Phase-type distributionA phase-type distribution is a probability distribution constructed by a convolution or mixture of exponential distributions. It results from a system of one or more inter-related Poisson processes occurring in sequence, or phases. The sequence in which each of the phases occurs may itself be a stochastic process. The distribution can be represented by a random variable describing the time until absorption of a Markov process with one absorbing state. Each of the states of the Markov process represents one of the phases.
GravelGravel (ˈɡrævəl) is a loose aggregation of rock fragments. Gravel occurs naturally on Earth as a result of sedimentary and erosive geological processes; it is also produced in large quantities commercially as crushed stone. Gravel is classified by particle size range and includes size classes from granule- to boulder-sized fragments. In the Udden-Wentworth scale gravel is categorized into granular gravel () and pebble gravel (). ISO 14688 grades gravels as fine, medium, and coarse, with ranges for fine and for coarse.
Marine sedimentMarine sediment, or ocean sediment, or seafloor sediment, are deposits of insoluble particles that have accumulated on the seafloor. These particles have their origins in soil and rocks and have been transported from the land to the sea, mainly by rivers but also by dust carried by wind and by the flow of glaciers into the sea. Additional deposits come from marine organisms and chemical precipitation in seawater, as well as from underwater volcanoes and meteorite debris.
Negative binomial distributionIn probability theory and statistics, the negative binomial distribution is a discrete probability distribution that models the number of failures in a sequence of independent and identically distributed Bernoulli trials before a specified (non-random) number of successes (denoted ) occurs. For example, we can define rolling a 6 on a dice as a success, and rolling any other number as a failure, and ask how many failure rolls will occur before we see the third success ().
Turbidity currentA turbidity current is most typically an underwater current of usually rapidly moving, sediment-laden water moving down a slope; although current research (2018) indicates that water-saturated sediment may be the primary actor in the process. Turbidity currents can also occur in other fluids besides water. Researchers from the Monterey Bay Aquarium Research Institute found that a layer of water-saturated sediment moved rapidly over the seafloor and mobilized the upper few meters of the preexisting seafloor.
Stable distributionIn probability theory, a distribution is said to be stable if a linear combination of two independent random variables with this distribution has the same distribution, up to location and scale parameters. A random variable is said to be stable if its distribution is stable. The stable distribution family is also sometimes referred to as the Lévy alpha-stable distribution, after Paul Lévy, the first mathematician to have studied it. Of the four parameters defining the family, most attention has been focused on the stability parameter, (see panel).
Lomax distributionThe Lomax distribution, conditionally also called the Pareto Type II distribution, is a heavy-tail probability distribution used in business, economics, actuarial science, queueing theory and Internet traffic modeling. It is named after K. S. Lomax. It is essentially a Pareto distribution that has been shifted so that its support begins at zero. The probability density function (pdf) for the Lomax distribution is given by with shape parameter and scale parameter .
UnimodalityIn mathematics, unimodality means possessing a unique mode. More generally, unimodality means there is only a single highest value, somehow defined, of some mathematical object. In statistics, a unimodal probability distribution or unimodal distribution is a probability distribution which has a single peak. The term "mode" in this context refers to any peak of the distribution, not just to the strict definition of mode which is usual in statistics. If there is a single mode, the distribution function is called "unimodal".
Clastic rockClastic rocks are composed of fragments, or clasts, of pre-existing minerals and rock. A clast is a fragment of geological detritus, chunks, and smaller grains of rock broken off other rocks by physical weathering. Geologists use the term clastic to refer to sedimentary rocks and particles in sediment transport, whether in suspension or as bed load, and in sediment deposits. Clastic sedimentary rocks are rocks composed predominantly of broken pieces or clasts of older weathered and eroded rocks.
Mixture distributionIn probability and statistics, a mixture distribution is the probability distribution of a random variable that is derived from a collection of other random variables as follows: first, a random variable is selected by chance from the collection according to given probabilities of selection, and then the value of the selected random variable is realized. The underlying random variables may be random real numbers, or they may be random vectors (each having the same dimension), in which case the mixture distribution is a multivariate distribution.
