当前位置:网站首页>Commonly used probability distributions: Bernoulli distribution, binomial distribution, polynomial distribution, Gaussian distribution, exponential distribution, Laplace distribution and Dirac delta d
Commonly used probability distributions: Bernoulli distribution, binomial distribution, polynomial distribution, Gaussian distribution, exponential distribution, Laplace distribution and Dirac delta d
2022-07-05 22:56:00 【YaoHa_】
Bernoulli distribution (Bernoulli distribution)
** Bernoulli distribution :** Distribution of single binary random variable . By a single parameter φ∈[0,1] control .
example : Flip a coin , The probability of facing up .
Binomial distribution (binomial distrubution)
Binomial distribution : stay n Events in this test A It happens k The probability of time .
Probability calculation :
In style k=0,1,2,…,n,
Expect to calculate :E(x)=np
Variance calculation :D(x)=np(1-p)
example : throw n The second coin , Face up m The probability of time .
Polynomial distribution (multinoulli distribution)
Polynomial distribution : have k Distribution on a single discrete random variable in different states , among k It's a finite value . Expansion of binomial distribution .
Probability calculation :
example : Multiple screen throwing , Count the probability of the number of times each side is thrown .
Gaussian distribution (Gaussian dis-tribution)
Gaussian distribution (Gaussian dis-tribution), Also known as normal distribution (normal distribution). namely :
notes : The normal distribution presents a classic “ A bell curve ” The shape of the , Of which the central peak x Coordinates from µ give , The width of the peak is affected by σ control . In this example , What we're showing is Standard normal distribution (standard normaldistribution), among µ=0,σ=1.
Expect to calculate :E(x)=µ
Variance calculation :D(x)=σ^2
An index distribution (exponential distribution)
An index distribution (exponential distribution): stay x=0 Get the boundary point (sharp point) The distribution of . namely :
Indicator function (indicator function):
The exponential distribution is made proper by the indicator function x The probability of taking a negative value is zero .
Laplacian distribution (Laplace distribution)
Laplacian distribution (Laplace distribution): Probability density function distribution of random variables . namely :
Dirac Distribution
Dirac delta function (Dirac delta function): Defined as in addition to 0 Values for all points except 0, But the integral is 1.
Dirac Distribution is often used as an empirical distribution (empirical distribution) A component of :
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