Generalized extreme value distributionIn probability theory and statistics, the generalized extreme value (GEV) distribution is a family of continuous probability distributions developed within extreme value theory to combine the Gumbel, Fréchet and Weibull families also known as type I, II and III extreme value distributions. By the extreme value theorem the GEV distribution is the only possible limit distribution of properly normalized maxima of a sequence of independent and identically distributed random variables.
Estimation theoryEstimation theory is a branch of statistics that deals with estimating the values of parameters based on measured empirical data that has a random component. The parameters describe an underlying physical setting in such a way that their value affects the distribution of the measured data. An estimator attempts to approximate the unknown parameters using the measurements.
Maximum likelihood estimationIn statistics, maximum likelihood estimation (MLE) is a method of estimating the parameters of an assumed probability distribution, given some observed data. This is achieved by maximizing a likelihood function so that, under the assumed statistical model, the observed data is most probable. The point in the parameter space that maximizes the likelihood function is called the maximum likelihood estimate. The logic of maximum likelihood is both intuitive and flexible, and as such the method has become a dominant means of statistical inference.
Heavy-tailed distributionIn probability theory, heavy-tailed distributions are probability distributions whose tails are not exponentially bounded: that is, they have heavier tails than the exponential distribution. In many applications it is the right tail of the distribution that is of interest, but a distribution may have a heavy left tail, or both tails may be heavy. There are three important subclasses of heavy-tailed distributions: the fat-tailed distributions, the long-tailed distributions, and the subexponential distributions.
Exponential distributionIn probability theory and statistics, the exponential distribution or negative exponential distribution is the probability distribution of the time between events in a Poisson point process, i.e., a process in which events occur continuously and independently at a constant average rate. It is a particular case of the gamma distribution. It is the continuous analogue of the geometric distribution, and it has the key property of being memoryless. In addition to being used for the analysis of Poisson point processes it is found in various other contexts.
ParameterA parameter (), generally, is any characteristic that can help in defining or classifying a particular system (meaning an event, project, object, situation, etc.). That is, a parameter is an element of a system that is useful, or critical, when identifying the system, or when evaluating its performance, status, condition, etc. Parameter has more specific meanings within various disciplines, including mathematics, computer programming, engineering, statistics, logic, linguistics, and electronic musical composition.
Statistical parameterIn statistics, as opposed to its general use in mathematics, a parameter is any measured quantity of a statistical population that summarises or describes an aspect of the population, such as a mean or a standard deviation. If a population exactly follows a known and defined distribution, for example the normal distribution, then a small set of parameters can be measured which completely describes the population, and can be considered to define a probability distribution for the purposes of extracting samples from this population.
Probability distribution fittingProbability distribution fitting or simply distribution fitting is the fitting of a probability distribution to a series of data concerning the repeated measurement of a variable phenomenon. The aim of distribution fitting is to predict the probability or to forecast the frequency of occurrence of the magnitude of the phenomenon in a certain interval. There are many probability distributions (see list of probability distributions) of which some can be fitted more closely to the observed frequency of the data than others, depending on the characteristics of the phenomenon and of the distribution.
Stone AgeThe Stone Age was a broad prehistoric period during which stone was widely used to make stone tools with an edge, a point, or a percussion surface. The period lasted for roughly 3.4 million years and ended between 4,000 BC and 2,000 BC, with the advent of metalworking. Though some simple metalworking of malleable metals, particularly the use of gold and copper for purposes of ornamentation, was known in the Stone Age, it is the melting and smelting of copper that marks the end of the Stone Age.
Ice ageAn ice age is a long period of reduction in the temperature of Earth's surface and atmosphere, resulting in the presence or expansion of continental and polar ice sheets and alpine glaciers. Earth's climate alternates between ice ages and greenhouse periods, during which there are no glaciers on the planet. Earth is currently in the ice age called Quaternary glaciation. Individual pulses of cold climate within an ice age are termed glacial periods (or, alternatively, glacials, glaciations, glacial stages, stadials, stades, or colloquially, ice ages), and intermittent warm periods within an ice age are called interglacials or interstadials.
Point estimationIn statistics, point estimation involves the use of sample data to calculate a single value (known as a point estimate since it identifies a point in some parameter space) which is to serve as a "best guess" or "best estimate" of an unknown population parameter (for example, the population mean). More formally, it is the application of a point estimator to the data to obtain a point estimate. Point estimation can be contrasted with interval estimation: such interval estimates are typically either confidence intervals, in the case of frequentist inference, or credible intervals, in the case of Bayesian inference.
Complex analysisComplex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers. It is helpful in many branches of mathematics, including algebraic geometry, number theory, analytic combinatorics, applied mathematics; as well as in physics, including the branches of hydrodynamics, thermodynamics, quantum mechanics, and twistor theory. By extension, use of complex analysis also has applications in engineering fields such as nuclear, aerospace, mechanical and electrical engineering.
Gumbel distributionIn probability theory and statistics, the Gumbel distribution (also known as the type-I generalized extreme value distribution) is used to model the distribution of the maximum (or the minimum) of a number of samples of various distributions. This distribution might be used to represent the distribution of the maximum level of a river in a particular year if there was a list of maximum values for the past ten years. It is useful in predicting the chance that an extreme earthquake, flood or other natural disaster will occur.
Mathematical analysisAnalysis is the branch of mathematics dealing with continuous functions, limits, and related theories, such as differentiation, integration, measure, infinite sequences, series, and analytic functions. These theories are usually studied in the context of real and complex numbers and functions. Analysis evolved from calculus, which involves the elementary concepts and techniques of analysis. Analysis may be distinguished from geometry; however, it can be applied to any space of mathematical objects that has a definition of nearness (a topological space) or specific distances between objects (a metric space).
Special functionsSpecial functions are particular mathematical functions that have more or less established names and notations due to their importance in mathematical analysis, functional analysis, geometry, physics, or other applications. The term is defined by consensus, and thus lacks a general formal definition, but the list of mathematical functions contains functions that are commonly accepted as special. Many special functions appear as solutions of differential equations or integrals of elementary functions.
Extreme weatherExtreme weather includes unexpected, unusual, severe, or unseasonal weather; weather at the extremes of the historical distribution—the range that has been seen in the past. Extreme events are based on a location's recorded weather history. They are defined as lying in the most unusual ten percent (10th or 90th percentile of a probability density function). The main types of extreme weather include heat waves, cold waves and heavy precipitation or storm events, such as tropical cyclones.
Extreme programmingExtreme programming (XP) is a software development methodology intended to improve software quality and responsiveness to changing customer requirements. As a type of agile software development, it advocates frequent releases in short development cycles, intended to improve productivity and introduce checkpoints at which new customer requirements can be adopted.
Java version historyThe Java language has undergone several changes since JDK 1.0 as well as numerous additions of classes and packages to the standard library. Since J2SE 1.4, the evolution of the Java language has been governed by the Java Community Process (JCP), which uses Java Specification Requests (JSRs) to propose and specify additions and changes to the Java platform. The language is specified by the Java Language Specification (JLS); changes to the JLS are managed under JSR 901.
Fecal incontinenceFecal incontinence (FI), or in some forms encopresis, is a lack of control over defecation, leading to involuntary loss of bowel contents, both liquid stool elements and mucus, or solid feces. When this loss includes flatus (gas), it is referred to as anal incontinence. FI is a sign or a symptom, not a diagnosis. Incontinence can result from different causes and might occur with either constipation or diarrhea. Continence is maintained by several interrelated factors, including the anal sampling mechanism, and incontinence usually results from a deficiency of multiple mechanisms.
AnismusAnismus or dyssynergic defecation is the failure of normal relaxation of pelvic floor muscles during attempted defecation. It can occur in both children and adults, and in both men and women (although it is more common in women). It can be caused by physical defects or it can occur for other reasons or unknown reasons. Anismus that has a behavioral cause could be viewed as having similarities with parcopresis, or psychogenic fecal retention. Symptoms include tenesmus (the sensation of incomplete emptying of the rectum after defecation has occurred) and constipation.
