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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 geophysics, primarily 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. 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 failure led many to question whether it was even possible. Demonstrabl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Exponential Distribution
In probability theory and statistics, the exponential distribution or negative exponential distribution is the probability distribution of the distance between events in a Poisson point process, i.e., a process in which events occur continuously and independently at a constant average rate; the distance parameter could be any meaningful mono-dimensional measure of the process, such as time between production errors, or length along a roll of fabric in the weaving manufacturing process. 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 includ ... [...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 * 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 ** 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, whose credibility has been seriously compromised See also * * * * Reliant (other) Reliant may also refer to: * Reliant Energy, an energy c ... [...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 some "extreme" environment *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 Ang ... [...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 give ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Extreme Value Theory
Extreme value theory or extreme value analysis (EVA) is the study of extremes in statistical distributions. It is widely used in many disciplines, such as structural engineering, finance, economics, earth sciences, traffic prediction, and Engineering geology, 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 (structure), 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 extract the annual maxima (minima), generating an ''annual maxima series'' (AMS). The second method relies on extracting, from a continuous record, the peak values reac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
100-year Flood
A 100-year flood, also called a 1% flood,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> is a flood event at a level that is reached or exceeded once per hundred years, long-run probability, on average. It has a 1 in 100 chance (1% probability) of being equaled or exceeded in any given year. The estimated boundaries of inundation in a 100-year flood are marked on flood maps. Maps, elevations and flow rates For coastal flooding and lake flooding, a 100-year flood is generally expressed as a water level elevation or depth, and includes a combination of tide, storm surge, and wind wave, waves. For river systems, a 100-year flood can be expressed as a Discharge (hydrology), flow rate, from which the flood elevation is derived. The resulting area of inundation is referred to as the ''100-year floodplain''. Estimates of the 100-year flood flow rate and other streamflow statistics for any ... [...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 Gau ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Poisson Point 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] |
Flood
A flood is an overflow of water (list of non-water floods, 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 of significant concern in agriculture, civil engineering and public health. Environmental issues, Human changes to the environment often increase the intensity and frequency of flooding. Examples for human changes are land use changes such as deforestation and Wetland conservation, removal of wetlands, changes in waterway course or flood controls such as with levees. Global environmental issues also influence causes of floods, namely climate change which causes an Effects of climate change on the water cycle, intensification of the water cycle and sea level rise. For example, climate change makes Extreme weather, extreme weather events more frequent and stronger. This leads to more intense floods and increased flood risk. Natural types of floods include riv ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Counting Process
A counting process is a stochastic process In probability theory and related fields, a stochastic () or random process is a mathematical object usually defined as a family of random variables in a probability space, where the index of the family often has the interpretation of time. Sto ... \ with values that are non-negative, integer, and non-decreasing: # N(t)\geq0. # N(t) is an integer. # If s\leq t then N(s)\leq N(t). If s [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
