# Is the renewal function really a distribution function?

I often read that the renewal function $$R(t)=\mathbb{E}(N_t)$$ is a distribution function. But shouldn't a distribution function (CDF) be smaller than $$1$$?

• Yes, CDF functions $P[X\leq x]$ have values between 0 and 1 and are not $E[N_t]$ functions. – Michael Jun 18 at 21:27
• "I often read ..." So, give us an example of this. – GEdgar Jun 18 at 21:58