laplace | R Documentation |

Maximum likelihood estimation of the 2-parameter classical Laplace distribution.

```
laplace(llocation = "identitylink", lscale = "loglink",
ilocation = NULL, iscale = NULL, imethod = 1, zero = "scale")
```

`llocation, lscale` |
Character.
Parameter link functions for location parameter |

`ilocation, iscale` |
Optional initial values. If given, it must be numeric and values are recycled to the appropriate length. The default is to choose the value internally. |

`imethod` |
Initialization method. Either the value 1 or 2. |

`zero` |
See |

The Laplace distribution is often known as the
*double-exponential* distribution and,
for modelling, has heavier tail than the normal distribution.
The Laplace density function is

```
f(y) = \frac{1}{2b} \exp \left( - \frac{|y-a|}{b}
\right)
```

where `-\infty<y<\infty`

,
`-\infty<a<\infty`

and
`b>0`

.
Its mean is `a`

and its variance is `2b^2`

.
This parameterization is called the *classical Laplace
distribution* by Kotz et al. (2001), and the density is symmetric
about `a`

.

For `y ~ 1`

(where `y`

is the response)
the maximum likelihood estimate (MLE) for the location
parameter is the sample median, and the MLE for `b`

is
`mean(abs(y-location))`

(replace location by its MLE
if unknown).

An object of class `"vglmff"`

(see `vglmff-class`

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

and `vgam`

.

This family function has not been fully tested.
The MLE regularity conditions do *not* hold for this
distribution, therefore misleading inferences may result, e.g.,
in the `summary`

and `vcov`

of the object. Hence this
family function might be withdrawn from VGAM in the future.

This family function uses Fisher scoring. Convergence may be slow for non-intercept-only models; half-stepping is frequently required.

T. W. Yee

Kotz, S., Kozubowski, T. J. and Podgorski, K. (2001).
*The Laplace distribution and generalizations:
a revisit with applications to communications,
economics, engineering, and finance*,
Boston: Birkhauser.

`rlaplace`

,
`alaplace2`

(which differs slightly from this parameterization),
`exponential`

,
`median`

.

```
ldata <- data.frame(y = rlaplace(nn <- 100, 2, scale = exp(1)))
fit <- vglm(y ~ 1, laplace, ldata, trace = TRUE)
coef(fit, matrix = TRUE)
Coef(fit)
with(ldata, median(y))
ldata <- data.frame(x = runif(nn <- 1001))
ldata <- transform(ldata, y = rlaplace(nn, 2, scale = exp(-1 + 1*x)))
coef(vglm(y ~ x, laplace(iloc = 0.2, imethod = 2, zero = 1), ldata,
trace = TRUE), matrix = TRUE)
```

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