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Frequency Of Exceedance
The frequency of exceedance, sometimes called the annual rate of exceedance, is the frequency with which a random process exceeds some critical value. Typically, the critical value is far from the mean. It is usually defined in terms of the number of peaks of the random process that are outside the boundary. It has applications related to predicting extreme events, such as major earthquakes and floods. Definition The frequency of exceedance is the number of times a stochastic process exceeds some critical value, usually a critical value far from the process' mean, per unit time. Counting exceedance of the critical value can be accomplished either by counting peaks of the process that exceed the critical value or by counting upcrossings of the critical value, where an ''upcrossing'' is an event where the instantaneous value of the process crosses the critical value with positive slope. This article assumes the two methods of counting exceedance are equivalent and that the process ha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Earthquake Prediction
Earthquake prediction is a branch of the science of seismology concerned with the specification of the time, location, and magnitude of future earthquakes within stated limits, and particularly "the determination of parameters for the ''next'' strong earthquake to occur in a region". Earthquake prediction is sometimes distinguished from ''earthquake forecasting'', which can be defined as the probabilistic assessment of ''general'' earthquake hazard, including the frequency and magnitude of damaging earthquakes in a given area over years or decades. Not all scientists distinguish "prediction" and "forecast", but the distinction is useful. Prediction can be further distinguished from earthquake warning systems, which upon detection of an earthquake, provide a real-time warning of seconds to neighboring regions that might be affected. In the 1970s, scientists were optimistic that a practical method for predicting earthquakes would soon be found, but by the 1990s continuing failur ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Exponential Distribution
In probability theory and statistics, the 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. The exponential distribution is not the same as the class of exponential families of distributions. This is a large class of probability distributions that includes the exponential distribution as one of its members, but also includes many other distributions, like the normal, binomial, gamma, and Poisson distributions. Definitions Probability density function The probability density function (pdf) of an exponential distribution is : f(x;\lambda) = \begin \lam ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reliability Analysis
Reliability, reliable, or unreliable may refer to: Science, technology, and mathematics Computing * Data reliability (other), a property of some disk arrays in computer storage * High availability * Reliability (computer networking), a category used to describe protocols * Reliability (semiconductor), outline of semiconductor device reliability drivers Other uses in science, technology, and mathematics * Reliability (statistics), the overall consistency of a measure * Reliability engineering, concerned with the ability of a system or component to perform its required functions under stated conditions for a specified time ** High reliability is informally reported in " nines" ** Human reliability in engineered systems * Reliability theory, as a theoretical concept, to explain biological aging and species longevity Other uses * Reliabilism, in philosophy and epistemology. * Unreliable narrator An unreliable narrator is a narrator whose credibility is compromised. The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Extreme Value Data
Extreme may refer to: Science and mathematics Mathematics *Extreme point, a point in a convex set which does not lie in any open line segment joining two points in the set *Maxima and minima, extremes on a mathematical function Science *Extremophile, an organism which thrives in or requires "extreme" *Extremes on Earth *List of extrasolar planet extremes Politics *Extremism, political ideologies or actions deemed outside the acceptable range * The Extreme (Italy) or Historical Far Left, a left-wing parliamentary group in Italy 1867–1904 Business *Extreme Networks, a California-based networking hardware company *Extreme Records, an Australia-based record label * Extreme Associates, a California-based adult film studio Computer science *Xtreme Mod, a peer-to-peer file sharing client for Windows Sports and entertainment Sport *Extreme sport *Extreme Sports Channel A global sports and lifestyle brand dedicated to extreme sports and youth culture *Los Angeles Xtreme, a defunc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rice's Formula
In probability theory, Rice's formula counts the average number of times an ergodic stationary process ''X''(''t'') per unit time crosses a fixed level ''u''. Adler and Taylor describe the result as "one of the most important results in the applications of smooth stochastic processes." The formula is often used in engineering. History The formula was published by Stephen O. Rice in 1944, having previously been discussed in his 1936 note entitled "Singing Transmission Lines." Formula Write ''D''''u'' for the number of times the ergodic stationary stochastic process ''x''(''t'') takes the value ''u'' in a unit of time (i.e. ''t'' ∈ ,1. Then Rice's formula states that ::\mathbb E(D_u) = \int_^\infty , x', p(u,x') \, \mathrmx' where ''p''(''x'',''x''') is the joint probability density of the ''x''(''t'') and its mean-square derivative ''x(''t''). If the process ''x''(''t'') is a Gaussian process and ''u'' = 0 then the formula simplifies significantly to giv ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Extreme Value Theory
Extreme value theory or extreme value analysis (EVA) is a branch of statistics dealing with the extreme deviations from the median of probability distributions. It seeks to assess, from a given ordered sample of a given random variable, the probability of events that are more extreme than any previously observed. Extreme value analysis is widely used in many disciplines, such as structural engineering, finance, earth sciences, traffic prediction, and geological engineering. For example, EVA might be used in the field of hydrology to estimate the probability of an unusually large flooding event, such as the 100-year flood. Similarly, for the design of a breakwater, a coastal engineer would seek to estimate the 50-year wave and design the structure accordingly. Data analysis Two main approaches exist for practical extreme value analysis. The first method relies on deriving block maxima (minima) series as a preliminary step. In many situations it is customary and convenient to e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cumulative Frequency Analysis
Cumulative frequency analysis is the analysis of the frequency of occurrence of values of a phenomenon less than a reference value. The phenomenon may be time- or space-dependent. Cumulative frequency is also called ''frequency of non-exceedance''. Cumulative frequency analysis is performed to obtain insight into how often a certain phenomenon (feature) is below a certain value. This may help in describing or explaining a situation in which the phenomenon is involved, or in planning interventions, for example in flood protection.Benson, M.A. 1960. Characteristics of frequency curves based on a theoretical 1000-year record. In: T.Dalrymple (ed.), Flood frequency analysis. U.S. Geological Survey Water Supply paper 1543-A, pp. 51–71 This statistical technique can be used to see how likely an event like a flood is going to happen again in the future, based on how often it happened in the past. It can be adapted to bring in things like climate change causing wetter winters and drie ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
100-year Flood
A 100-year flood is a flood event that has a 1 in 100 chance (1% probability) of being equaled or exceeded in any given year. The 100-year flood is also referred to as the 1% flood, since its annual exceedance probability is 1%.Holmes, R.R., Jr., and Dinicola, K. (2010) ''100-Year flood–it's all about chance 'U.S. Geological Survey General Information Product 106/ref> For coastal or lake flooding, the 100-year flood is generally expressed as a flood elevation or depth, and may include wave effects. For river systems, the 100-year flood is generally expressed as a flowrate. Based on the expected 100-year flood flow rate, the flood water level can be mapped as an area of inundation. The resulting floodplain map is referred to as the 100-year floodplain. Estimates of the 100-year flood flowrate and other streamflow statistics for any stream in the United States are available.Ries, K.G., and others (2008) ''StreamStats: A water resources web application 'U.S. Geological Survey, Fac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Residence Time (statistics)
In statistics, the residence time is the average amount of time it takes for a random process to reach a certain boundary value, usually a boundary far from the mean. Definition Suppose is a real, scalar stochastic process with initial value , mean and two critical values , where and . Define the first passage time of from within the interval as : \tau(y_0) = \inf\, where "inf" is the infimum. This is the smallest time after the initial time that is equal to one of the critical values forming the boundary of the interval, assuming is within the interval. Because proceeds randomly from its initial value to the boundary, is itself a random variable. The mean of is the residence time, : \bar(y_0) = E tau(y_0)\mid y_0 For a Gaussian process and a boundary far from the mean, the residence time equals the inverse of the frequency of exceedance of the smaller critical value, : \bar = N^(\min(y_,\ y_)), where the frequency of exceedance is is the variance of the Gaus ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Poisson Point Process
In probability, statistics and related fields, a Poisson point process is a type of random 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 Poisson point process is often called simply the Poisson process, but it is also called a Poisson random measure, Poisson random point field or Poisson point field. This point process has convenient mathematical properties, which has led to its being frequently defined in Euclidean space and used as a mathematical model for seemingly random processes in numerous disciplines such as astronomy,G. J. Babu and E. D. Feigelson. Spatial point processes in astronomy. ''Journal of statistical planning and inference'', 50(3):311–326, 1996. biology,H. G. Othmer, S. R. Dunbar, and W. Alt. Models of dispersal in biological systems. ''Journal of mathematical biology'', 26(3):263–298, 1988. ecology,H. Thompson. Spatial point processes, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Flood
A flood is an overflow of water ( or rarely other fluids) that submerges land that is usually dry. In the sense of "flowing water", the word may also be applied to the inflow of the tide. Floods are an area of study of the discipline hydrology and are of significant concern in agriculture, civil engineering and public health. Human changes to the environment often increase the intensity and frequency of flooding, for example land use changes such as deforestation and removal of wetlands, changes in waterway course or flood controls such as with levees, and larger environmental issues such as climate change and sea level rise. In particular climate change's increased rainfall and extreme weather events increases the severity of other causes for flooding, resulting in more intense floods and increased flood risk. Flooding may occur as an overflow of water from water bodies, such as a river, lake, or ocean, in which the water overtops or breaks levees, resulting in s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Counting Process
A counting process is a stochastic process with values that are non-negative, integer, and non-decreasing: # ''N''(''t'') ≥ 0. # ''N''(''t'') is an integer. # If ''s'' ≤ ''t'' then ''N''(''s'') ≤ ''N''(''t''). If ''s'' < ''t'', then ''N''(''t'') − ''N''(''s'') is the number of events occurred during the interval |
