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

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.

Answer 1

[Nick Hobbs]

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.