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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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Erlang Dist Pdf2
Erlang may refer to: Science and technology * Erlang (programming language), a programming language * Erlang (unit), a unit to measure traffic in telecommunications or other domains * Erlang distribution, a probability distribution describing the time between events Places * Mount Erlang, a mountain in China * Erlang railway station, on the Chinese Qinghai–Tibet Railway Other uses * Agner Krarup Erlang (1878–1929), mathematician and engineer after whom several concepts are named * Erlang Shen, a Chinese deity See also * Erlangen, Germany * Erlanger (other) {{Disambiguation, surname ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cumulative Distribution Function
In probability theory and statistics, the cumulative distribution function (CDF) of a real-valued random variable X, or just distribution function of X, evaluated at x, is the probability that X will take a value less than or equal to x. Every probability distribution supported on the real numbers, discrete or "mixed" as well as continuous, is uniquely identified by an ''upwards continuous'' ''monotonic increasing'' cumulative distribution function F : \mathbb R \rightarrow ,1/math> satisfying \lim_F(x)=0 and \lim_F(x)=1. In the case of a scalar continuous distribution, it gives the area under the probability density function from minus infinity to x. Cumulative distribution functions are also used to specify the distribution of multivariate random variables. Definition The cumulative distribution function of a real-valued random variable X is the function given by where the right-hand side represents the probability that the random variable X takes on a value less th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gamma Function
In mathematics, the gamma function (represented by , 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 , \Gamma(n) = (n-1)!\,. Derived by Daniel Bernoulli, for complex numbers with a positive real part, the gamma function is defined via a convergent improper integral: \Gamma(z) = \int_0^\infty t^ e^\,dt, \ \qquad \Re(z) > 0\,. 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. The gamma function has no zeroes, so the reciprocal gamma function is an entire function. In fact, the gamma function corresponds to the Mellin transform of the negative exponential function: \Gamma(z) = \mathcal M ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cumulative Distribution Function (CDF)
In probability theory and statistics, the cumulative distribution function (CDF) of a real-valued random variable X, or just distribution function of X, evaluated at x, is the probability that X will take a value less than or equal to x. Every probability distribution supported on the real numbers, discrete or "mixed" as well as continuous, is uniquely identified by an ''upwards continuous'' ''monotonic increasing'' cumulative distribution function F : \mathbb R \rightarrow ,1/math> satisfying \lim_F(x)=0 and \lim_F(x)=1. In the case of a scalar continuous distribution, it gives the area under the probability density function from minus infinity to x. Cumulative distribution functions are also used to specify the distribution of multivariate random variables. Definition The cumulative distribution function of a real-valued random variable X is the function given by where the right-hand side represents the probability that the random variable X takes on a value less than ... [...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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Independent And Identically Distributed Random Variables
In probability theory and statistics, a collection of random variables is independent and identically distributed if each random variable has the same probability distribution as the others and all are mutually independent. This property is usually abbreviated as ''i.i.d.'', ''iid'', or ''IID''. IID was first defined in statistics and finds application in different fields such as data mining and signal processing. Introduction In statistics, we commonly deal with random samples. A random sample can be thought of as a set of objects that are chosen randomly. Or, more formally, it’s “a sequence of independent, identically distributed (IID) random variables”. In other words, the terms ''random sample'' and ''IID'' are basically one and the same. In statistics, we usually say “random sample,” but in probability it’s more common to say “IID.” * Identically Distributed means that there are no overall trends–the distribution doesn’t fluctuate and all items in th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Carcinogenesis
Carcinogenesis, also called oncogenesis or tumorigenesis, is the formation of a cancer, whereby normal cells are transformed into cancer cells. The process is characterized by changes at the cellular, genetic, and epigenetic levels and abnormal cell division. Cell division is a physiological process that occurs in almost all tissues and under a variety of circumstances. Normally, the balance between proliferation and programmed cell death, in the form of apoptosis, is maintained to ensure the integrity of tissues and organs. According to the prevailing accepted theory of carcinogenesis, the somatic mutation theory, mutations in DNA and epimutations that lead to cancer disrupt these orderly processes by interfering with the programming regulating the processes, upsetting the normal balance between proliferation and cell death. This results in uncontrolled cell division and the evolution of those cells by natural selection in the body. Only certain mutations lead to canc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Disease Incidence
In epidemiology, incidence is a measure of the probability of occurrence of a given medical condition in a population within a specified period of time. Although sometimes loosely expressed simply as the number of new cases during some time period, it is better expressed as a proportion or a rate with a denominator. Incidence proportion Incidence proportion (IP), also known as cumulative incidence, is defined as the probability that a particular event, such as occurrence of a particular disease, has occurred before a given time. It is calculated dividing the number of new cases during a given period by the number of subjects at risk in the population initially at risk at the beginning of the study. Where the period of time considered is an entire lifetime, the incidence proportion is called lifetime risk. For example, if a population initially contains 1,000 persons and 28 develop a condition since the disease first occurred until two years later, the cumulative incidence prop ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cancer
Cancer is a group of diseases involving abnormal cell growth with the potential to invade or spread to other parts of the body. These contrast with benign tumors, which do not spread. Possible signs and symptoms include a lump, abnormal bleeding, prolonged cough, unexplained weight loss, and a change in bowel movements. While these symptoms may indicate cancer, they can also have other causes. Over 100 types of cancers affect humans. Tobacco use is the cause of about 22% of cancer deaths. Another 10% are due to obesity, poor diet, lack of physical activity or excessive drinking of alcohol. Other factors include certain infections, exposure to ionizing radiation, and environmental pollutants. In the developing world, 15% of cancers are due to infections such as ''Helicobacter pylori'', hepatitis B, hepatitis C, human papillomavirus infection, Epstein–Barr virus and human immunodeficiency virus (HIV). These factors act, at least partly, by changing the genes of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Call Center
A call centre ( Commonwealth spelling) or call center (American spelling; see spelling differences) is a managed capability that can be centralised or remote that is used for receiving or transmitting a large volume of enquiries by telephone. An inbound call centre is operated by a company to administer incoming product or service support or information enquiries from consumers. Outbound call centres are usually operated for sales purposes such as telemarketing, for solicitation of charitable or political donations, debt collection, market research, emergency notifications, and urgent/critical needs blood banks. A contact centre is a further extension to call centres telephony based capabilities, administers centralised handling of individual communications, including letters, faxes, live support software, social media, instant message, and email. A call center was previously seen to be an open workspace for call center agents, with workstations that include a computer ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Erlang Unit
The erlang (symbol E) is a dimensionless unit that is used in telephony as a measure of offered load or carried load on service-providing elements such as telephone circuits or telephone switching equipment. A single cord circuit has the capacity to be used for 60 minutes in one hour. Full utilization of that capacity, 60 minutes of traffic, constitutes 1 erlang. Carried traffic in erlangs is the average number of concurrent calls measured over a given period (often one hour), while offered traffic is the traffic that would be carried if all call-attempts succeeded. How much offered traffic is carried in practice will depend on what happens to unanswered calls when all servers are busy. The CCITT named the international unit of telephone traffic the erlang in 1946 in honor of Agner Krarup Erlang. In Erlang's analysis of efficient telephone line usage he derived the formulae for two important cases, Erlang-B and Erlang-C, which became foundational results in teletraffic enginee ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Erlang-B
The erlang (symbol E) is a dimensionless unit that is used in telephony as a measure of offered load or carried load on service-providing elements such as telephone circuits or telephone switching equipment. A single cord circuit has the capacity to be used for 60 minutes in one hour. Full utilization of that capacity, 60 minutes of traffic, constitutes 1 erlang. Carried traffic in erlangs is the average number of concurrent calls measured over a given period (often one hour), while offered traffic is the traffic that would be carried if all call-attempts succeeded. How much offered traffic is carried in practice will depend on what happens to unanswered calls when all servers are busy. The CCITT named the international unit of telephone traffic the erlang in 1946 in honor of Agner Krarup Erlang. In Erlang's analysis of efficient telephone line usage he derived the formulae for two important cases, Erlang-B and Erlang-C, which became foundational results in teletraffic enginee ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
