Normal-gamma distributionIn probability theory and statistics, the normal-gamma distribution (or Gaussian-gamma distribution) is a bivariate four-parameter family of continuous probability distributions. It is the conjugate prior of a normal distribution with unknown mean and precision. For a pair of random variables, (X,T), suppose that the conditional distribution of X given T is given by meaning that the conditional distribution is a normal distribution with mean and precision — equivalently, with variance Suppose also that the marginal distribution of T is given by where this means that T has a gamma distribution.
Log-logistic distributionIn probability and statistics, the log-logistic distribution (known as the Fisk distribution in economics) is a continuous probability distribution for a non-negative random variable. It is used in survival analysis as a parametric model for events whose rate increases initially and decreases later, as, for example, mortality rate from cancer following diagnosis or treatment. It has also been used in hydrology to model stream flow and precipitation, in economics as a simple model of the distribution of wealth or income, and in networking to model the transmission times of data considering both the network and the software.
Variance-gamma distributionThe variance-gamma distribution, generalized Laplace distribution or Bessel function distribution is a continuous probability distribution that is defined as the normal variance-mean mixture where the mixing density is the gamma distribution. The tails of the distribution decrease more slowly than the normal distribution. It is therefore suitable to model phenomena where numerically large values are more probable than is the case for the normal distribution. Examples are returns from financial assets and turbulent wind speeds.
AerosolAn aerosol is a suspension of fine solid particles or liquid droplets in air or another gas. Aerosols can be natural or anthropogenic. Examples of natural aerosols are fog or mist, dust, forest exudates, and geyser steam. Examples of anthropogenic aerosols include particulate air pollutants, mist from the discharge at hydroelectric dams, irrigation mist, perfume from atomizers, smoke, dust, steam from a kettle, sprayed pesticides, and medical treatments for respiratory illnesses.
Gamma functionIn mathematics, the gamma function (represented by Γ, the capital letter gamma from the Greek alphabet) is one commonly used extension of the factorial function to complex numbers. The gamma function is defined for all complex numbers except the non-positive integers. For every positive integer n, Derived by Daniel Bernoulli, for complex numbers with a positive real part, the gamma function is defined via a convergent improper integral: The gamma function then is defined as the analytic continuation of this integral function to a meromorphic function that is holomorphic in the whole complex plane except zero and the negative integers, where the function has simple poles.
Cloud albedoCloud albedo is a measure of the albedo or reflectivity of a cloud. Clouds regulate the amount of solar radiation absorbed by a planet and its solar surface irradiance. Generally, increased cloud cover correlates to a higher albedo and a lower absorption of solar energy. Cloud albedo strongly influences the Earth's energy budget, accounting for approximately half of Earth's albedo. Cloud albedo depends on the total mass of water, the size and shape of the droplets or particles and their distribution in space.
Coalescence (physics)Coalescence is the process by which two or more droplets, bubbles, or particles merge during contact to form a single daughter droplet, bubble, or particle. Coalescence manifests itself from a microscopic scale in meteorology to a macroscopic scale in astrophysics. For example, it is seen in the formation of raindrops as well as planetary and star formation. In meteorology, its role is crucial in the formation of rain. As droplets are carried by the updrafts and downdrafts in a cloud, they collide and coalesce to form larger droplets.
Incomplete gamma functionIn mathematics, the upper and lower incomplete gamma functions are types of special functions which arise as solutions to various mathematical problems such as certain integrals. Their respective names stem from their integral definitions, which are defined similarly to the gamma function but with different or "incomplete" integral limits. The gamma function is defined as an integral from zero to infinity. This contrasts with the lower incomplete gamma function, which is defined as an integral from zero to a variable upper limit.
Generalized gamma distributionThe generalized gamma distribution is a continuous probability distribution with two shape parameters (and a scale parameter). It is a generalization of the gamma distribution which has one shape parameter (and a scale parameter). Since many distributions commonly used for parametric models in survival analysis (such as the exponential distribution, the Weibull distribution and the gamma distribution) are special cases of the generalized gamma, it is sometimes used to determine which parametric model is appropriate for a given set of data.
Cloud condensation nucleiCloud condensation nuclei (CCNs), also known as cloud seeds, are small particles typically 0.2 μm, or one hundredth the size of a cloud droplet. CCNs are a unique subset of aerosols in the atmosphere on which water vapour condenses. This can affect the radiative properties of clouds and the overall atmosphere. Water requires a non-gaseous surface to make the transition from a vapour to a liquid; this process is called condensation. In the atmosphere of Earth, this surface presents itself as tiny solid or liquid particles called CCNs.
