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- What is the normal approximation of the multinomial distribution . . .
You can approximate it with the multivariate normal distribution in the same way that binomial distribution is approximated by univariate normal distribution Check Elements of Distribution Theory and Multinomial Distribution pages 15-16-17
- Why is the Dirichlet distribution the prior for the multinomial . . .
The uniform distribution is actually a special case of the Dirichlet distribution, corresponding to the case α1 = α2 = ⋯ = αk = 1 So is the least-informative Jeffreys prior, for which α1 = ⋯ = αk = 1 2 The fact that the Dirichlet class includes these natural "non-informative" priors is another reason for using it
- Dirichlet distribution vs Multinomial distribution? - Cross Validated
A first difference is that multinomial distribution M(N,p) M (N, p) is discrete (it generalises binomial disrtibution) whereas Dirichlet distribution is continuous (it generalizes Beta distribution) But if you were to make N N go to infinity in order to get an approximately continuous outcome, then the marginal distributions of components of a multinomial random variables will become gaussian
- Expected value of a multinomial distribution - Cross Validated
4 I think that you mean that you take N draws from a multinomial distribution and the expected value of getting object k is Npk The easiest way to show this is to reduce the problem to N draws from a binomial distribution, with the options "not get object k " and "get object k " Consider K of these separate binomial problems and you get the
- Confidence interval and sample size multinomial probabilities
I have a question that relates to a multinomial distribution (not even 100% sure about this) that I hope somebody can help me with If I take a sample (lets assume n = 400 n = 400) on a categorical variable that has more than two possible outcomes (e g blue, black, green, yellow) and plot the frequencies so that I can derive the probabilities
- How to derive the determinant of the variance of a negative multinomial . . .
Taking x0 x 0 to be fixed as the number of successful draws from the "first" group, the mean vector and variance matrix of the distribution of the remaining m m values are given respectively by: μ = x0 p0 p Σ = x0 p20 pp′ + x0 p0 diag(p) μ = x 0 p 0 p Σ = x 0 p 0 2 p p ′ + x 0 p 0 d i a g (p)
- Real examples of multinomial distribution - Cross Validated
What a distribution can describe is a process for selecting the n n students from a population For the multinomial distribution to apply, that process has to be analogous to picking slips of paper--one per student--out of a well-mixed bowl of a great many such slips
- multinomial distribution - Expectation-Maximization Algorithm for . . .
To do so, I will consider a multinomial with five classes formed from the original multinomial by splitting the first class into two with probabilities 1 2 and θ 4 The original variable x1 is split into x1 = x11 +x12 Now, we have a MLE of θ by considering x12 +x4 to be a realization of a binomial with n = x12 +x4 +x2 + x3 and p = θ
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