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Is negative binomial continuous?
The negative binomial distribution also arises as a continuous mixture of Poisson distributions (i.e. a compound probability distribution) where the mixing distribution of the Poisson rate is a gamma distribution.
Can you have a continuous binomial distribution?
The binomial distribution is a common discrete distribution used in statistics, as opposed to a continuous distribution, such as the normal distribution. The binomial distribution, therefore, represents the probability for x successes in n trials, given a success probability p for each trial.
What is the distribution that is discrete and has more than two possible outcomes?
A binomial distribution has a finite set of just two possible outcomes: zero or one—for instance, lipping a coin gives you the list {Heads, Tails}. The Poisson distribution is a discrete distribution that counts the frequency of occurrences as integers, whose list {0, 1, 2.} can be infinite.
Which is the continuous version of the negative binomial distribution?
Look at this paper: Chandra, Nimai Kumar, and Dilip Roy. A continuous version of the negative binomial distribution. Statistica 72, no. 1 (2012): 81. It’s defined in the paper as the survival function, which is a natural approach since neg binomial was introduced in reliability analysis:
Does it make sense to consider a continuous distribution on non-negative reals?
Does it make sense to consider a continuous distribution on non-negative reals defined by the same formula (replacing k ∈ N 0 by x ∈ R ≥ 0 )? The binomial coefficient can be rewritten as a product of ( k + 1) ⋅ … ⋅ ( k + r − 1), which is well-defined for any real k. So we would have a PDF f ( x; r, p) ∝ ∏ i = 1 r − 1 ( x + i) ⋅ p x ( 1 − p) r.
Is the normalizing constant the same for the discrete Poisson distribution?
So the normalizing constant is virtually 1 and the mean and variance are almost exactly the same as for the discrete Poisson distribution. The approximation is improved even more if we add a continuity correction, integrating from − 1 / 2 to ∞ instead of from 0.
How is the NB distribution used in bioinformatics?
The NB distribution arises in bioinformatics as a gamma mixture of Poisson distributions (see the Wikipedia negative binomial article or McCarthy et al below). The continuous NB distribution arises simply by replacing the Poisson distribution with its continuous analog with pdf