|
Hyper-Erlang Distribution
In probability theory, a hyper-Erlang distribution is a continuous probability distribution which takes a particular Erlang distribution E''i'' with probability ''p''''i''. A hyper-Erlang distributed random variable ''X'' has a probability density function given by : A(x) = \sum_^n p_i E_(x) where each ''p''''i'' > 0 with the ''p''''i'' summing to 1 and each of the E''l''''i'' being an Erlang distribution The Erlang distribution is a two-parameter family of continuous probability distributions with support x \in independent exponential distribution">exponential variables with mean 1/\lambda each. Equivalently, it is the distribution of the tim ... with ''l''''i'' stages each of which has parameter ''λ''''i''. See also * Phase-type distribution References {{ProbDistributions, continuous-semi-infinite Continuous distributions ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hyper-Erlang Distribution
In probability theory, a hyper-Erlang distribution is a continuous probability distribution which takes a particular Erlang distribution E''i'' with probability ''p''''i''. A hyper-Erlang distributed random variable ''X'' has a probability density function given by : A(x) = \sum_^n p_i E_(x) where each ''p''''i'' > 0 with the ''p''''i'' summing to 1 and each of the E''l''''i'' being an Erlang distribution The Erlang distribution is a two-parameter family of continuous probability distributions with support x \in independent exponential distribution">exponential variables with mean 1/\lambda each. Equivalently, it is the distribution of the tim ... with ''l''''i'' stages each of which has parameter ''λ''''i''. See also * Phase-type distribution References {{ProbDistributions, continuous-semi-infinite Continuous distributions ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probability Theory
Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set of axioms. Typically these axioms formalise probability in terms of a probability space, which assigns a measure taking values between 0 and 1, termed the probability measure, to a set of outcomes called the sample space. Any specified subset of the sample space is called an event. Central subjects in probability theory include discrete and continuous random variables, probability distributions, and stochastic processes (which provide mathematical abstractions of non-deterministic or uncertain processes or measured quantities that may either be single occurrences or evolve over time in a random fashion). Although it is not possible to perfectly predict random events, much can be said about their behavior. Two major results in probability ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Continuous Probability Distribution
In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment. It is a mathematical description of a random phenomenon in terms of its sample space and the probabilities of events (subsets of the sample space). For instance, if is used to denote the outcome of a coin toss ("the experiment"), then the probability distribution of would take the value 0.5 (1 in 2 or 1/2) for , and 0.5 for (assuming that the coin is fair). Examples of random phenomena include the weather conditions at some future date, the height of a randomly selected person, the fraction of male students in a school, the results of a survey to be conducted, etc. Introduction A probability distribution is a mathematical description of the probabilities of events, subsets of the sample space. The sample space, often denoted by \Omega, is the set of all possible outcomes of a random phe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Erlang Distribution
The Erlang distribution is a two-parameter family of continuous probability distributions with support x \in independent exponential distribution">exponential variables with mean 1/\lambda each. Equivalently, it is the distribution of the time until the ''k''th event of a Poisson process with a rate of \lambda. The Erlang and Poisson distributions are complementary, in that while the Poisson distribution counts the number of events that occur in a fixed amount of time, the Erlang distribution counts the amount of time until the occurrence of a fixed number of events. When k=1, the distribution simplifies to the exponential distribution. The Erlang distribution is a special case of the gamma distribution wherein the shape of the distribution is discretised. The Erlang distribution was developed by A. K. Erlang to examine the number of telephone calls which might be made at the same time to the operators of the switching stations. This work on telephone traffic engineering has ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probability Density Function
In probability theory, a probability density function (PDF), or density of a continuous random variable, is a function whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) can be interpreted as providing a ''relative likelihood'' that the value of the random variable would be close to that sample. Probability density is the probability per unit length, in other words, while the ''absolute likelihood'' for a continuous random variable to take on any particular value is 0 (since there is an infinite set of possible values to begin with), the value of the PDF at two different samples can be used to infer, in any particular draw of the random variable, how much more likely it is that the random variable would be close to one sample compared to the other sample. In a more precise sense, the PDF is used to specify the probability of the random variable falling ''within a particular range of values'', as opposed to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
IEEE Transactions On Communications
''IEEE Transactions on Communications'' is a monthly peer-reviewed scientific journal published by the IEEE Communications Society that focuses on all aspects of telecommunication technology, including telephone, telegraphy, facsimile, and point-to-point television by electromagnetic propagation. The editor-in-chief is Tolga M. Duman (Bilkent University). According to the ''Journal Citation Reports'', the journal has a 2018 impact factor of 5.69. History The journal traces back to the establishment of the ''Transactions of the American Institute of Electrical Engineers Transaction or transactional may refer to: Commerce *Financial transaction, an agreement, communication, or movement carried out between a buyer and a seller to exchange an asset for payment *Debits and credits in a Double-entry bookkeeping syst ...'' in 1884. The journal has gone through several name changes and splits over the years. *1884–1951: ''Transactions of the American Institute of Electrical Engineers ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Phase-type Distribution
A 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. It has a discrete-time equivalent the discrete phase-type distribution. The set of phase-type distributions is dense in the field of all positive-valued distributions, that is, it can be used to approximate any positive-valued distribution. Definition Consider a continuous-time Markov process with ''m'' + 1 states, where ''m'' ≥ 1, such that the states 1,...,''m'' are transient states and state 0 is an absorbing state. Further, let the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
.svg "Click for more on -> Probability Theory")
.svg "Click for more on -> Continuous Probability Distribution")
