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Its often easier to work with the log-likelihood in these situations than the likelihood. Note that the minimum/maximum of the log-likelihood is exactly the same as the min/max of the likelihood.
In comparing bernoulli_distribution's default constructor (50/50 chance of true/false) and uniform_int_distribution{0, 1} (uniform likely chance of 0 or 1) I find that bernoulli_distributions are at least 2x and upwards of 6x slower than uniform_int_distribution despite the fact that they give equivalent results.
Original post: Dan's answer is actually incorrect, not to offend anyone. A z-test is used only if your data follows a standard normal distribution. In this case, your data follows a binomial distribution, therefore a use a chi-squared test if your sample is large or fisher's test if your sample is small. Edit: My mistake, apologies to @Dan.
The Wilson score interval performs well in general for inference for the binomial probability parameter. The performance of various confidence intervals is examined in Brown, Cai and DasGupta (2001) and the Wilson score interval performs well compared to other intervals; in particular, it performs better than the Wald interval.
Thus there is not just one Bernoulli distribution, but rather a family of Bernoulli distributions, indexed by p. For example, if X ~ Bern(1/3), it would be correct but incomplete to say “X is Bernoulli”; to fully specify the distribution of X, we should both say its name (Bernoulli) and its parameter value (1/3), which is the point of the ...
First of all, for a bernoulli variable, a random sample could only be 0 or 1, on the other hand, the range of normal variable could be from -inf to inf. Secondly, If we have a random distribution with mean p, and variance p(1-p), once we draw lots of samples from this distribution and add them together, their summation distribution will also ...
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Well, Bernoulli is a probability distribution. Specifically, torch.distributions.Bernoulli() samples from the distribution and returns a binary value (i.e. either 0 or 1). Here, it returns 1 with probability p and return 0 with probability 1-p.
size can also be an array of indices, in which case a whole np.array with the given size will be filled with independent draws from the Binomial distribution. Note that the Binomial distribution is a generalisation of the Bernoulli distribution - in the case that n=1, Bin(n,p) has the same distribution as Ber(p).
In probability theory and statistics, the Bernoulli distribution. is the discrete probability distribution of a random variable which takes the value 1 with probability p and the value 0 with probability ${\displaystyle q=1-p}$. The probability mass function f of this distribution, over possible outcomes k, is