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Hypoexponential Distribution
In probability theory the hypoexponential distribution or the generalized Erlang distribution is a continuous distribution, that has found use in the same fields as the Erlang distribution, such as queueing theory, teletraffic engineering and more generally in stochastic processes. It is called the hypoexponetial distribution as it has a coefficient of variation less than one, compared to the hyper-exponential distribution which has coefficient of variation greater than one and the exponential distribution which has coefficient of variation of one. Overview The Erlang distribution is a series of ''k'' exponential distributions all with rate \lambda. The hypoexponential is a series of ''k'' exponential distributions each with their own rate \lambda_, the rate of the i^ exponential distribution. If we have ''k'' independently distributed exponential random variables \boldsymbol_, then the random variable, : \boldsymbol=\sum^_\boldsymbol_ is hypoexponentially distributed. The hypo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Real Number
In mathematics, a real number is a number that can be used to measure a continuous one- dimensional quantity such as a duration or temperature. Here, ''continuous'' means that pairs of values can have arbitrarily small differences. Every real number can be almost uniquely represented by an infinite decimal expansion. The real numbers are fundamental in calculus (and in many other branches of mathematics), in particular by their role in the classical definitions of limits, continuity and derivatives. The set of real numbers, sometimes called "the reals", is traditionally denoted by a bold , often using blackboard bold, . The adjective ''real'', used in the 17th century by René Descartes, distinguishes real numbers from imaginary numbers such as the square roots of . The real numbers include the rational numbers, such as the integer and the fraction . The rest of the real numbers are called irrational numbers. Some irrational numbers (as well as all the rationals) a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Density Function
In probability theory, a probability density function (PDF), density function, or density of an absolutely continuous random variable, is a Function (mathematics), function whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) can be interpreted as providing a ''relative likelihood'' that the value of the random variable would be equal to that sample. Probability density is the probability per unit length, in other words, while the ''absolute likelihood'' for a continuous random variable to take on any particular value is 0 (since there is an infinite set of possible values to begin with), the value of the PDF at two different samples can be used to infer, in any particular draw of the random variable, how much more likely it is that the random variable would be close to one sample compared to the other sample. More precisely, the PDF is used to specify the probability of the random variable falling ''within ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Marcel F
Marcel may refer to: People * Marcel (given name), people with the given name Marcel * Marcel (footballer, born August 1981), Marcel Silva Andrade, Brazilian midfielder * Marcel (footballer, born November 1981), Marcel Augusto Ortolan, Brazilian striker * Marcel (footballer, born 1983), Marcel Silva Cardoso, Brazilian left back * Marcel (footballer, born 1992), Marcel Henrique Garcia Alves Pereira, Brazilian midfielder * Marcel (singer), American country music singer * Étienne Marcel (died 1358), provost of merchants of Paris * Gabriel Marcel (1889–1973), French philosopher, Christian existentialist and playwright * Jean Marcel (died 1980), Madagascan Anglican bishop * Jean-Jacques Marcel (1931–2014), French football player * Rosie Marcel (born 1977), English actor * Sylvain Marcel (born 1974), Canadian actor * Terry Marcel (born 1942), British film director * Claude Marcel (1793-1876), French diplomat and applied linguist Other uses * Marcel (''Friends''), a fictional ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Phase-type Distribution
A phase-type distribution is a probability distribution constructed by a convolution or mixture of exponential distributions. It results from a system of one or more inter-related Poisson processes occurring in sequence, or phases. The sequence in which each of the phases occurs may itself be a stochastic process. The distribution can be represented by a random variable describing the time until absorption of a Markov process with one absorbing state. Each of the Markov process, states of the Markov process represents one of the phases. It has a discrete time, discrete-time equivalent the discrete phase-type distribution. The set of phase-type distributions is dense in the field of all positive-valued distributions, that is, it can be used to approximate any positive-valued distribution. Definition Consider a continuous-time Markov process with ''m'' + 1 states, where ''m'' ≥ 1, such that the states 1,...,''m'' are transient states and state 0 is an absorbi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vrije Universiteit Amsterdam
The (abbreviated as ''VU Amsterdam'' or simply ''VU'' when in context) is a public university, public research university in Amsterdam, Netherlands, founded in 1880. The VU Amsterdam is one of two large, publicly funded research universities in the city, the other being the University of Amsterdam (UvA). The literal translation of the Dutch name is "Free University". "Free" refers to independence of the university from both the State (polity), State and the Dutch Reformed Church. Both within and outside the university, the institution is commonly referred to as "the VU". Although founded as a private institution, the VU has received government funding on a parity basis with public universities since 1970. The university is located on a compact urban campus in the southern Buitenveldert neighbourhood of Amsterdam and adjacent to the modern Zuidas business district. As of October 2021, the VU had 29,796 registered students, most of whom were full-time students. That year, the uni ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of Theoretical Biology
The ''Journal of Theoretical Biology'' is a biweekly peer-reviewed scientific journal covering theoretical biology, as well as mathematical, computational, and statistical aspects of biology. Some research areas covered by the journal include cell biology, evolutionary biology, population genetics, morphogenesis, and immunology. The journal was established in 1961. Its founding editor-in-chief was English biologist James F. Danielli, who remained editor until his death in 1984. The journal is published by Elsevier and, , the editors-in-chief are Denise Kirschner ( University of Michigan Medical School), Mark Chaplain ( University of St. Andrews), and Akira Sasaki (The university for advanced studies, SOKENDAI, Hayama). Lewis Wolpert served as editor-in-chief for more than 55 years. According to the ''Journal Citation Reports'' the journal has a 2020 impact factor of 2.691. Notable articles The following are the most highly cited articles (more than 2,000 citations at April ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Molecular Biology And Evolution
''Molecular Biology and Evolution'' (''MBE'') is a monthly peer-reviewed scientific journal published by Oxford University Press on behalf of the Society for Molecular Biology and Evolution. It publishes work in the intersection of molecular biology and evolutionary biology. The founding editors were Walter Fitch and Masatoshi Nei; the present editors-in-chief are Brandon Gaut and Claudia Russo. Subject matter Evolution is the most fundamental of biological processes. MBE publishes patterns and processes that impact the evolution of life at molecular levels, across a full breadth of taxonomy, genomic organization, and functions, forms, and phenotypes. MBE's Methods, Resource, and Protocol sections include research tools that enable discoveries, while the Reviews and Perspectives synthesize different aspects of the evolutionary thought. Editorial process All MBE manuscripts are peer-reviewed. Decisions to publish are made by the Board of Editors, led by the Editors-in-Chief (Ei ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Laplace Transform
In mathematics, the Laplace transform, named after Pierre-Simon Laplace (), is an integral transform that converts a Function (mathematics), function of a Real number, real Variable (mathematics), variable (usually t, in the ''time domain'') to a function of a Complex number, complex variable s (in the complex-valued frequency domain, also known as ''s''-domain, or ''s''-plane). The transform is useful for converting derivative, differentiation and integral, integration in the time domain into much easier multiplication and Division (mathematics), division in the Laplace domain (analogous to how logarithms are useful for simplifying multiplication and division into addition and subtraction). This gives the transform many applications in science and engineering, mostly as a tool for solving linear differential equations and dynamical systems by simplifying ordinary differential equations and integral equations into algebraic equation, algebraic polynomial equations, and by simplifyin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lagrange Polynomial
In numerical analysis, the Lagrange interpolating polynomial is the unique polynomial of lowest degree that interpolates a given set of data. Given a data set of coordinate pairs (x_j, y_j) with 0 \leq j \leq k, the x_j are called ''nodes'' and the y_j are called ''values''. The Lagrange polynomial L(x) has degree \leq k and assumes each value at the corresponding node, L(x_j) = y_j. Although named after Joseph-Louis Lagrange, who published it in 1795, the method was first discovered in 1779 by Edward Waring. It is also an easy consequence of a formula published in 1783 by Leonhard Euler. Uses of Lagrange polynomials include the Newton–Cotes method of numerical integration, Shamir's secret sharing scheme in cryptography, and Reed–Solomon error correction in coding theory. For equispaced nodes, Lagrange interpolation is susceptible to Runge's phenomenon of large oscillation. Definition Given a set of k + 1 nodes \, which must all be distinct, x_j \neq x_m for ind ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Matrix Exponential
In mathematics, the matrix exponential is a matrix function on square matrix, square matrices analogous to the ordinary exponential function. It is used to solve systems of linear differential equations. In the theory of Lie groups, the matrix exponential gives the exponential map (Lie theory), exponential map between a matrix Lie algebra and the corresponding Lie group. Let be an real number, real or complex number, complex matrix (mathematics), matrix. The exponential of , denoted by or , is the matrix given by the power series e^X = \sum_^\infty \frac X^k where X^0 is defined to be the identity matrix I with the same dimensions as X, and . The series always converges, so the exponential of is well-defined. Equivalently, e^X = \lim_ \left(I + \frac \right)^k for integer-valued , where is the identity matrix. Equivalently, given by the solution to the differential equation \frac d e^ = X e^, \quad e^ = I When is an diagonal matrix then will be an diagonal matr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Column Vector
In linear algebra, a column vector with elements is an m \times 1 matrix consisting of a single column of entries, for example, \boldsymbol = \begin x_1 \\ x_2 \\ \vdots \\ x_m \end. Similarly, a row vector is a 1 \times n matrix for some , consisting of a single row of entries, \boldsymbol a = \begin a_1 & a_2 & \dots & a_n \end. (Throughout this article, boldface is used for both row and column vectors.) The transpose (indicated by ) of any row vector is a column vector, and the transpose of any column vector is a row vector: \begin x_1 \; x_2 \; \dots \; x_m \end^ = \begin x_1 \\ x_2 \\ \vdots \\ x_m \end and \begin x_1 \\ x_2 \\ \vdots \\ x_m \end^ = \begin x_1 \; x_2 \; \dots \; x_m \end. The set of all row vectors with entries in a given field (such as the real numbers) forms an -dimensional vector space; similarly, the set of all column vectors with entries forms an -dimensional vector space. The space of row vectors with entries can be regarded as the dual sp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cumulative Distribution Function
In probability theory and statistics, the cumulative distribution function (CDF) of a real-valued random variable X, or just distribution function of X, evaluated at x, is the probability that X will take a value less than or equal to x. Every probability distribution Support (measure theory), supported on the real numbers, discrete or "mixed" as well as Continuous variable, continuous, is uniquely identified by a right-continuous Monotonic function, monotone increasing function (a càdlàg function) F \colon \mathbb R \rightarrow [0,1] satisfying \lim_F(x)=0 and \lim_F(x)=1. In the case of a scalar continuous distribution, it gives the area under the probability density function from negative infinity to x. Cumulative distribution functions are also used to specify the distribution of multivariate random variables. Definition The cumulative distribution function of a real-valued random variable X is the function given by where the right-hand side represents the probability ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
