Limitation of Law of Large Numbers
Various limitations of the Law of Large Numbers are:
- Sample Size: When the sample size is genuinely huge, the Law of huge Numbers operates most effectively. A limited sample size could mean that the results do not represent the underlying population and that the law does not hold.
- Independence: Law of Large Numbers presupposes that the events or observations are unrelated to one another. The law might not apply correctly if there is any dependence or correlation between the observations.
- Rate of Convergence: Law of Large Numbers states that as the sample size grows, the sample mean will converge to the population mean, but it doesn’t say how quickly this convergence will happen. Sometimes, the convergence could be sluggish, and a huge sample size might be needed to get the appropriate degree of precision.
- Outliers and Extreme Values: The existence of outliers or extreme values in the data can have a significant impact on the Law of Large Numbers. Even with a high sample size, a few extreme observations can considerably affect the sample mean.
- Observations Not Identically Distributed: Law of Large Numbers presupposes that the data come from a single probability distribution. The law might not hold if the underlying distribution varies over time or if the data are drawn from disparate distributions.
- Biased Sampling: Law of Large Numbers may not apply and the sample mean may not converge to the true population mean if the sampling procedure is biased or non-random.
- Finite Population: In general, an infinite population is used to state the Law of Large Numbers. The law might need to be changed or altered when working with a finite population to take into consideration the population’s finite size.
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