累积分布函数 Cumulative distribution function
（重定向自CCDF）
累积分布函数，又叫分布函数，是概率密度函数的积分，能完整描述一个实随机变量X的概率分布。一般以大写“CDF”（Cumulative Distribution Function）表记。
对于所有实数x ，累积分布函数定义如下：
CCDF
中文百科
![F(x) = \operatorname{P}(X\leq x)](/Images/godic/202501/03/5ab3ef37703a0f5eda7e17711e8b18fc0313.png")
英语百科
Cumulative distribution function 累积分布函数
（重定向自CCDF）
![Cumulative Distribution Function for the normal distribution](/Images/godic/202501/03/Normal_Distribution_CDF.svg0314.png")
![From top to bottom, the cumulative distribution function of a discrete probability distribution, continuous probability distribution, and a distribution which has both a continuous part and a discrete part.](/Images/godic/202501/03/Discrete_probability_distribution_illustration.svg0314.png")
![Example of the folded cumulative distribution for a normal distribution function with an expected value of 0 and a standard deviation of 1.](/Images/godic/202501/03/Folded-cumulative-distribution-function.svg0314.png")
In probability theory and statistics, the cumulative distribution function (CDF) of a real-valued random variable X, or just distribution function of X, evaluated at x, is the probability that X will take a value less than or equal to x.
In the case of a continuous distribution, it gives the area under the probability density function from minus infinity to x. Cumulative distribution functions are also used to specify the distribution of multivariate random variables.