Density, cumulative distribution function, quantile function and random
generation for the set of distributions
supported by the `survreg`

function.

```
dsurvreg(x, mean, scale=1, distribution='weibull', parms)
psurvreg(q, mean, scale=1, distribution='weibull', parms)
qsurvreg(p, mean, scale=1, distribution='weibull', parms)
rsurvreg(n, mean, scale=1, distribution='weibull', parms)
```

density (`dsurvreg`

),
probability (`psurvreg`

),
quantile (`qsurvreg`

), or
for the requested distribution with mean and scale
parameters `mean`

and
`sd`

.

- x
vector of quantiles. Missing values (

`NA`

s) are allowed.- q
vector of quantiles. Missing values (

`NA`

s) are allowed.- p
vector of probabilities. Missing values (

`NA`

s) are allowed.- n
number of random deviates to produce

- mean
vector of location (linear predictor) parameters for the model. This is replicated to be the same length as

`p`

,`q`

or`n`

.- scale
vector of (positive) scale factors. This is replicated to be the same length as

`p`

,`q`

or`n`

.- distribution
character string giving the name of the distribution. This must be one of the elements of

`survreg.distributions`

- parms
optional parameters, if any, of the distribution. For the t-distribution this is the degrees of freedom.

Elements of `q`

or
`p`

that are missing will cause the corresponding
elements of the result to be missing.

The `location`

and `scale`

values are as they would be for `survreg`

.
The label "mean" was an unfortunate choice (made in mimicry of qnorm);
a more correct label would be "linear predictor".
Since almost none of these distributions are symmetric the location
parameter is not actually a mean.

The `survreg`

routines use the parameterization found in chapter
2 of Kalbfleisch and Prentice.
Translation to the usual parameterization found in a textbook is not
always obvious.
For example, the Weibull distribution has cumulative distribution
function
\(F(t) = 1 - e^{-(\lambda t)^p}\).
The actual fit uses the fact that \(\log(t)\) has an extreme
value distribution, with location and scale of
\(\alpha, \sigma\), which are the location and scale parameters
reported by the `survreg`

function.
The parameters are related by \(\sigma= 1/p\) and
\(\alpha = -\log(\lambda\).
The `stats::dweibull`

routine is parameterized in terms of
shape and scale parameters which correspond to \(p\) and
\(1/\lambda\) in the K and P notation.
Combining these we see that shape = \(1/\sigma\) and
scale = \(\exp{alpha}\).

Kalbfleisch, J. D. and Prentice, R. L., The statistical analysis of failure time data, Wiley, 2002.

`survreg`

,
`Normal`