|
Complete Spatial Randomness
Complete spatial randomness (CSR) describes a point process whereby point events occur within a given study area in a completely random fashion. It is synonymous with a ''homogeneous spatial Poisson process''.O. Maimon, L. Rokach, ''Data Mining and Knowledge Discovery Handbook'', Second Edition, Springer 2010, pages 851-852 Such a process is modeled using only one parameter \rho, i.e. the density of points within the defined area. The term complete spatial randomness is commonly used in Applied Statistics in the context of examining certain point patterns, whereas in most other statistical contexts it is referred to the concept of a spatial Poisson process. Model Data in the form of a set of points, irregularly distributed within a region of space, arise in many different contexts; examples include locations of trees in a forest, of nests of birds, of nuclei in tissue, of ill people in a population at risk. We call any such data-set a spatial point pattern and refer to the loc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Point Process
In statistics and probability theory, a point process or point field is a set of a random number of mathematical points randomly located on a mathematical space such as the real line or Euclidean space. Kallenberg, O. (1986). ''Random Measures'', 4th edition. Academic Press, New York, London; Akademie-Verlag, Berlin. , .Daley, D.J, Vere-Jones, D. (1988). ''An Introduction to the Theory of Point Processes''. Springer, New York. , . Point processes on the real line form an important special case that is particularly amenable to study,Last, G., Brandt, A. (1995).''Marked point processes on the real line: The dynamic approach.'' Probability and its Applications. Springer, New York. , because the points are ordered in a natural way, and the whole point process can be described completely by the (random) intervals between the points. These point processes are frequently used as models for random events in time, such as the arrival of customers in a queue (queueing theory), of impulses i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spatial Poisson Process
In probability theory, statistics and related fields, a Poisson point process (also known as: Poisson random measure, Poisson random point field and Poisson point field) is a type of mathematical object that consists of points randomly located on a mathematical space with the essential feature that the points occur independently of one another. The process's name derives from the fact that the number of points in any given finite region follows a Poisson distribution. The process and the distribution are named after French mathematician Siméon Denis Poisson. The process itself was discovered independently and repeatedly in several settings, including experiments on radioactive decay, telephone call arrivals and actuarial science. This point process is used as a mathematical model for seemingly random processes in numerous disciplines including astronomy,G. J. Babu and E. D. Feigelson. Spatial point processes in astronomy. ''Journal of statistical planning and inference'', 50( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Poisson Distribution
In 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. It can also be used for the number of events in other types of intervals than time, and in dimension greater than 1 (e.g., number of events in a given area or volume). The Poisson distribution is named after French mathematician Siméon Denis Poisson. It plays an important role for discrete-stable distributions. Under a Poisson distribution with the expectation of ''λ'' events in a given interval, the probability of ''k'' events in the same interval is: :\frac . For instance, consider a call center which receives an average of ''λ ='' 3 calls per minute at all times of day. If the calls are independent, receiving one does not change the probability of when the next on ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Uniform Probability Distribution
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. The bounds are defined by the parameters, a and b, which are the minimum and maximum values. The interval can either be closed (i.e. ,b/math>) or open (i.e. (a,b)). Therefore, the distribution is often abbreviated U(a,b), where U stands for uniform distribution. The difference between the bounds defines the interval length; all intervals of the same length on the distribution's support are equally probable. It is the maximum entropy probability distribution for a random variable X under no constraint other than that it is contained in the distribution's support. Definitions Probability density function The probability density function of the continuous uniform distribution is f(x) = \begin \dfrac & \tex ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Carol A
Carol may refer to: People with the name *Carol (given name) *Avedon Carol (born 1951), British writer and feminist *Henri Carol (1910–1984), French composer and organist *Martine Carol (1920–1967), French film actress *Sue Carol (1906–1982), American actress and talent agent, wife of actor Alan Ladd Arts, entertainment, and media Music * Carol (music), a festive or religious song; historically also a dance ** Christmas carol, a song sung during Christmas * Carol (Carol Banawa album), ''Carol'' (Carol Banawa album) (1997) * Carol (Chara album), ''Carol'' (Chara album) (2009) * Carol (Chuck Berry song), "Carol" (Chuck Berry song), a rock 'n roll song written and recorded by Chuck Berry in 1958 * Carol, a Japanese rock band that Eikichi Yazawa once belonged to *"The Carol", a song by Loona from ''HaSeul'' *"Carol", a song by Slint from ''Tweez'' Other uses in arts, entertainment, and media * Carol (anime), ''Carol'' (anime), an anime OVA featuring character designs by Yun Kou ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Average
In colloquial, ordinary language, an average is a single number or value that best represents a set of data. The type of average taken as most typically representative of a list of numbers is the arithmetic mean the sum of the numbers divided by how many numbers are in the list. For example, the mean or average of the numbers 2, 3, 4, 7, and 9 (summing to 25) is 5. Depending on the context, the most representative statistics, statistic to be taken as the average might be another measure of central tendency, such as the mid-range, median, Mode (statistics), mode or geometric mean. For example, the average income, personal income is often given as the median the number below which are 50% of personal incomes and above which are 50% of personal incomes because the mean would be higher by including personal incomes from a few billionaires. General properties If all numbers in a list are the same number, then their average is also equal to this number. This property is shared by each o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gamma Function
In mathematics, the gamma function (represented by Γ, capital Greek alphabet, Greek letter gamma) is the most common extension of the factorial function to complex numbers. Derived by Daniel Bernoulli, the gamma function \Gamma(z) is defined for all complex numbers z except non-positive integers, and for every positive integer z=n, \Gamma(n) = (n-1)!\,.The gamma function can be defined via a convergent improper integral for complex numbers with positive real part: \Gamma(z) = \int_0^\infty t^ e^\textt, \ \qquad \Re(z) > 0\,.The gamma function then is defined in the complex plane as the analytic continuation of this integral function: it is a meromorphic function which is holomorphic function, holomorphic except at zero and the negative integers, where it has simple Zeros and poles, poles. The gamma function has no zeros, so the reciprocal gamma function is an entire function. In fact, the gamma function corresponds to the Mellin transform of the negative exponential functi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Factorial
In mathematics, the factorial of a non-negative denoted is the Product (mathematics), product of all positive integers less than or equal The factorial also equals the product of n with the next smaller factorial: \begin n! &= n \times (n-1) \times (n-2) \times (n-3) \times \cdots \times 3 \times 2 \times 1 \\ &= n\times(n-1)!\\ \end For example, 5! = 5\times 4! = 5 \times 4 \times 3 \times 2 \times 1 = 120. The value of 0! is 1, according to the convention for an empty product. Factorials have been discovered in several ancient cultures, notably in Indian mathematics in the canonical works of Jain literature, and by Jewish mystics in the Talmudic book ''Sefer Yetzirah''. The factorial operation is encountered in many areas of mathematics, notably in combinatorics, where its most basic use counts the possible distinct sequences – the permutations – of n distinct objects: there In mathematical analysis, factorials are used in power series for the ex ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Social Sciences
Social science (often rendered in the plural as the social sciences) is one of the branches of science, devoted to the study of society, societies and the Social relation, relationships among members within those societies. The term was formerly used to refer to the field of sociology, the original "science of society", established in the 18th century. It now encompasses a wide array of additional academic disciplines, including anthropology, archaeology, economics, geography, history, linguistics, management, communication studies, psychology, culturology, and political science. The majority of Positivism, positivist social scientists use methods resembling those used in the natural sciences as tools for understanding societies, and so define science in its stricter Modern science, modern sense. Speculative social scientists, otherwise known as Antipositivism, interpretivist scientists, by contrast, may use social critique or symbolic interpretation rather than constructing Em ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistics
Statistics (from German language, German: ', "description of a State (polity), 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. Populations can be diverse groups of people or objects such as "all people living in a country" or "every atom composing a crystal". Statistics deals with every aspect of data, including the planning of data collection in terms of the design of statistical survey, surveys and experimental design, experiments. When census data (comprising every member of the target population) cannot be collected, statisticians collect data by developing specific experiment designs and survey sample (statistics), samples. Representative sampling assures that inferences and conclusions can reasonably extend from the sample ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monte Carlo Method
Monte Carlo methods, or Monte Carlo experiments, are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. The underlying concept is to use randomness to solve problems that might be deterministic in principle. The name comes from the Monte Carlo Casino in Monaco, where the primary developer of the method, mathematician Stanisław Ulam, was inspired by his uncle's gambling habits. Monte Carlo methods are mainly used in three distinct problem classes: optimization, numerical integration, and generating draws from a probability distribution. They can also be used to model phenomena with significant uncertainty in inputs, such as calculating the risk of a nuclear power plant failure. Monte Carlo methods are often implemented using computer simulations, and they can provide approximate solutions to problems that are otherwise intractable or too complex to analyze mathematically. Monte Carlo methods are widely used in va ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spatial Analysis
Spatial analysis is any of the formal Scientific technique, techniques which study entities using their topological, geometric, or geographic properties, primarily used in Urban design, Urban Design. Spatial analysis includes a variety of techniques using different analytic approaches, especially ''spatial statistics''. It may be applied in fields as diverse as astronomy, with its studies of the placement of galaxies in the cosmos, or to chip fabrication engineering, with its use of "place and route" algorithms to build complex wiring structures. In a more restricted sense, spatial analysis is geospatial analysis, the technique applied to structures at the human scale, most notably in the analysis of geographic data. It may also applied to genomics, as in Spatial transcriptomics, transcriptomics data, but is primarily for spatial data. Complex issues arise in spatial analysis, many of which are neither clearly defined nor completely resolved, but form the basis for current resear ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
