Parametric modelIn statistics, a parametric model or parametric family or finite-dimensional model is a particular class of statistical models. Specifically, a parametric model is a family of probability distributions that has a finite number of parameters. A statistical model is a collection of probability distributions on some sample space. We assume that the collection, P, is indexed by some set Θ. The set Θ is called the parameter set or, more commonly, the parameter space.
PrecipitationIn meteorology, precipitation is any product of the condensation of atmospheric water vapor that falls from clouds due to gravitational pull. The main forms of precipitation include drizzle, rain, sleet, snow, ice pellets, graupel and hail. Precipitation occurs when a portion of the atmosphere becomes saturated with water vapor (reaching 100% relative humidity), so that the water condenses and "precipitates" or falls. Thus, fog and mist are not precipitation but colloids, because the water vapor does not condense sufficiently to precipitate.
Cloud physicsCloud physics is the study of the physical processes that lead to the formation, growth and precipitation of atmospheric clouds. These aerosols are found in the troposphere, stratosphere, and mesosphere, which collectively make up the greatest part of the homosphere. Clouds consist of microscopic droplets of liquid water (warm clouds), tiny crystals of ice (cold clouds), or both (mixed phase clouds), along with microscopic particles of dust, smoke, or other matter, known as condensation nuclei.
Parametric statisticsParametric statistics is a branch of statistics which assumes that sample data comes from a population that can be adequately modeled by a probability distribution that has a fixed set of parameters. Conversely a non-parametric model does not assume an explicit (finite-parametric) mathematical form for the distribution when modeling the data. However, it may make some assumptions about that distribution, such as continuity or symmetry. Most well-known statistical methods are parametric.
Nonparametric statisticsNonparametric statistics is the type of statistics that is not restricted by assumptions concerning the nature of the population from which a sample is drawn. This is opposed to parametric statistics, for which a problem is restricted a priori by assumptions concerning the specific distribution of the population (such as the normal distribution) and parameters (such the mean or variance).
Semiparametric modelIn statistics, a semiparametric model is a statistical model that has parametric and nonparametric components. A statistical model is a parameterized family of distributions: indexed by a parameter . A parametric model is a model in which the indexing parameter is a vector in -dimensional Euclidean space, for some nonnegative integer . Thus, is finite-dimensional, and . With a nonparametric model, the set of possible values of the parameter is a subset of some space , which is not necessarily finite-dimensional.
StatisticsStatistics (from German: Statistik, () "description of a state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model to be studied. Populations can be diverse groups of people or objects such as "all people living in a country" or "every atom composing a crystal".
Statistical inferenceStatistical inference is the process of using data analysis to infer properties of an underlying distribution of probability. Inferential statistical analysis infers properties of a population, for example by testing hypotheses and deriving estimates. It is assumed that the observed data set is sampled from a larger population. Inferential statistics can be contrasted with descriptive statistics. Descriptive statistics is solely concerned with properties of the observed data, and it does not rest on the assumption that the data come from a larger population.
Parametric familyIn mathematics and its applications, a parametric family or a parameterized family is a family of objects (a set of related objects) whose differences depend only on the chosen values for a set of parameters. Common examples are parametrized (families of) functions, probability distributions, curves, shapes, etc. Statistical model For example, the probability density function fX of a random variable X may depend on a parameter θ. In that case, the function may be denoted to indicate the dependence on the parameter θ.
Normal distributionIn statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is The parameter is the mean or expectation of the distribution (and also its median and mode), while the parameter is its standard deviation. The variance of the distribution is . A random variable with a Gaussian distribution is said to be normally distributed, and is called a normal deviate.
Cauchy distributionThe Cauchy distribution, named after Augustin Cauchy, is a continuous probability distribution. It is also known, especially among physicists, as the Lorentz distribution (after Hendrik Lorentz), Cauchy–Lorentz distribution, Lorentz(ian) function, or Breit–Wigner distribution. The Cauchy distribution is the distribution of the x-intercept of a ray issuing from with a uniformly distributed angle. It is also the distribution of the ratio of two independent normally distributed random variables with mean zero.
Precipitation typesIn meteorology, the different types of precipitation often include the character, formation, or phase of the precipitation which is falling to ground level. There are three distinct ways that precipitation can occur. Convective precipitation is generally more intense, and of shorter duration, than stratiform precipitation. Orographic precipitation occurs when moist air is forced upwards over rising terrain and condenses on the slope, such as a mountain.
Ice crystalIce crystals are solid ice in symmetrical shapes including hexagonal columns, hexagonal plates, and dendritic crystals. Ice crystals are responsible for various atmospheric optic displays and cloud formations. At ambient temperature and pressure, water molecules have a V shape. The two hydrogen atoms bond to the oxygen atom at a 105° angle. Ice crystals have a hexagonal crystal lattice, meaning the water molecules arrange themselves into layered hexagons upon freezing.
Multivariate normal distributionIn probability theory and statistics, the multivariate normal distribution, multivariate Gaussian distribution, or joint normal distribution is a generalization of the one-dimensional (univariate) normal distribution to higher dimensions. One definition is that a random vector is said to be k-variate normally distributed if every linear combination of its k components has a univariate normal distribution. Its importance derives mainly from the multivariate central limit theorem.
Sequential analysisIn statistics, sequential analysis or sequential hypothesis testing is statistical analysis where the sample size is not fixed in advance. Instead data are evaluated as they are collected, and further sampling is stopped in accordance with a pre-defined stopping rule as soon as significant results are observed. Thus a conclusion may sometimes be reached at a much earlier stage than would be possible with more classical hypothesis testing or estimation, at consequently lower financial and/or human cost.
CloudIn meteorology, a cloud is an aerosol consisting of a visible mass of miniature liquid droplets, frozen crystals, or other particles suspended in the atmosphere of a planetary body or similar space. Water or various other chemicals may compose the droplets and crystals. On Earth, clouds are formed as a result of saturation of the air when it is cooled to its dew point, or when it gains sufficient moisture (usually in the form of water vapor) from an adjacent source to raise the dew point to the ambient temperature.
Electric power distributionElectric power distribution is the final stage in the delivery of electricity. Electricity is carried from the transmission system to individual consumers. Distribution substations connect to the transmission system and lower the transmission voltage to medium voltage ranging between 2kV and 33kV with the use of transformers. Primary distribution lines carry this medium voltage power to distribution transformers located near the customer's premises.
Analysis of varianceAnalysis of variance (ANOVA) is a collection of statistical models and their associated estimation procedures (such as the "variation" among and between groups) used to analyze the differences among means. ANOVA was developed by the statistician Ronald Fisher. ANOVA is based on the law of total variance, where the observed variance in a particular variable is partitioned into components attributable to different sources of variation.
Star formationStar formation is the process by which dense regions within molecular clouds in interstellar space, sometimes referred to as "stellar nurseries" or "star-forming regions", collapse and form stars. As a branch of astronomy, star formation includes the study of the interstellar medium (ISM) and giant molecular clouds (GMC) as precursors to the star formation process, and the study of protostars and young stellar objects as its immediate products. It is closely related to planet formation, another branch of astronomy.
Voltage dropIn electronics, voltage drop is the decrease of electric potential along the path of a current flowing in a circuit. Voltage drops in the internal resistance of the source, across conductors, across contacts, and across connectors are undesirable because some of the energy supplied is dissipated. The voltage drop across the load is proportional to the power available to be converted in that load to some other useful form of energy. For example, an electric space heater may have a resistance of ten ohms, and the wires that supply it may have a resistance of 0.
