Simulate a non-homogeneous poisson process

I was trying to simulate a non-homogeneous poisson process with hazard rate function $$\lambda(t)=3+\sin(2\pi t)$$ I tried to use the property that given $N=n$, arrivals in $[0,T]$ are distributed with pdf $$f(t)=\frac{\lambda(t)}{\int_0^T\lambda(s)ds}\textbf{1}\{t\in[0,T]\}=\frac{1}{15}(3+\sin(2\pi t))\textbf{1}\{t\in[0,T]\}$$ first generate a poisson r.v. with mean $\int_0^T\lambda(t)dt$ and then generate the arrivals using the pdf above but ran into a problem. I cannot find a method to simulate $t$ with pdf $f(t)$

I tried using inverse transformation but the cdf is $F(t)=-\frac{1}{15}(3t-2\pi\cos(2\pi t))$ and I cannot find a close form solution for $t$ in terms of $F(t)$. Any suggestions as for how should I proceed? maybe using acceptance-rejection?

• assuming $T=5$. – ANKI_YUME Mar 2 '16 at 2:17