常見概率分佈總結
阿新 • • 發佈:2018-12-11
Discrete
Bernoulli distribution
- pmf
- expectation
Binomial distribution
- pmf
- expectation
- variance
Geometric distribution
- pmf
- expectation
Negative binomial distribution
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The negative binomial distribution arises as a generalization of the geometric distribution.
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Suppose that a sequence of independent trials each with probability of success is performed until there are successes in all.
- so can be denote as
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pmf
Hypergeometric distribution
- Suppose that an urn contains balls, of which are black and are white. Let denote the number of black balls drawn when taking balls without replacement.
- pmf
Possion distribution
- can be derived as the limit of a binomial distribution as the number of trials approaches infinity and the probability of success on each trial approaches zero in such a way that , can be seen as the successful trials
- pmf
Continuous
Uniform distribution
- A uniform r.v on the interval [a,b] is a model for what we mean when we say “choose a number at random between a and b”
- pdf
Exponential distribution
- Exponential distribution is often used to model lifetimes or waiting times, in which context it is conventional to replace by .
- pdf
- cdf(easy to get)
- expectation
- variance
property
- let are independent Poisson r.v.s with ,then
Gamma distribution
- pdf
- expectation