# Definitions for renewal theoryre·new·al the·o·ry

### WikipediaRate this definition:0.0 / 0 votes

1. 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

1. Chaldean Numerology

The numerical value of renewal theory in Chaldean Numerology is: 6

2. Pythagorean Numerology

The numerical value of renewal theory in Pythagorean Numerology is: 7

### Translation

#### Find a translation for the renewal theory definition in other languages:

Select another language:

• - Select -
• 简体中文 (Chinese - Simplified)
• Español (Spanish)
• Esperanto (Esperanto)
• 日本語 (Japanese)
• Português (Portuguese)
• Deutsch (German)
• العربية (Arabic)
• Français (French)
• Русский (Russian)
• 한국어 (Korean)
• עברית (Hebrew)
• Gaeilge (Irish)
• Українська (Ukrainian)
• اردو (Urdu)
• Magyar (Hungarian)
• मानक हिन्दी (Hindi)
• Indonesia (Indonesian)
• Italiano (Italian)
• தமிழ் (Tamil)
• Türkçe (Turkish)
• తెలుగు (Telugu)
• ภาษาไทย (Thai)
• Tiếng Việt (Vietnamese)
• Čeština (Czech)
• Polski (Polish)
• Bahasa Indonesia (Indonesian)
• Românește (Romanian)
• Nederlands (Dutch)
• Ελληνικά (Greek)
• Latinum (Latin)
• Svenska (Swedish)
• Dansk (Danish)
• Suomi (Finnish)
• فارسی (Persian)
• ייִדיש (Yiddish)
• հայերեն (Armenian)
• Norsk (Norwegian)
• English (English)

## Citation

#### Use the citation below to add this definition to your bibliography:

Style:MLAChicagoAPA

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

## Are we missing a good definition for renewal theory? Don't keep it to yourself...

### renewal theory

Credit »

#### Free, no signup required:

Get instant definitions for any word that hits you anywhere on the web!

#### Free, no signup required:

Get instant definitions for any word that hits you anywhere on the web!

»
A inspire
B obligate
C accompany
D doom