# dsurvreg: Distributions available in survreg. In survival: Survival Analysis

## Description

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

## Usage

 ```1 2 3 4``` ```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) ```

## Arguments

 `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 linear predictors 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.

## Details

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); since almost none of these distributions are symmetric it will not actually be a mean, but corresponds instead to the linear predictor of a fitted model. Translation to the usual parameterization found in a textbook is not always obvious. For example, the Weibull distribution is fit using the Extreme value distribution along with a log transformation. Letting F(t) = 1 - exp(-(at)^p) be the cumulative distribution of the Weibull using a standard parameterization in terms of a and p, the survreg location corresponds to -log(a) and the scale to 1/p (Kalbfleisch and Prentice, section 2.2.2).

## Value

density (`dsurvreg`), probability (`psurvreg`), quantile (`qsurvreg`), or for the requested distribution with mean and scale parameters `mean` and `sd`.

## References

Kalbfleisch, J. D. and Prentice, R. L. (1970). The Statistical Analysis of Failure Time Data Wiley, New York.

`survreg`, `Normal`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17``` ```# List of distributions available names(survreg.distributions) ## Not run:  "extreme" "logistic" "gaussian" "weibull" "exponential"  "rayleigh" "loggaussian" "lognormal" "loglogistic" "t" ## End(Not run) # Compare results all.equal(dsurvreg(1:10, 2, 5, dist='lognormal'), dlnorm(1:10, 2, 5)) # Hazard function for a Weibull distribution x <- seq(.1, 3, length=30) haz <- dsurvreg(x, 2, 3)/ (1-psurvreg(x, 2, 3)) ## Not run: plot(x, haz, log='xy', ylab="Hazard") #line with slope (1/scale -1) ## End(Not run) ```