Probability distributionMathematical function for the probability a given outcome occurs in an experimentIn probability theory and statistics, a probability distribution describes how probabilities are assigned to the possible results of a random phenomenon—more precisely, to events, which are sets of possible outcomes of a probabilistic experiment. Informally, a probability distribution tells us how likely different results are.
Cauchy distributionProbability distributionThe Cauchy distribution, named after Augustin-Louis Cauchy, is a continuous probability distribution. It is also known, especially among physicists, as the Lorentz distribution (after Hendrik Lorentz), Cauchy–Lorentz distribution, Lorentz(ian) function, or Breit–Wigner distribution.
Exponential distributionProbability distributionIn probability theory and statistics, the exponential distribution or negative exponential distribution is the probability distribution of the distance between events in a Poisson point process, i.e., a process in which events occur continuously and independently at a constant average rate; the distance parameter could be any meaningful mono-dimensional measure of the process, such as time between production errors, or length along a roll of fabric in the weaving manufacturing process.
Binomial distributionIn probability theory and statistics, the binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a sequence of nindependentexperiments, each asking a yes–no question, and each with its own Boolean-valued outcome: success (with probability p) or failure (with probability q = 1 − p).
Poisson distributionDiscrete probability distributionIn probability theory and statistics, the Poisson distribution () is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time if these events occur with a known constant mean rate and independently of the time since the last event.
Chi-squared distributionProbability distribution and special case of gamma distributionIn probability theory and statistics, the χ2{\displaystyle \chi ^{2}}-distribution with k{\displaystyle k}degrees of freedom is the distribution of a sum of the squares of k{\displaystyle k}independentstandard normal random variables. The chi-squared distribution χk2{\displaystyle \chi _{k}^{2}} is a special case of the gamma distribution and the univariate Wishart distribution.
Normal distributionProbability distributionIn probability theory and statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valuedrandom variable. The general form of its probability density function is f(x)=12πσ2exp(−(x−μ)22σ2).{\displaystyle f(x)={\frac {1}{\sqrt {2\pi \sigma ^{2}}}}\exp {\left(-{\frac {(x-\mu )^{2}}{2\sigma ^{2}}} ight)}\,.} The parameter μ{\displaystyle \mu } is the mean or expectation of the distribution (…
Mode (statistics)In statistics, the mode is the value that appears most often in a set of data values. If X is a discrete random variable, the mode is the value x at which the probability mass functionP(X) takes its maximum value, i.e., x = argmaxxi P(X = xi). In other words, it is the value that is most likely to be sampled. Like the statistical mean and median, the mode is a summary statistic about the central tendency of a random variable or a population.
Student's t-distributionProbability distributionIn probability theory and statistics, Student's t distribution (or simply the t distribution) tν{\displaystyle t_{ u }} is a continuous probability distribution that generalizes the standard normal distribution. Like the latter, it is symmetric around zero and bell-shaped. However, tν{\displaystyle t_{ u }} has heavier tails, and the amount of probability mass in the tails is controlled by the parameter ν{\displaystyle u }.
StatisticsStatistics (from German: Statistik, orig. "description of a state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model to be studied.
Mathematical objectA mathematical object is an abstract entity arising in mathematics. Typically, a mathematical object can be a value that can be assigned to a symbol, and therefore can be involved in formulas. Commonly encountered mathematical objects include numbers, expressions, shapes, functions, and sets. Mathematical objects can be very complex; for example, theorems, proofs, and even formal theories are considered as mathematical objects in proof theory.
MathematicsField of knowledgeIlluminated letter P at the beginning of Adelard of Bath's translation of Euclid's Elements, which starts "Punctum est illud cui pars non est" ('A point is that which has no part'). Geometry is shown personified as a woman, following Martianus Capella's De nuptiis Philologiae et Mercurii.Mathematics is a field of knowledge concerned with abstract concepts such as numbers, geometric shapes, sets, functions, and probabilities.*As an Amazon Associate I earn from qualifying purchases.