Zero-inflated density constructer — zero

Constructs a zero-inflated density function from a given probability density function

Usage

zero_inflate(dist, discrete = NULL)

Arguments

dist: either a probability density function or a probability mass function
discrete: logical; if TRUE, the density for x = 0 will be zeroprob + (1-zeroprob) * dist(0, ...). Otherwise it will just be zeroprob. In standard cases, this will be determined automatically. For non-standard cases, set this to TRUE or FALSE depending on the type of dist. See details.

Value

zero-inflated density function with first argument x, second argument zeroprob, and additional arguments ... that will be passed to dist.

Details

The definition of zero-inflation is different for discrete and continuous distributions. For discrete distributions with p.m.f. $f$ and zero-inflation probability $p$, we have $$\Pr(X = 0) = p + (1 - p) \cdot f(0),$$ and $$\Pr(X = x) = (1 - p) \cdot f(x), \quad x > 0.$$

For continuous distributions with p.d.f. $f$, we have $$f_{\text{zinfl}}(x) = p \cdot \delta_0(x) + (1 - p) \cdot f(x),$$ where $\delta_0$ is the Dirac delta function at zero.

Examples

# Zero-inflated normal distribution
dzinorm <- zero_inflate(dnorm)
dzinorm(c(NA, 0, 2), 0.5, mean = 1, sd = 1)
#> [1]        NA 0.5000000 0.1209854

# Zero-inflated Poisson distribution
zipois <- zero_inflate(dpois)
zipois(c(NA, 0, 1), 0.5, 1)
#> [1]        NA 0.6839397 0.1839397

# Non-standard case: Zero-inflated reparametrised beta distribution
dzibeta2 <- zero_inflate(dbeta2, discrete = FALSE)