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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 $1$?

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

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