[수리통계학] Discrete Distributions

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오늘은 대표적인 이산형 분포의 종류를 나열해보겠습니다.

 

1. Discrete Uniform Distribution 

 : When a pmf is constant on the space R of X; we say that the distribution is a discrete uniform abbreviated by DU.

 

2. Hypergeometric Distribution

 : Suppose there are N1 success objects and N2 failure objects in a collection N = N1 + N2 of similar objects. When n objects are selected from these N objects at random with without replacement. Let the random variable X be the number of success objects among the n objects.

 

3. Bernoulli Distribution

 : A random experiment, the outcome of which can be classified in but one of two mutually exclusive and exhaustive ways - say, success and failure. When Bernoulli experiment is performed several independent times and probability of success(p) remains the same from trial to trial. In addition, we shall frequently let q = 1 - p denote the probability of failure.

 

4. Binomial Distribution

 : 1. A Bernoulli experiment is performed n times

   2. The trials are independent

   3. The probability of success on each trial is a constant p

   4. The random variable X equals the number of successes in the n trials

 

Let X be a random variable associated with a binomial experiment, we say that X has a binomial distribution with the prob of success p.

 

5. Geometric Distribution

 : A random experiment of observing a sequence of independent Bernoulli trials (probability of success p) until exactly the first success occur. Let X be the number of Bernoulli trials until the first success occur.

 

6. Negative Binomial Distribution

 : A random experiment of observing a sequence of independent Bernoulli trials (probability of success p) until exactly the r-th success occur. Let X be the number of Bernoulli trials until the r-th success occur.

 

7. Poisson Distribution

 : An experiment that counts the number of times a particular event occur in a given time or on given physical object (where mean occurring rate is λ). If we set X to be the number of times a particular event occur in the Poisson experiment.

Relationships between Discrete Distributions

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