spf: A utility function

In PWEALL: Design and Monitoring of Survival Trials Accounting for Complex Situations

A utility function

Description

A utility function to calculate a ratio.

Usage

spf(x=seq(-1,1,by=0.2),eps=1.0e-3)

Arguments

x	A vector
eps	tolerance

Details

This is to calculate

\Phi_l(x)=\frac{\int_0^x s^le^{-s}ds}{x^{l+1}},\hspace{0.5cm}l=0,1,2.

This function is well defined even when x=0. However, it is numerical chanllenging to calculate it when x is small. So when |x|\le \code{eps} we approximate this function and the absolute error is \code{eps}^5.

Value

fx1	when l=0;
fx2	when l=1;
fx3	when l=2.

Note

Version 1.0 (7/19/2016)

Author(s)

Xiaodong Luo

References

Luo, et al. (2017)

Examples

fun<-spf(x=seq(-1,1,by=0.2),eps=1.0e-3)
fun

PWEALL documentation built on Aug. 9, 2023, 9:08 a.m.