Category Archives: [:ja]統計[:en]Statistics[:]

Test in the Expectation and the Variance in a Sampling Distribution


Test the expectation and the variance in a sampling distribution with a program.

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Simulation of the Law of the Large Numbers


Simulation is important to develop our intuitive understanding. So when the difficult content appears, try considering a sample. If there’s no handy sample, creating a sample with R is very efficient, simulation in other words.

When we want to understand the law of the large number, we can also generate it virtually. Here, I will show you the simulation. Consider the function which takes \(x \in [0, 3)\) and the value is in \([0, 1)\), such as \( g(x) = \frac{1}{4} x(3-x)(x-0.75)^2\). (\(g(x)\) can’t be a density function for the random variable, because \(\int _0 ^1 g(x) dx \neq 1\). It is the probability to admit \(x\) value generated by randomly. It is for creating trial data.)

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[Simulation] the Law of Large Numbers and the Central Limit Theorem


Seeing samples, simulation in other words, is a good way to understand the concept, so I’ll explain with an example. At first, I’ll show the explanation of the law and theorem, and then I’ll provide the example.

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Similarity among Binomial, Poisson and Normal Distributions


Binomial Distribution \(\textrm{Binomial}(m, p)\) is similar to Normal and Poisson distributions.

Especially \(n\) is large, it can be approximated as a normal distribution, according to the central limit theorem.

Let’s see the similarity with graphics.

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