🕷️ Crawler Inspector

| | | |---|---| | Zipois {VGAM} | R Documentation | ## Zero-Inflated Poisson Distribution ### Description Density, distribution function, quantile function and random generation for the zero-inflated and zero-deflated Poisson distribution with parameter `pstr0`. ### Usage ``` dzipois(x, lambda, pstr0 = 0, log = FALSE) pzipois(q, lambda, pstr0 = 0) qzipois(p, lambda, pstr0 = 0) rzipois(n, lambda, pstr0 = 0) ``` ### Arguments | | | |---|---| | `x`, `q` | vector of quantiles. | | `p` | vector of probabilities. | | `n` | number of observations. Must be a single positive integer. | | `lambda` | Vector of positive means. | | `pstr0` | Probability of a structural zero (i.e., ignoring the Poisson distribution), called `\phi`. The default value of `\phi = 0` corresponds to the response having an ordinary Poisson distribution. If `\phi` lies in (0, 1) then this is known as the zero-inflated Poisson (ZIP) distribution. This argument may be negative to allow for 0-deflation, hence its interpretation as a probability ceases. | | `log` | Logical. Return the logarithm of the answer? | ### Details The probability function of `Y` is 0 with probability `\phi`, and `Poisson(\lambda)` with probability `1-\phi`. Thus `P(Y=0) =\phi + (1-\phi) P(W=0)` where `W` is distributed `Poisson(\lambda)`. ### Value `dzipois` gives the density, `pzipois` gives the distribution function, `qzipois` gives the quantile function, and `rzipois` 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 the *zero-deflated Poisson* (ZDP) distribution. Here, `pstr0` is also permitted to lie in the interval `[-1/expm1(lambda), 0]`. The resulting probability of a zero count is *less than* the nominal Poisson value, and the use of `pstr0` to stand for the probability of a structural zero loses its meaning. When `pstr0` equals `-1/expm1(lambda)` this corresponds to the positive-Poisson distribution (e.g., see `Gaitdpois`), also called the zero-truncated Poisson or ZTP. The zero-*modified* Poisson (ZMP) is a combination of the ZIP and ZDP and ZTP distributions. The family function ### Author(s) T. W. Yee ### See Also `zipoisson`, `Gaitdpois`, `dpois`, `rzinegbin`. ### Examples ``` lambda <- 3; pstr0 <- 0.2; x <- (-1):7 (ii <- dzipois(x, lambda, pstr0 = pstr0)) max(abs(cumsum(ii) - pzipois(x, lambda, pstr0 = pstr0))) # 0? table(rzipois(100, lambda, pstr0 = pstr0)) table(qzipois(runif(100), lambda, pstr0)) round(dzipois(0:10, lambda, pstr0 = pstr0) * 100) # Similar? ## Not run: x <- 0:10 par(mfrow = c(2, 1)) # Zero-inflated Poisson barplot(rbind(dzipois(x, lambda, pstr0 = pstr0), dpois(x, lambda)), beside = TRUE, col = c("blue", "orange"), main = paste0("ZIP(", lambda, ", pstr0 = ", pstr0, ") (blue) vs", " Poisson(", lambda, ") (orange)"), names.arg = as.character(x)) deflat.limit <- -1 / expm1(lambda) # Zero-deflated Poisson newpstr0 <- round(deflat.limit / 1.5, 3) barplot(rbind(dzipois(x, lambda, pstr0 = newpstr0), dpois(x, lambda)), beside = TRUE, col = c("blue","orange"), main = paste0("ZDP(", lambda, ", pstr0 = ", newpstr0, ")", " (blue) vs Poisson(", lambda, ") (orange)"), names.arg = as.character(x)) ## End(Not run) ``` *** \[Package *VGAM* version 1.1-11 [Index](https://search.r-project.org/CRAN/refmans/VGAM/html/00Index.html)\]