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Utilization Distribution
A utilization distribution is a probability distribution giving the probability density that an animal is found at a given point in space. It is estimated from data sampling the location of an individual or individuals in space over a period of time using, for example, telemetry or GPS based methods. Estimation of utilization distribution was traditionally based on histograms but newer nonparametric methods based on Fourier transformations, kernel density and local convex hull methods have been developed. The typical application for this distribution is estimating the home range distribution of animals. According to Lichti & Swihart (2011), kernel density methods provided, in many cases, less biased home-range area estimates compared to convex hull methods. See also *Home range *Local convex hull Local convex hull (LoCoH) is a method for estimating size of the home range of an animal or a group of animals (e.g. a pack of wolves, a pride of lions, or herd of buffaloes), and for c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probability Distribution
In probability theory and statistics, a probability distribution is a Function (mathematics), function that gives the probabilities of occurrence of possible events for an Experiment (probability theory), experiment. It is a mathematical description of a Randomness, random phenomenon in terms of its sample space and the Probability, probabilities of Event (probability theory), 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 fair coin, the coin is fair). More commonly, probability distributions are used to compare the relative occurrence of many different random values. Probability distributions can be defined in different ways and for discrete or for continuous variables. Distributions with special properties or for especially important applications are given specific names. Introduction A prob ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Telemetry
Telemetry is the in situ collection of measurements or other data at remote points and their automatic transmission to receiving equipment (telecommunication) for monitoring. The word is derived from the Greek roots ''tele'', 'far off', and ''metron'', 'measure'. Systems that need external instructions and data to operate require the counterpart of telemetry: telecommand. Although the term commonly refers to wireless data transfer mechanisms (e.g., using radio, ultrasonic, or infrared systems), it also encompasses data transferred over other media such as a telephone or computer network, optical link or other wired communications like power line carriers. Many modern telemetry systems take advantage of the low cost and ubiquity of GSM networks by using SMS to receive and transmit telemetry data. A ''telemeter'' is a physical device used in telemetry. It consists of a sensor, a transmission path, and a display, recording, or control device. Electronic devices are widely u ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Histogram
A histogram is a visual representation of the frequency distribution, distribution of quantitative data. To construct a histogram, the first step is to Data binning, "bin" (or "bucket") the range of values— divide the entire range of values into a series of intervals—and then count how many values fall into each interval. The bins are usually specified as consecutive, non-overlapping interval (mathematics), intervals of a variable. The bins (intervals) are adjacent and are typically (but not required to be) of equal size. Histograms give a rough sense of the density of the underlying distribution of the data, and often for density estimation: estimating the probability density function of the underlying variable. The total area of a histogram used for probability density is always normalized to 1. If the length of the intervals on the ''x''-axis are all 1, then a histogram is identical to a relative frequency plot. Histograms are sometimes confused with bar charts. In a his ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nonparametric
Nonparametric statistics is a type of statistical analysis that makes minimal assumptions about the underlying distribution of the data being studied. Often these models are infinite-dimensional, rather than finite dimensional, as in parametric statistics. Nonparametric statistics can be used for descriptive statistics or statistical inference. Nonparametric tests are often used when the assumptions of parametric tests are evidently violated. Definitions The term "nonparametric statistics" has been defined imprecisely in the following two ways, among others: The first meaning of ''nonparametric'' involves techniques that do not rely on data belonging to any particular parametric family of probability distributions. These include, among others: * Methods which are ''distribution-free'', which do not rely on assumptions that the data are drawn from a given parametric family of probability distributions. * Statistics defined to be a function on a sample, without dependency on a pa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fourier Transformations
In mathematics, the Fourier transform (FT) is an integral transform that takes a function as input then outputs another function that describes the extent to which various frequencies are present in the original function. The output of the transform is a complex-valued function of frequency. The term ''Fourier transform'' refers to both this complex-valued function and the mathematical operation. When a distinction needs to be made, the output of the operation is sometimes called the frequency domain representation of the original function. The Fourier transform is analogous to decomposing the sound of a musical chord into the intensities of its constituent pitches. Functions that are localized in the time domain have Fourier transforms that are spread out across the frequency domain and vice versa, a phenomenon known as the uncertainty principle. The critical case for this principle is the Gaussian function, of substantial importance in probability theory and statistics as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kernel Density Estimation
In statistics, kernel density estimation (KDE) is the application of kernel smoothing for probability density estimation, i.e., a non-parametric method to estimate the probability density function of a random variable based on '' kernels'' as weights. KDE answers a fundamental data smoothing problem where inferences about the population are made based on a finite data sample. In some fields such as signal processing and econometrics it is also termed the Parzen–Rosenblatt window method, after Emanuel Parzen and Murray Rosenblatt, who are usually credited with independently creating it in its current form. One of the famous applications of kernel density estimation is in estimating the class-conditional marginal densities of data when using a naive Bayes classifier, which can improve its prediction accuracy. Definition Let be independent and identically distributed samples drawn from some univariate distribution with an unknown density at any given point . We are in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Local Convex Hull
Local convex hull (LoCoH) is a method for estimating size of the home range of an animal or a group of animals (e.g. a pack of wolves, a pride of lions, or herd of buffaloes), and for constructing a utilization distribution. The latter is a probability distribution that represents the probabilities of finding an animal within a given area of its home range at any point in time; or, more generally, at points in time for which the utilization distribution has been constructed. In particular, different utilization distributions can be constructed from data pertaining to particular periods of a diurnal or seasonal cycle. Utilization distributions are constructed from data providing the location of an individual or several individuals in space at different points in time by associating a local distribution function with each point and then summing and normalizing these local distribution functions to obtain a distribution function that pertains to the data as a whole.Seaman DE, Powell R ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Home Range
A home range is the area in which an animal lives and moves on a periodic basis. It is related to the concept of an animal's territory which is the area that is actively defended. The concept of a home range was introduced by W. H. Burt in 1943. He drew maps showing where the animal had been observed at different times. An associated concept is the utilization distribution which examines where the animal is likely to be at any given time. Data for mapping a home range used to be gathered by careful observation, but in more recent years, the animal is fitted with a transmission collar or similar GPS device. The simplest way of measuring the home range is to construct the smallest possible convex polygon around the data but this tends to overestimate the range. The best known methods for constructing utilization distributions are the so-called bivariate Gaussian or normal distribution kernel density methods. More recently, nonparametric methods such as the Burgman and Fox's alp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Biased Estimator
In statistics, the bias of an estimator (or bias function) is the difference between this estimator's expected value and the true value of the parameter being estimated. An estimator or decision rule with zero bias is called ''unbiased''. In statistics, "bias" is an property of an estimator. Bias is a distinct concept from consistency: consistent estimators converge in probability to the true value of the parameter, but may be biased or unbiased (see bias versus consistency for more). All else being equal, an unbiased estimator is preferable to a biased estimator, although in practice, biased estimators (with generally small bias) are frequently used. When a biased estimator is used, bounds of the bias are calculated. A biased estimator may be used for various reasons: because an unbiased estimator does not exist without further assumptions about a population; because an estimator is difficult to compute (as in unbiased estimation of standard deviation); because a biased estima ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Home Range
A home range is the area in which an animal lives and moves on a periodic basis. It is related to the concept of an animal's territory which is the area that is actively defended. The concept of a home range was introduced by W. H. Burt in 1943. He drew maps showing where the animal had been observed at different times. An associated concept is the utilization distribution which examines where the animal is likely to be at any given time. Data for mapping a home range used to be gathered by careful observation, but in more recent years, the animal is fitted with a transmission collar or similar GPS device. The simplest way of measuring the home range is to construct the smallest possible convex polygon around the data but this tends to overestimate the range. The best known methods for constructing utilization distributions are the so-called bivariate Gaussian or normal distribution kernel density methods. More recently, nonparametric methods such as the Burgman and Fox's alp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Local Convex Hull
Local convex hull (LoCoH) is a method for estimating size of the home range of an animal or a group of animals (e.g. a pack of wolves, a pride of lions, or herd of buffaloes), and for constructing a utilization distribution. The latter is a probability distribution that represents the probabilities of finding an animal within a given area of its home range at any point in time; or, more generally, at points in time for which the utilization distribution has been constructed. In particular, different utilization distributions can be constructed from data pertaining to particular periods of a diurnal or seasonal cycle. Utilization distributions are constructed from data providing the location of an individual or several individuals in space at different points in time by associating a local distribution function with each point and then summing and normalizing these local distribution functions to obtain a distribution function that pertains to the data as a whole.Seaman DE, Powell R ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
