# ２つの正規分布の重なりI calculate the heap of two normal distribution

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k2 on 16 Jul 2015
Answered: Nick Hobbs on 21 Jul 2015
２つの正規分布（各分布の合計は１）の重なる面積（割合）を計算する方法（若しくはコマンド）を知りたい。
２つの正規分布のμとσが分かっているので、μとσから算出する方法をお願いいたします。
I want to know a method (or, command) to calculate the area (a ratio) to occur at the same time of two normal distribution (as for total 1 of each distribution).
Because I understand μ and σ of two normal distribution, I ask for a method to calculate from μ and σ.

Nick Hobbs on 21 Jul 2015
If you only need to find the area shared by two normal distributions, this can be done using an anonymous function, normpdf, and integral.
myNormalDistribution = @(x) min(normpdf(x, 0, 1), normpdf(x, 1, 1))
integralValue = integral(myNormalDistribution, -inf, inf)
integralValue will now contain the total area of the intersection of the two normal distributions (0.6171). This can be visualized with the following code:
x = -3:0.01:3;
plot(x, normpdf(x, 0, 1), x, normpdf(x, 1, 1))
hold on
area(x, myNormalDistribution(x))
The plot from the above code is shown below. ### Categories

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