LoggingLogging is the process of cutting, processing, and moving trees to a location for transport. It may include skidding, on-site processing, and loading of trees or logs onto trucks or skeleton cars. In forestry, the term logging is sometimes used narrowly to describe the logistics of moving wood from the stump to somewhere outside the forest, usually a sawmill or a lumber yard. In common usage, however, the term may cover a range of forestry or silviculture activities.
Compound Poisson processA compound Poisson process is a continuous-time stochastic process with jumps. The jumps arrive randomly according to a Poisson process and the size of the jumps is also random, with a specified probability distribution. To be precise, a compound Poisson process, parameterised by a rate and jump size distribution G, is a process given by where, is the counting variable of a Poisson process with rate , and are independent and identically distributed random variables, with distribution function G, which are also independent of When are non-negative integer-valued random variables, then this compound Poisson process is known as a stuttering Poisson process.
Extended negative binomial distributionIn probability and statistics the extended negative binomial distribution is a discrete probability distribution extending the negative binomial distribution. It is a truncated version of the negative binomial distribution for which estimation methods have been studied. In the context of actuarial science, the distribution appeared in its general form in a paper by K. Hess, A. Liewald and K.D. Schmidt when they characterized all distributions for which the extended Panjer recursion works.
Beta negative binomial distributionIn probability theory, a beta negative binomial distribution is the probability distribution of a discrete random variable equal to the number of failures needed to get successes in a sequence of independent Bernoulli trials. The probability of success on each trial stays constant within any given experiment but varies across different experiments following a beta distribution. Thus the distribution is a compound probability distribution.
Poisson point processIn probability, statistics and related fields, a Poisson point process is a type of random mathematical object that consists of points randomly located on a mathematical space with the essential feature that the points occur independently of one another. The Poisson point process is often called simply the Poisson process, but it is also called a Poisson random measure, Poisson random point field or Poisson point field.
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 ().
Beta-binomial distributionIn probability theory and statistics, the beta-binomial distribution is a family of discrete probability distributions on a finite support of non-negative integers arising when the probability of success in each of a fixed or known number of Bernoulli trials is either unknown or random. The beta-binomial distribution is the binomial distribution in which the probability of success at each of n trials is not fixed but randomly drawn from a beta distribution.
Expected valueIn probability theory, the expected value (also called expectation, expectancy, expectation operator, mathematical expectation, mean, average, or first moment) is a generalization of the weighted average. Informally, the expected value is the arithmetic mean of a large number of independently selected outcomes of a random variable. The expected value of a random variable with a finite number of outcomes is a weighted average of all possible outcomes. In the case of a continuum of possible outcomes, the expectation is defined by integration.
Transaction logIn the field of databases in computer science, a transaction log (also transaction journal, database log, binary log or audit trail) is a history of actions executed by a database management system used to guarantee ACID properties over crashes or hardware failures. Physically, a log is a listing changes to the database, stored in a stable storage format. If, after a start, the database is found in an inconsistent state or not been shut down properly, the database management system reviews the database logs for uncommitted transactions and rolls back the changes made by these transactions.
Log probabilityIn probability theory and computer science, a log probability is simply a logarithm of a probability. The use of log probabilities means representing probabilities on a logarithmic scale , instead of the standard unit interval. Since the probabilities of independent events multiply, and logarithms convert multiplication to addition, log probabilities of independent events add. Log probabilities are thus practical for computations, and have an intuitive interpretation in terms of information theory: the negative of the average log probability is the information entropy of an event.
