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Standard normal table. In statistics, a standard normal table, also called the unit normal table or Z table, [ 1 ] is a mathematical table for the values of Φ, the cumulative distribution function of the normal distribution. It is used to find the probability that a statistic is observed below, above, or between values on the standard normal ...
Probability theory. 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 The parameter is the mean or expectation of the distribution (and also its median and mode), while ...
The Bernoulli distribution, which takes value 1 with probability p and value 0 with probability q = 1 − p. The Rademacher distribution, which takes value 1 with probability 1/2 and value −1 with probability 1/2. The binomial distribution, which describes the number of successes in a series of independent Yes/No experiments all with the same ...
The cumulative distribution function of a real-valued random variable is the function given by [2]: p. 77. (Eq.1) where the right-hand side represents the probability that the random variable takes on a value less than or equal to . The probability that lies in the semi-closed interval , where , is therefore [2]: p. 84.
In probability theory and statistics, the chi-squared distribution (also chi-square or -distribution) with degrees of freedom is the distribution of a sum of the squares of independent standard normal random variables. The chi-squared distribution is a special case of the gamma distribution and the univariate Wishart distribution.
t. e. 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, a log-normal (or lognormal) distribution is a continuous probability distribution of a random variable whose logarithm is normally distributed. Thus, if the random variable X is log-normally distributed, then Y = ln (X) has a normal distribution. [2][3] Equivalently, if Y has a normal distribution, then the exponential ...
The t distribution is often used as an alternative to the normal distribution as a model for data, which often has heavier tails than the normal distribution allows for; see e.g. Lange et al. [26] The classical approach was to identify outliers (e.g., using Grubbs's test) and exclude or downweight them in some way.