> 
#>  0  1  2  3  4  5 
#> 46 12 20 15  6  1 
round(dzibinom(0:10, size, prob, pstr0 = pstr0) * 100)  # Similar?
#>  [1] 55 13 15 10  4  1  0  0  0  0  0

if (FALSE)  x <- 0:size
barplot(rbind(dzibinom(x, size, prob, pstr0 = pstr0),
                dbinom(x, size, prob)),
    beside = TRUE, col = c("blue", "green"), ylab = "Probability",
    main = paste0("ZIB(", size, ", ", prob, ", pstr0 = ", pstr0, ")",
                 " (blue) vs Binomial(", size, ", ", prob, ") (green)"),
    names.arg = as.character(x), las = 1, lwd = 2)  # \dontrun{}
#> Error: object 'x' not found