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Wakeby Distribution
The Wakeby distribution is a five-parameter probability distribution defined by its quantile function, :W(p) =\xi + \frac(1 - (1-p)^) - \frac(1 - (1-p)^), and by its quantile density function, :W'(p) = w(p) = \alpha (1-p)^ + \gamma (1-p)^, where 0 \le p \le 1, ξ is a location parameter, α and γ are scale parameters and β and δ are shape parameters. This distribution was first proposed by Harold A. Thomas Jr., who named it after Wakeby Pond in Cape Cod. Applications The Wakeby distribution has been used for modeling distributions of * flood flows, * citation counts, * extreme rainfall, * tidal current speeds, * and peak flows of rivers. Parameters and domain The following restrictions apply to the parameters of this distribution: * \beta + \delta \ge 0 * Either \beta + \delta > 0 or \beta = \gamma = \delta = 0 * If \gamma > 0 , then \delta > 0 * \gamma \ge 0 * \alpha + \gamma \ge 0 The domain of the Wakeby distribution ... [...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] |
Location Parameter
In geography, location or place are used to denote a region (point, line, or area) on Earth's surface or elsewhere. The term ''location'' generally implies a higher degree of certainty than ''place'', the latter often indicating an entity with an ambiguous boundary, relying more on human or social attributes of place identity and sense of place than on geometry. Types Locality A suburb, locality, human settlement, settlement, or populated place is likely to have a well-defined name but a boundary that is not well defined varies by context. London, for instance, has a legal boundary, but this is unlikely to completely match with general usage. An area within a town, such as Covent Garden in London, also almost always has some ambiguity as to its extent. In geography, location is considered to be more precise than "place". Relative location A relative location, or situation, is described as a displacement from another site. An example is "3 miles northwest of Seattle". Absolute lo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Shape Parameter
In probability theory and statistics, a shape parameter (also known as form parameter) is a kind of numerical parameter of a parametric family of probability distributionsEveritt B.S. (2002) Cambridge Dictionary of Statistics. 2nd Edition. CUP. that is neither a location parameter nor a scale parameter (nor a function of these, such as a rate parameter). Such a parameter must affect the ''shape'' of a distribution rather than simply shifting it (as a location parameter does) or stretching/shrinking it (as a scale parameter does). For example, "peakedness" refers to how round the main peak is. Estimation Many estimators measure location or scale; however, estimators for shape parameters also exist. Most simply, they can be estimated in terms of the higher moments, using the method of moments, as in the ''skewness'' (3rd moment) or ''kurtosis'' (4th moment), if the higher moments are defined and finite. Estimators of shape often involve higher-order statistics (non-linear functi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wakeby Pond
Mashpee Pond and Wakeby Pond are adjoining ponds in Mashpee and Sandwich, Massachusetts. When considered together, these two ponds cover and constitute the largest freshwater pond on Cape Cod. This pair is deep at its deepest point. The Fishing Record for most bass caught in a day belongs to James Dean on August 21,2016. The record for most fishing trips without a single fish caught belongs to P.J Keliher at 26. These kettleholes are fed by groundwater and have no inlet streams. The ponds' sole outlet stream, the Mashpee River, flows south to Popponesset Bay. Boating access to the ponds is possible via a state-maintained concrete launching ramp off Route 130 in Mashpee. The ponds are heavily used for boating, swimming, bass fishing and trout fishing. However, there is no public beach on the lakes on which boats may be put ashore. Ice fishing and fly fishing take place on these waters in addition to bait-casting. In 2006, a few fish pulled from Mashpee and Wakeb ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cape Cod
Cape Cod is a peninsula extending into the Atlantic Ocean from the southeastern corner of mainland Massachusetts, in the northeastern United States. Its historic, maritime character and ample beaches attract heavy tourism during the summer months. The name Cape Cod, coined in 1602 by Bartholomew Gosnold, is the ninth oldest English place-name in the U.S. As defined by the Cape Cod Commission's enabling legislation, Cape Cod is conterminous with Barnstable County, Massachusetts. It extends from Provincetown in the northeast to Woods Hole in the southwest, and is bordered by Plymouth to the northwest. The Cape is divided into fifteen towns, several of which are in turn made up of multiple named villages. Cape Cod forms the southern boundary of the Gulf of Maine, which extends north-eastward to Nova Scotia. Since 1914, most of Cape Cod has been separated from the mainland by the Cape Cod Canal. The canal cuts roughly across the base of the peninsula, though small portions of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rainfall
Rain is water droplets that have condensed from atmospheric water vapor and then fall under gravity. Rain is a major component of the water cycle and is responsible for depositing most of the fresh water on the Earth. It provides water for hydroelectric power plants, crop irrigation, and suitable conditions for many types of ecosystems. The major cause of rain production is moisture moving along three-dimensional zones of temperature and moisture contrasts known as weather fronts. If enough moisture and upward motion is present, precipitation falls from convective clouds (those with strong upward vertical motion) such as cumulonimbus (thunder clouds) which can organize into narrow rainbands. In mountainous areas, heavy precipitation is possible where upslope flow is maximized within windward sides of the terrain at elevation which forces moist air to condense and fall out as rainfall along the sides of mountains. On the leeward side of mountains, desert climates can exi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tidal Current
Tides are the rise and fall of sea levels caused by the combined effects of the gravitational forces exerted by the Moon (and to a much lesser extent, the Sun) and are also caused by the Earth and Moon orbiting one another. Tide tables can be used for any given locale to find the predicted times and amplitude (or " tidal range"). The predictions are influenced by many factors including the alignment of the Sun and Moon, the phase and amplitude of the tide (pattern of tides in the deep ocean), the amphidromic systems of the oceans, and the shape of the coastline and near-shore bathymetry (see '' Timing''). They are however only predictions, the actual time and height of the tide is affected by wind and atmospheric pressure. Many shorelines experience semi-diurnal tides—two nearly equal high and low tides each day. Other locations have a diurnal tide—one high and low tide each day. A "mixed tide"—two uneven magnitude tides a day—is a third regular category. Tides ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
River Flow
Streamflow, or channel runoff, is the flow of water in streams and other channels, and is a major element of the water cycle. It is one component of the movement of water from the land to waterbodies, the other component being surface runoff. Water flowing in channels comes from surface runoff from adjacent hillslopes, from groundwater flow out of the ground, and from water discharged from pipes. The discharge of water flowing in a channel is measured using stream gauges or can be estimated by the Manning equation. The record of flow over time is called a hydrograph. Flooding occurs when the volume of water exceeds the capacity of the channel. Role in the water cycle Streams play a critical role in the hydrologic cycle that is essential for all life on Earth. A diversity of biological species, from unicellular organisms to vertebrates, depend on flowing-water systems for their habitat and food resources. Rivers are major aquatic landscapes for all manners of plants and animals. Riv ... [...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 supported on the real numbers, discrete or "mixed" as well as continuous, is uniquely identified by an ''upwards continuous'' ''monotonic increasing'' cumulative distribution function F : \mathbb R \rightarrow ,1/math> 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 minus 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 that the random variable X takes on a value less tha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probability Density Function
In probability theory, a probability density function (PDF), or density of a continuous random variable, is a 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 close 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. In a more precise sense, the PDF is used to specify the probability of the random variable falling ''within a particular range of values'', as opposed to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dataplot
Dataplot is a public domain software system for scientific visualization and statistical analysis. It was developed and is being maintained at the National Institute of Standards and Technology. Dataplot's source code In computing, source code, or simply code, is any collection of code, with or without comments, written using a human-readable programming language, usually as plain text. The source code of a program is specially designed to facilitate the wo ... is available and in public domain. External linksNIST website References [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Generalized Pareto Distribution
In statistics, the generalized Pareto distribution (GPD) is a family of continuous probability distributions. It is often used to model the tails of another distribution. It is specified by three parameters: location \mu, scale \sigma, and shape \xi. Sometimes it is specified by only scale and shape and sometimes only by its shape parameter. Some references give the shape parameter as \kappa = - \xi \,. Definition The standard cumulative distribution function (cdf) of the GPD is defined by : F_(z) = \begin 1 - \left(1 + \xi z\right)^ & \text\xi \neq 0, \\ 1 - e^ & \text\xi = 0. \end where the support is z \geq 0 for \xi \geq 0 and 0 \leq z \leq - 1 /\xi for \xi 0, and \xi\in\mathbb R) is : F_(x) = \begin 1 - \left(1+ \frac\right)^ & \text\xi \neq 0, \\ 1 - \exp \left(-\frac\right) & \text\xi = 0, \end where the support of X is x \geqslant \mu when \xi \geqslant 0 \,, and \mu \leqslant x \leqslant \mu - \sigma /\xi when \xi < 0. The |
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