Questions tagged [law-of-large-numbers]

Several theorems stating that sample mean converges to the expected value as $n\to\infty$. There is a weak law and a strong law of large numbers.

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Does the Law of Large Numbers work better for some Distributions? [closed]

Here are two popular principles in Statistics: 1) Law of Large Numbers: If $X$ is a random variable with a probability density function $f(x)$ and an expected value $E[X] = \mu$. If we take a sample ...
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Timeseries problem with law of large numbers

Let us have an AR(1) model with individual efect $$y_t = \alpha + \theta y_{t-1} + \varepsilon_t$$ with $|\theta|<1$ for stacionarity and $\varepsilon_i$ i.i.d. from distribution with mean $0$ and ...
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When is a function of an ergodic stationary process itself ergodic stationary?

I am working with a function which has the form $f(X_1, \dots, X_n)$, where $\\{X_n\\}$ is an ergodic stationary process. Theorem 5.6 in "A first course in stochastic processes" by Karlin &...
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Convergence of estimated Survival Functions

Q1 part A&B I have so far $$\underset{n\rightarrow\infty} {\lim} \frac{1}{n}\sum_{i=1}^nI(T_i>x)$$ since we are summing an indicator variable we can say it has a Bernoulli distribution with ...
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Is the Law of Large Numbers Related to the Occurrence of Rare Events Over Many Trials?

I recently watched an episode of "The Big Bang Theory" where Sheldon makes a comment about the Law of Large Numbers. In the episode, Sheldon realizes he needs eggs, and almost immediately ...
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Probability Theory. Moving from finite to continuous

This has probably been asked before, as this is (I think) a fundamental theory of statistical theory, but I don't know what it is called, hence I have not yet found an answer. Consider a box which ...
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What is the rigorous justification for applying LLN or CLT to finite probability spaces?

Both CLT and LLN are stated in terms of a fixed probability space that admits an infinite sequence of IID RVs. It is a common-place in many probability and statistics texts/notes that such a sequence ...
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Asymptotic normality in central limit theorem

I am a bit confused by Classical CLT section of the central limit theorem on Wikipedia. It basically says at the sample size gets larger, the difference between the sample mean and true mean ...
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Is this point estimate for mean biased?

I was wondering if this point estimate for mean: $\frac{1}{n+1}\sum_{i = 1}^{n}x_i$ is biased? My first thought was that $\frac{1}{n+1}\sum_{i = 1}^{n}x_i \neq \frac{1}{n}\sum_{i = 1}^{n}x_i$, so then ...
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Law of Large Numbers for whole distributions

I'm aware of the Law(s) of Large Numbers, concerning the means. However, intuitively, I'd expect not just the mean, but also the observed relative frequencies (or the histogram, if we have a ...
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How can I edit this code to determine the accuracy of data? [closed]

My employer has asked me to perform a few analysis on a data about wood piles which contains their diameter and bark thickness. I am a beginner in R and started with some basic descriptive analysis ...
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