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Ratio Distribution
A ratio distribution (also known as a quotient distribution) is a probability distribution constructed as the distribution of the ratio of random variables having two other known distributions. Given two (usually independent) random variables ''X'' and ''Y'', the distribution of the random variable ''Z'' that is formed as the ratio ''Z'' = ''X''/''Y'' is a ''ratio distribution''. An example is the Cauchy distribution (also called the ''normal ratio distribution''), which comes about as the ratio of two normally distributed variables with zero mean. Two other distributions often used in test-statistics are also ratio distributions: the ''t''-distribution arises from a Gaussian random variable divided by an independent chi-distributed random variable, while the ''F''-distribution originates from the ratio of two independent chi-squared distributed random variables. More general ratio distributions have been considered in the literature. Often the ratio distributions are heavy- ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probability Distribution
In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment. 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). For instance, if is used to denote the outcome of a coin toss ("the experiment"), then the probability distribution of would take the value 0.5 (1 in 2 or 1/2) for , and 0.5 for (assuming that the coin is fair). Examples of random phenomena include the weather conditions at some future date, the height of a randomly selected person, the fraction of male students in a school, the results of a survey to be conducted, etc. Introduction A probability distribution is a mathematical description of the probabilities of events, subsets of the sample space. The sample space, often denoted by \Omega, is the set of all possible outcomes of a random phe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Management Science (journal)
''For the theoretical and practical problem-solving subfield of Management, see Management Science.'' ''Management Science'' is a peer-reviewed academic journal that covers research on all aspects of management related to strategy, entrepreneurship, innovation, information technology, and organizations as well as all functional areas of business, such as accounting, finance, marketing, and operations. It is published by the Institute for Operations Research and the Management Sciences and was established in 1954 by the institute's precursor, the Institute of Management Sciences. C. West Churchman was the founding editor-in-chief. According to the ''Journal Citation Reports'', the journal has a 2018 impact factor of 4.219. Editors-in-chief The following persons are, or have been, editors-in-chief: *2018–2020: David Simchi-Levi *2014–2018: Teck-Hua Ho *2009–2014: Gérard Cachon *2003–2008: Wallace Hopp *1997–2002: Hau L. Lee *1993–1997: Gabriel R. Bitran *1983–199 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Product Distribution
A product distribution is a probability distribution constructed as the distribution of the product of random variables having two other known distributions. Given two statistically independent random variables ''X'' and ''Y'', the distribution of the random variable ''Z'' that is formed as the product Z = XY is a ''product distribution''. Algebra of random variables The product is one type of algebra for random variables: Related to the product distribution are the ratio distribution, sum distribution (see List of convolutions of probability distributions) and difference distribution. More generally, one may talk of combinations of sums, differences, products and ratios. Many of these distributions are described in Melvin D. Springer's book from 1979 ''The Algebra of Random Variables''. Derivation for independent random variables If X and Y are two independent, continuous random variables, described by probability density functions f_X and f_Y then the probability density ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mellin Transform
In mathematics, the Mellin transform is an integral transform that may be regarded as the multiplicative version of the two-sided Laplace transform. This integral transform is closely connected to the theory of Dirichlet series, and is often used in number theory, mathematical statistics, and the theory of asymptotic expansions; it is closely related to the Laplace transform and the Fourier transform, and the theory of the gamma function and allied special functions. The Mellin transform of a function is :\left\(s) = \varphi(s)=\int_0^\infty x^ f(x) \, dx. The inverse transform is :\left\(x) = f(x)=\frac \int_^ x^ \varphi(s)\, ds. The notation implies this is a line integral taken over a vertical line in the complex plane, whose real part ''c'' need only satisfy a mild lower bound. Conditions under which this inversion is valid are given in the Mellin inversion theorem. The transform is named after the Finnish mathematician Hjalmar Mellin, who introduced it in a paper publishe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Melvin D
Melvin is a masculine given name and surname, likely a variant of Melville and a descendant of the French surname de Maleuin and the later Melwin. It may alternatively be spelled as Melvyn or, in Welsh, Melfyn and the name Melivinia or Melva may be used a feminine form. Of Norman French origin, originally Malleville, which translates to "bad town," it likely made its way into usage in Scotland as a result of the Norman conquest of England. It came into use as a given name as early as the 19th century, in English-speaking populations. As a name Given name Academics *Melvin Calvin (1911–1997), American chemist who discovered the Calvin cycle *Melvin Day (1923–2016), New Zealand artist and art historian *Melvin Hochster (born 1943), American mathematician *Melvin Konner (born 1946), Professor of Anthropology *Melvin Schwartz (1932–2006), American physicist who won the Nobel Prize in Physics in 1988 * Melvin Alvah Traylor, Jr. (1915–2008), American ornithologist Busin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Difference Distribution
Difference, The Difference, Differences or Differently may refer to: Music * ''Difference'' (album), by Dreamtale, 2005 * ''Differently'' (album), by Cassie Davis, 2009 ** "Differently" (song), by Cassie Davis, 2009 * ''The Difference'' (album), Pendleton, 2008 * "The Difference" (The Wallflowers song), 1997 * "The Difference", a song by Westlife from the 2009 album ''Where We Are'' * "The Difference", a song by Nick Jonas from the 2016 album ''Last Year Was Complicated'' * "The Difference", a song by Meek Mill featuring Quavo, from the 2016 mixtape '' DC4'' * "The Difference", a song by Matchbox Twenty from the 2002 album '' More Than You Think You Are'' * "The Difference", a 2020 song by Flume featuring Toro y Moi * "The Difference", a 2022 song by Ni/Co which represented Alabama in the ''American Song Contest'' * "Differences" (song), by Ginuwine, 2001 Science and mathematics * Difference (mathematics), the result of a subtraction * Difference equation, a type of recur ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sum Distribution
Sum most commonly means the total of two or more numbers added together; see addition. Sum can also refer to: Mathematics * Sum (category theory), the generic concept of summation in mathematics * Sum, the result of summation, the addition of a sequence of numbers * 3SUM, a term from computational complexity theory * Band sum, a way of connecting mathematical knots * Connected sum, a way of gluing manifolds * Digit sum, in number theory * Direct sum, a combination of algebraic objects ** Direct sum of groups ** Direct sum of modules ** Direct sum of permutations ** Direct sum of topological groups * Einstein summation, a way of contracting tensor indices * Empty sum, a sum with no terms * Indefinite sum, the inverse of a finite difference * Kronecker sum, an operation considered a kind of addition for matrices * Matrix addition, in linear algebra * Minkowski addition, a sum of two subsets of a vector space * Power sum symmetric polynomial, in commutative algebra * Prefix ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Product Distribution
A product distribution is a probability distribution constructed as the distribution of the product of random variables having two other known distributions. Given two statistically independent random variables ''X'' and ''Y'', the distribution of the random variable ''Z'' that is formed as the product Z = XY is a ''product distribution''. Algebra of random variables The product is one type of algebra for random variables: Related to the product distribution are the ratio distribution, sum distribution (see List of convolutions of probability distributions) and difference distribution. More generally, one may talk of combinations of sums, differences, products and ratios. Many of these distributions are described in Melvin D. Springer's book from 1979 ''The Algebra of Random Variables''. Derivation for independent random variables If X and Y are two independent, continuous random variables, described by probability density functions f_X and f_Y then the probability density ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proc Natl Acad Sci U S A
''Proceedings of the National Academy of Sciences of the United States of America'' (often abbreviated ''PNAS'' or ''PNAS USA'') is a peer-reviewed multidisciplinary scientific journal. It is the official journal of the National Academy of Sciences, published since 1915, and publishes original research, scientific reviews, commentaries, and letters. According to ''Journal Citation Reports'', the journal has a 2021 impact factor of 12.779. ''PNAS'' is the second most cited scientific journal, with more than 1.9 million cumulative citations from 2008 to 2018. In the mass media, ''PNAS'' has been described variously as "prestigious", "sedate", "renowned" and "high impact". ''PNAS'' is a delayed open access journal, with an embargo period of six months that can be bypassed for an author fee ( hybrid open access). Since September 2017, open access articles are published under a Creative Commons license. Since January 2019, ''PNAS'' has been online-only, although print issues are ava ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Median
In statistics and probability theory, the median is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution. For a data set, it may be thought of as "the middle" value. The basic feature of the median in describing data compared to the mean (often simply described as the "average") is that it is not skewed by a small proportion of extremely large or small values, and therefore provides a better representation of a "typical" value. Median income, for example, may be a better way to suggest what a "typical" income is, because income distribution can be very skewed. The median is of central importance in robust statistics, as it is the most resistant statistic, having a breakdown point of 50%: so long as no more than half the data are contaminated, the median is not an arbitrarily large or small result. Finite data set of numbers The median of a finite list of numbers is the "middle" number, when those numbers are list ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistical Test
A statistical hypothesis test is a method of statistical inference used to decide whether the data at hand sufficiently support a particular hypothesis. Hypothesis testing allows us to make probabilistic statements about population parameters. History Early use While hypothesis testing was popularized early in the 20th century, early forms were used in the 1700s. The first use is credited to John Arbuthnot (1710), followed by Pierre-Simon Laplace (1770s), in analyzing the human sex ratio at birth; see . Modern origins and early controversy Modern significance testing is largely the product of Karl Pearson ( ''p''-value, Pearson's chi-squared test), William Sealy Gosset (Student's t-distribution), and Ronald Fisher ("null hypothesis", analysis of variance, "significance test"), while hypothesis testing was developed by Jerzy Neyman and Egon Pearson (son of Karl). Ronald Fisher began his life in statistics as a Bayesian (Zabell 1992), but Fisher soon grew disenchanted with the s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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