multinomial distribution


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mul·ti·nom·i·al dis·tri·bu·tion

probability distribution associated with the classification of each of a sample of individuals into one of several mutually exclusive and exhaustive categories.
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(2013), to statistically determine the expected diameter at each ovarian stage, a multinomial distribution was used, and its probability density function (PDF) was expressed as described by Haddon (2001):
In the Table 2, the estimates of the M3 parameters in conjunction with the confidence intervals at p < 0.95 had similar [[sigma].sup.2.sub.b] for the binomial and the beta-binomial distributions ([[sigma].sup.2.sub.b] = 0.93) but lower for both n conditions when we fit the multinomial distribution ([[sigma].sup.2.sub.b] = 0.72 for [pi[].sub.1] and [[sigma].sup.2.sub.b] = 0.76 for n2).
where the document is created by learner l, z is a topic, K is all topics, [[theta].sub.l] is the multinomial distribution of the learner l over topics, [0.sub.z] is the multinomial distribution of the topic z over words.
Each topic defines a multinomial distribution over the original features and is assumed to have been drawn from a Dirichlet.
When the adult geese were resighted, each observation was assigned to one of the six habitat categories (listed in Table 1) resulting in a dataset that was treated as a multinomial distribution with six mutually exclusive and independent possible outcomes.
In Figure 2, [[beta].sub.k] is a vector consisting of the parameters of multinomial distribution corresponding to the kth function label.
A multinomial model is a stochastic process where the observations follow a multinomial distribution. It is sufficient to model observations instead of states, since the observations in a multinomial model can represent states correspondingly with absolute state knowledge.
Therefore, some researchers assume that the volatility of the price of underlying assets follows a multinomial distribution and use multinomial pricing model to price options (e.g., Madan et al.
They model each patient trace as mixtures of multiple topics, while each topic is modeled as a multinomial distribution over clinical activities.
In stochastic pooling, the pooled maps are determined by sampling from each pooling region using a multinomial distribution. We first calculate the probabilities for each pooling region [R.sub.j] by normalizing the values of the nodes within the region in previous convolution layer as follows:
Additional material examines probability distributions, elements of set theory, multinomial distribution of single-voxel imaging, and other subjects.