Types of Law of Large Numbers
Various of the Law of Large Numbers are:
Weak Law of Large Numbers (WLLN)
Imagine you have a fair coin and flip it several times to determine Weak Law of Large Numbers (WLLN). The Weak Law of Large Numbers indicates that the proportion of heads (or tails) seen will get closer and closer to 0.5 (since the coin is fair, and the probability of obtaining a head or a tail is 0.5). As you increase the number of coin flips.
Generally speaking, the WLLN states that as the number of observations rises the sample average will converge to the theoretical mean if your series of independent and identically distributed random variables (such as coin flips).
Strong Law of Large Numbers (SLLN)
An improved form of the WLLN is the Strong Law of Large Numbers. It says the sample average not only will converge to the expected value but also offers a gauge of the speed at which this convergence occurs.
Returning to the coin flipping example, the SLLN indicates that as the number of coin flips rises the likelihood of the sample average deviating from the expected value (0.5) by a notable amount falls. Stated differently, when more observations are gathered, the likelihood of the sample average deviating significantly from the expected value becomes even more rare.
Both versions essentially mean that with enough trials, the results will stabilize around the expected average.
Law of Large Numbers
Law of Large Numbers (LLN) is a mathematical theorem that states the average of the results obtained from many independent random samples.
In this article, we have discussed the Law of Large Numbers definition, its limitations, examples and others in detail.
Table of Content
- What is Law of Large Numbers?
- Limitation of Law of Large Numbers
- Types of Law of Large Numbers
- Why is Law of Large Numbers Important?
- Law of Large Numbers (LLN) and Central Limit Theorem (CLT)
- Examples of Law of Large Numbers
- Law of Large Numbers in Finance