Random walkIn mathematics, a random walk is a random process that describes a path that consists of a succession of random steps on some mathematical space. An elementary example of a random walk is the random walk on the integer number line which starts at 0, and at each step moves +1 or −1 with equal probability. Other examples include the path traced by a molecule as it travels in a liquid or a gas (see Brownian motion), the search path of a foraging animal, or the price of a fluctuating stock and the financial status of a gambler.
Wiener processIn mathematics, the Wiener process is a real-valued continuous-time stochastic process named in honor of American mathematician Norbert Wiener for his investigations on the mathematical properties of the one-dimensional Brownian motion. It is often also called Brownian motion due to its historical connection with the physical process of the same name originally observed by Scottish botanist Robert Brown.
Degenerate distributionIn mathematics, a degenerate distribution is, according to some, a probability distribution in a space with support only on a manifold of lower dimension, and according to others a distribution with support only at a single point. By the latter definition, it is a deterministic distribution and takes only a single value. Examples include a two-headed coin and rolling a die whose sides all show the same number. This distribution satisfies the definition of "random variable" even though it does not appear random in the everyday sense of the word; hence it is considered degenerate.
Genealogical DNA testA genealogical DNA test is a DNA-based genetic test used in genetic genealogy that looks at specific locations of a person's genome in order to find or verify ancestral genealogical relationships, or (with lower reliability) to estimate the ethnic mixture of an individual. Since different testing companies use different ethnic reference groups and different matching algorithms, ethnicity estimates for an individual vary between tests, sometimes dramatically.
GenealogyGenealogy () is the study of families, family history, and the tracing of their lineages. Genealogists use oral interviews, historical records, genetic analysis, and other records to obtain information about a family and to demonstrate kinship and pedigrees of its members. The results are often displayed in charts or written as narratives. The field of family history is broader than genealogy, and covers not just lineage but also family and community history and biography.
Family treeA family tree, also called a genealogy or a pedigree chart, is a chart representing family relationships in a conventional tree structure. More detailed family trees, used in medicine and social work, are known as genograms. Genealogical data can be represented in several formats, for example, as a pedigree or . Family trees are often presented with the oldest generations at the top of the tree and the younger generations at the bottom.
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.
Genetic genealogyGenetic genealogy is the use of genealogical DNA tests, i.e., DNA profiling and DNA testing, in combination with traditional genealogical methods, to infer genetic relationships between individuals. This application of genetics came to be used by family historians in the 21st century, as DNA tests became affordable. The tests have been promoted by amateur groups, such as surname study groups or regional genealogical groups, as well as research projects such as the Genographic Project. about 30 million people had been tested.
Σ-finite measureIn mathematics, a positive (or signed) measure μ defined on a σ-algebra Σ of subsets of a set X is called a finite measure if μ(X) is a finite real number (rather than ∞), and a set A in Σ is of finite measure if μ(A) < ∞. The measure μ is called σ-finite if X is a countable union of measurable sets each with finite measure. A set in a measure space is said to have σ-finite measure if it is a countable union of measurable sets with finite measure. A measure being σ-finite is a weaker condition than being finite, i.
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).
