tikuv | R Documentation |

Fits the short-tailed symmetric distribution of Tiku and Vaughan (1999).

```
tikuv(d, lmean = "identitylink", lsigma = "loglink",
isigma = NULL, zero = "sigma")
```

`d` |
The |

`lmean, lsigma` |
Link functions for the mean and standard
deviation parameters of the usual univariate normal distribution
(see |

`isigma` |
Optional initial value for |

`zero` |
A vector specifying which
linear/additive predictors are modelled as intercept-only.
The values can be from the set {1,2}, corresponding
respectively to |

The short-tailed symmetric distribution of Tiku and Vaughan (1999) has a probability density function that can be written

```
f(y) = \frac{K}{\sqrt{2\pi} \sigma}
\left[ 1 + \frac{1}{2h}
\left( \frac{y-\mu}{\sigma} \right)^2
\right]^2
\exp\left( -\frac12
(y-\mu)^2 / \sigma^2 \right)
```

where `h=2-d>0`

,
`K`

is a function of `h`

,
`-\infty < y < \infty`

,
`\sigma > 0`

.
The mean of `Y`

is
`E(Y) = \mu`

and this is returned
as the fitted values.

An object of class `"vglmff"`

(see `vglmff-class`

).
The object is used by modelling functions
such as `vglm`

,
and `vgam`

.

Under- or over-flow may occur if the data is ill-conditioned,
e.g., when `d`

is very close to 2 or approaches `-Inf`

.

The density function is the product of a univariate normal
density and a polynomial in the response `y`

.
The distribution is bimodal if `d>0`

, else is unimodal.
A normal distribution arises as the limit
as `d`

approaches
`-\infty`

, i.e., as `h`

approaches `\infty`

.
Fisher scoring is implemented.
After fitting the value of `d`

is
stored in `@misc`

with
component name `d`

.

Thomas W. Yee

Akkaya, A. D. and Tiku, M. L. (2008).
Short-tailed distributions and inliers.
*Test*, **17**, 282–296.

Tiku, M. L. and Vaughan, D. C. (1999).
A family of short-tailed symmetric distributions.
*Technical report, McMaster University, Canada*.

`dtikuv`

,
`uninormal`

.

```
m <- 1.0; sigma <- exp(0.5)
tdata <- data.frame(y = rtikuv(1000, d = 1, m = m, s = sigma))
tdata <- transform(tdata, sy = sort(y))
fit <- vglm(y ~ 1, tikuv(d = 1), data = tdata, trace = TRUE)
coef(fit, matrix = TRUE)
(Cfit <- Coef(fit))
with(tdata, mean(y))
## Not run: with(tdata, hist(y, prob = TRUE))
lines(dtikuv(sy, d = 1, m = Cfit[1], s = Cfit[2]) ~ sy,
data = tdata, col = "orange")
## End(Not run)
```

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