Log-normal distributionIn probability theory, a log-normal (or lognormal) distribution is a continuous probability distribution of a random variable whose logarithm is normally distributed. Thus, if the random variable X is log-normally distributed, then Y = ln(X) has a normal distribution. Equivalently, if Y has a normal distribution, then the exponential function of Y, X = exp(Y), has a log-normal distribution. A random variable which is log-normally distributed takes only positive real values.
Statistical modelA statistical model is a mathematical model that embodies a set of statistical assumptions concerning the generation of sample data (and similar data from a larger population). A statistical model represents, often in considerably idealized form, the data-generating process. When referring specifically to probabilities, the corresponding term is probabilistic model. A statistical model is usually specified as a mathematical relationship between one or more random variables and other non-random variables.
Wastewater treatmentWastewater treatment is a process which removes and eliminates contaminants from wastewater and converts this into an effluent that can be returned to the water cycle. Once returned to the water cycle, the effluent creates an acceptable impact on the environment or is reused for various purposes (called water reclamation). The treatment process takes place in a wastewater treatment plant. There are several kinds of wastewater which are treated at the appropriate type of wastewater treatment plant.
Industrial wastewater treatmentIndustrial wastewater treatment describes the processes used for treating wastewater that is produced by industries as an undesirable by-product. After treatment, the treated industrial wastewater (or effluent) may be reused or released to a sanitary sewer or to a surface water in the environment. Some industrial facilities generate wastewater that can be treated in sewage treatment plants.
Sewage treatmentSewage treatment (or domestic wastewater treatment, municipal wastewater treatment) is a type of wastewater treatment which aims to remove contaminants from sewage to produce an effluent that is suitable to discharge to the surrounding environment or an intended reuse application, thereby preventing water pollution from raw sewage discharges. Sewage contains wastewater from households and businesses and possibly pre-treated industrial wastewater. There are a high number of sewage treatment processes to choose from.
Confidence intervalIn frequentist statistics, a confidence interval (CI) is a range of estimates for an unknown parameter. A confidence interval is computed at a designated confidence level; the 95% confidence level is most common, but other levels, such as 90% or 99%, are sometimes used. The confidence level, degree of confidence or confidence coefficient represents the long-run proportion of CIs (at the given confidence level) that theoretically contain the true value of the parameter; this is tantamount to the nominal coverage probability.
Climate variability and changeClimate variability includes all the variations in the climate that last longer than individual weather events, whereas the term climate change only refers to those variations that persist for a longer period of time, typically decades or more. Climate change may refer to any time in Earth's history, but the term is now commonly used to describe contemporary climate change. Since the Industrial Revolution, the climate has increasingly been affected by human activities.
Water treatmentWater treatment is any process that improves the quality of water to make it appropriate for a specific end-use. The end use may be drinking, industrial water supply, irrigation, river flow maintenance, water recreation or many other uses, including being safely returned to the environment. Water treatment removes contaminants and undesirable components, or reduces their concentration so that the water becomes fit for its desired end-use. This treatment is crucial to human health and allows humans to benefit from both drinking and irrigation use.
Secondary treatmentSecondary treatment (mostly biological wastewater treatment) is the removal of biodegradable organic matter (in solution or suspension) from sewage or similar kinds of wastewater. The aim is to achieve a certain degree of effluent quality in a sewage treatment plant suitable for the intended disposal or reuse option. A "primary treatment" step often precedes secondary treatment, whereby physical phase separation is used to remove settleable solids.
Shape parameterIn probability theory and statistics, a shape parameter (also known as form parameter) is a kind of numerical parameter of a parametric family of probability distributions 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.
Decentralized wastewater systemDecentralized wastewater systems (also referred to as decentralized wastewater treatment systems) convey, treat and dispose or reuse wastewater from small and low-density communities, buildings and dwellings in remote areas, individual public or private properties. Wastewater flow is generated when appropriate water supply is available within the buildings or close to them. Decentralized wastewater systems treat, reuse or dispose the effluent in relatively close vicinity to its source of generation.
Water purificationWater purification is the process of removing undesirable chemicals, biological contaminants, suspended solids, and gases from water. The goal is to produce water that is fit for specific purposes. Most water is purified and disinfected for human consumption (drinking water), but water purification may also be carried out for a variety of other purposes, including medical, pharmacological, chemical, and industrial applications. The history of water purification includes a wide variety of methods.
Confidence distributionIn statistical inference, the concept of a confidence distribution (CD) has often been loosely referred to as a distribution function on the parameter space that can represent confidence intervals of all levels for a parameter of interest. Historically, it has typically been constructed by inverting the upper limits of lower sided confidence intervals of all levels, and it was also commonly associated with a fiducial interpretation (fiducial distribution), although it is a purely frequentist concept.
Generalized normal distributionThe generalized normal distribution or generalized Gaussian distribution (GGD) is either of two families of parametric continuous probability distributions on the real line. Both families add a shape parameter to the normal distribution. To distinguish the two families, they are referred to below as "symmetric" and "asymmetric"; however, this is not a standard nomenclature. The symmetric generalized normal distribution, also known as the exponential power distribution or the generalized error distribution, is a parametric family of symmetric distributions.
Prediction intervalIn statistical inference, specifically predictive inference, a prediction interval is an estimate of an interval in which a future observation will fall, with a certain probability, given what has already been observed. Prediction intervals are often used in regression analysis.
Credible intervalIn Bayesian statistics, a credible interval is an interval within which an unobserved parameter value falls with a particular probability. It is an interval in the domain of a posterior probability distribution or a predictive distribution. The generalisation to multivariate problems is the credible region. Credible intervals are analogous to confidence intervals and confidence regions in frequentist statistics, although they differ on a philosophical basis: Bayesian intervals treat their bounds as fixed and the estimated parameter as a random variable, whereas frequentist confidence intervals treat their bounds as random variables and the parameter as a fixed value.
VirusA virus is a submicroscopic infectious agent that replicates only inside the living cells of an organism. Viruses infect all life forms, from animals and plants to microorganisms, including bacteria and archaea. Since Dmitri Ivanovsky's 1892 article describing a non-bacterial pathogen infecting tobacco plants and the discovery of the tobacco mosaic virus by Martinus Beijerinck in 1898, more than 11,000 of the millions of virus species have been described in detail.
Generalized beta distributionIn probability and statistics, the generalized beta distribution is a continuous probability distribution with four shape parameters (however it's customary to make explicit the scale parameter as a fifth parameter, while the location parameter is usually left implicit), including more than thirty named distributions as limiting or special cases. It has been used in the modeling of income distribution, stock returns, as well as in regression analysis.
Introduction to virusesA virus is a tiny infectious agent that reproduces inside the cells of living hosts. When infected, the host cell is forced to rapidly produce thousands of identical copies of the original virus. Unlike most living things, viruses do not have cells that divide; new viruses assemble in the infected host cell. But unlike simpler infectious agents like prions, they contain genes, which allow them to mutate and evolve. Over 4,800 species of viruses have been described in detail out of the millions in the environment.
Weibull distributionIn probability theory and statistics, the Weibull distribution ˈwaɪbʊl is a continuous probability distribution. It models a broad range of random variables, largely in the nature of a time to failure or time between events. Examples are maximum one-day rainfalls and the time a user spends on a web page. The distribution is named after Swedish mathematician Waloddi Weibull, who described it in detail in 1939, although it was first identified by Maurice René Fréchet and first applied by to describe a particle size distribution.
