Considering " p " as the only parameter, it follows that the log likelihood for the Bernoulli distribution is
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Thus the measure is used to evaluate how data compares to a fixed-probability-of-success Bernoulli distribution.
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The Bernoulli distribution is a special case of the binomial distribution where a single experiment / trial is conducted ( n = 1 ).
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First, the conditional distribution y \ mid x is a Bernoulli distribution rather than a Gaussian distribution, because the dependent variable is binary.
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It is a member of the exponential family, has the Poisson distribution and geometric distribution as special cases and the Bernoulli distribution as a limiting case.
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Well-known discrete probability distributions used in statistical modeling include the Poisson distribution, the Bernoulli distribution, the binomial distribution, the geometric distribution, and the negative binomial distribution.
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We can create a mixture model with K = 10 different components, where each component is a vector of size N ^ 2 of Bernoulli distributions ( one per pixel ).
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The maximum value ( 1.0 ) is reached only by a Bernoulli distribution with only two distinct values or the sum of two different Dirac delta functions ( a bi-delta distribution ).
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Because of their importance, these variables are often considered a separate category, with a separate distribution ( the Bernoulli distribution ) and separate regression models ( logistic regression, probit regression, etc . ).
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For the multinomial distribution, and for the vector form of the categorical distribution, the expected values of the elements of the vector can be related to the predicted probabilities similarly to the binomial and Bernoulli distributions.
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