# qpwu: Piecewise uniform distribution: quantile function In PWEALL: Design and Monitoring of Survival Trials Accounting for Complex Situations

## Description

This will provide the quantile function of the specified piecewise uniform distribution

## Usage

 `1` ```qpwu(p=seq(0,1,by=0.1),u=c(0,5,0.5),ut=c(1,2)) ```

## Arguments

 `p` a vector of probabilities `u` piecewise constant density `ut` time points at which event rate changes. This must be an strictly increasing sequence. `ut` and `u` must have the same length.

## Details

Let f(t)=∑_{j=1}^m u_j I(t_{j-1}<t≤ t_j) be the density function, where u_1,…,u_m are the corresponding elements of u and t_1,…,t_{m} are the corresponding elements of ut and t_0=0. The distribution function

F(t)=∑_{j=1}^m u_j(t\wedge t_j-t\wedge t_{j-1}).

User must make sure that ∑_{j=1}^m u_j (t_j-t_{j-1})=1 before using this function.

## Value

 `q` quantiles

## Note

This provides the quantile function related to the piecewise uniform distribution

Xiaodong Luo

## References

Luo, et al. (2017)

piecewise uniform

## Examples

 ```1 2 3 4 5``` ```p<-seq(0,1,by=0.1) u<-c(0.6,0.4) ut<-c(1,2) pwuq<-qpwu(p=p,u=u,ut=ut) pwuq ```

### Example output

```\$q
[1] 0.0000000 0.1666667 0.3333333 0.5000000 0.6666667 0.8333333 1.0000000
[8] 1.2500000 1.5000000 1.7500000 2.0000000
```

PWEALL documentation built on May 2, 2019, 4:16 a.m.