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In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of possible outcomes for an experiment. [1] [2] It is a mathematical description of a random phenomenon in terms of its sample space and the probabilities of events (subsets of the sample space). [3]
In probability theory and statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable.The general form of its probability density function is [2] [3] = ().
Descriptive statistics are most often concerned with two sets of properties of a distribution (sample or population): central tendency (or location) seeks to characterize the distribution's central or typical value, while dispersion (or variability) characterizes the extent to which members of the distribution depart from its center and each other.
In statistics, a sampling distribution or finite-sample distribution is the probability distribution of a given random-sample-based statistic.For an arbitrarily large number of samples where each sample, involving multiple observations (data points), is separately used to compute one value of a statistic (for example, the sample mean or sample variance) per sample, the sampling distribution is ...
In statistics, "random sample" is the typical terminology, but in probability, it is more common to say "IID." Identically distributed means that there are no overall trends — the distribution does not fluctuate and all items in the sample are taken from the same probability distribution.
The log-normal distribution is the maximum entropy probability distribution for a random variate X —for which the mean and variance of ln(X) are specified. [ 5 ] Definitions
In probability theory and statistics, the continuous uniform distributions or rectangular distributions are a family of symmetric probability distributions.Such a distribution describes an experiment where there is an arbitrary outcome that lies between certain bounds. [1]
The distribution of a linguistic element is the set of environments in which it occurs, which may be in complementary distribution, contrastive distribution, or free variation with another such element, and which is the basis of distributional semantics