Test the expectation and the variance in a sampling distribution with a program.
Category Archives: [:ja]統計[:en]Statistics[:]
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.)
[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.
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.
Continuous Uniform Distribution and its expectation and variance
Here I wrote the expectation and variance of a continuous uniform distribution. It is very simple calculation because of the simple density function.