matlab - 如何标准化直方图

Question

我可以使用逆方法创建指数分布。我想标准化直方图。我该怎么做？

这是我的代码

N=100;
Lambda=2;
r=rand(N,1);
X=-log(1-r)/Lambda;
hist(X), colormap(bone);

t = 0:0.01:5;
pdf=Lambda*exp(-Lambda*t);
hold on, plot(t,pdf,'LineWidth',2)

Answer 1

直方图应归一化为单位面积，以便与理论pdf进行比较。要归一化为单位面积，您需要除以样本数和 bin 宽度:

N = 100;
Lambda=2;
r = rand(N,1);
X = -log(1-r)/Lambda;
[hy, hx] = hist(X); %/ get histogram values
hy = hy/numel(X)/(hx(2)-hx(1)); %//normalize histogram
bar(hx, hy) %// plot histogram
t = 0:0.01:5;
pdf = Lambda*exp(-Lambda*t);
hold on, plot(t,pdf,'LineWidth',2) %// plot pdf

或者使用新的histogram函数(R2014b 中引入)，根据指定的标准化选项自动标准化:

N = 100;
Lambda=2;
r = rand(N,1);
X = -log(1-r)/Lambda;
histogram(X, 'Normalization', 'pdf') %// plot normalized histogram
t = 0:0.01:5;
pdf = Lambda*exp(-Lambda*t);
hold on, plot(t,pdf,'LineWidth',2) %// plot pdf