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This is the theoretical distribution model for a balanced coin, an unbiased die, a casino roulette, or the first card of a well-shuffled deck. The hypergeometric distribution, which describes the number of successes in the first m of a series of n consecutive Yes/No experiments, if the total number of successes is known. This distribution ...
A generative model is a statistical model of the joint probability distribution (,) on a given observable variable X and target variable Y; [1] A generative model can be used to "generate" random instances of an observation x.
A probability distribution whose sample space is one-dimensional (for example real numbers, list of labels, ordered labels or binary) is called univariate, while a distribution whose sample space is a vector space of dimension 2 or more is called multivariate.
In probability theory and statistics, the Weibull distribution / ˈ w aɪ b ʊ l / is a continuous probability distribution. It models a broad range of random variables, largely in the nature of a time to failure or time between events. Examples are maximum one-day rainfalls and the time a user spends on a web page.
The Poisson distribution may be useful to model events such as: the number of meteorites greater than 1-meter diameter that strike Earth in a year; the number of laser photons hitting a detector in a particular time interval; the number of students achieving a low and high mark in an exam; and; locations of defects and dislocations in materials.
For example, we could use the negative binomial distribution to model the number of days n (random) a certain machine works (specified by r) before it breaks down. The negative binomial distribution has a variance μ / p {\displaystyle \mu /p} , with the distribution becoming identical to Poisson in the limit p → 1 {\displaystyle p\to 1} for ...
Two statistical models are nested if the first model can be transformed into the second model by imposing constraints on the parameters of the first model. As an example, the set of all Gaussian distributions has, nested within it, the set of zero-mean Gaussian distributions: we constrain the mean in the set of all Gaussian distributions to get ...
The Pareto distribution, named after the Italian civil engineer, economist, and sociologist Vilfredo Pareto, [2] is a power-law probability distribution that is used in description of social, quality control, scientific, geophysical, actuarial, and many other types of observable phenomena; the principle originally applied to describing the distribution of wealth in a society, fitting the trend ...