# tikuvUC: A Short-tailed Symmetric Distribution In VGAM: Vector Generalized Linear and Additive Models

## Description

Density, cumulative distribution function, quantile function and random generation for the short-tailed symmetric distribution of Tiku and Vaughan (1999).

## Usage

 ```1 2 3 4``` ```dtikuv(x, d, mean = 0, sigma = 1, log = FALSE) ptikuv(q, d, mean = 0, sigma = 1, lower.tail = TRUE, log.p = FALSE) qtikuv(p, d, mean = 0, sigma = 1, lower.tail = TRUE, log.p = FALSE, ...) rtikuv(n, d, mean = 0, sigma = 1, Smallno = 1.0e-6) ```

## Arguments

 `x, q` vector of quantiles. `p` vector of probabilities. `n` number of observations. Same as in `runif`. `d, mean, sigma ` arguments for the parameters of the distribution. See `tikuv` for more details. For `rtikuv`, arguments `mean` and `sigma` must be of length 1. `Smallno` Numeric, a small value used by the rejection method for determining the lower and upper limits of the distribution. That is, `ptikuv(L) < Smallno` and `ptikuv(U) > 1-Smallno` where `L` and `U` are the lower and upper limits respectively. `...` Arguments that can be passed into `uniroot`. `log` Logical. If `log = TRUE` then the logarithm of the density is returned. `lower.tail, log.p` Same meaning as in `pnorm` or `qnorm`.

## Details

See `tikuv` for more details.

## Value

`dtikuv` gives the density, `ptikuv` gives the cumulative distribution function, `qtikuv` gives the quantile function, and `rtikuv` generates random deviates.

## Author(s)

T. W. Yee and Kai Huang

`tikuv`.
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21``` ```## Not run: par(mfrow = c(2, 1)) x <- seq(-5, 5, len = 401) plot(x, dnorm(x), type = "l", col = "black", ylab = "", las = 1, main = "Black is standard normal, others are dtikuv(x, d)") lines(x, dtikuv(x, d = -10), col = "orange") lines(x, dtikuv(x, d = -1 ), col = "blue") lines(x, dtikuv(x, d = 1 ), col = "green") legend("topleft", col = c("orange","blue","green"), lty = rep(1, len = 3), legend = paste("d =", c(-10, -1, 1))) plot(x, pnorm(x), type = "l", col = "black", ylab = "", las = 1, main = "Black is standard normal, others are ptikuv(x, d)") lines(x, ptikuv(x, d = -10), col = "orange") lines(x, ptikuv(x, d = -1 ), col = "blue") lines(x, ptikuv(x, d = 1 ), col = "green") legend("topleft", col = c("orange","blue","green"), lty = rep(1, len = 3), legend = paste("d =", c(-10, -1, 1))) ## End(Not run) probs <- seq(0.1, 0.9, by = 0.1) ptikuv(qtikuv(p = probs, d = 1), d = 1) - probs # Should be all 0 ```