### What does **renewal theory** mean?

# Definitions for renewal theory

re·new·al the·o·ry

#### This dictionary definitions page includes all the possible meanings, example usage and translations of the word **renewal theory**.

### Wikipedia

Renewal theory

Renewal theory is the branch of probability theory that generalizes the Poisson process for arbitrary holding times. Instead of exponentially distributed holding times, a renewal process may have any independent and identically distributed (IID) holding times that have finite mean. A renewal-reward process additionally has a random sequence of rewards incurred at each holding time, which are IID but need not be independent of the holding times. A renewal process has asymptotic properties analogous to the strong law of large numbers and central limit theorem. The renewal function m ( t ) {\displaystyle m(t)} (expected number of arrivals) and reward function g ( t ) {\displaystyle g(t)} (expected reward value) are of key importance in renewal theory. The renewal function satisfies a recursive integral equation, the renewal equation. The key renewal equation gives the limiting value of the convolution of m ′ ( t ) {\displaystyle m'(t)} with a suitable non-negative function. The superposition of renewal processes can be studied as a special case of Markov renewal processes. Applications include calculating the best strategy for replacing worn-out machinery in a factory and comparing the long-term benefits of different insurance policies. The inspection paradox relates to the fact that observing a renewal interval at time t gives an interval with average value larger than that of an average renewal interval.

### Numerology

Chaldean Numerology

The numerical value of renewal theory in Chaldean Numerology is:

**6**Pythagorean Numerology

The numerical value of renewal theory in Pythagorean Numerology is:

**7**

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"renewal theory." *Definitions.net.* STANDS4 LLC, 2024. Web. 14 Apr. 2024. <https://www.definitions.net/definition/renewal+theory>.

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