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# Topic: Exponential distribution

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 Exponential distribution - Wikipedia, the free encyclopedia The exponential distribution may be viewed as a continuous counterpart of the geometric distribution, which describes the number of Bernoulli trials necessary for a discrete process to change state. An important property of the exponential distribution is that it is memoryless. The conjugate prior for the exponential distribution is the gamma distribution (of which the exponential distribution is a special case). en.wikipedia.org /wiki/Exponential_distribution   (1380 words)

 Exponential decay - Wikipedia, the free encyclopedia Many decay processes that are often treated as exponential, are really only exponential so long as the sample is large and the law of large numbers holds. In a sample of a radionuclide that undergoes radioactive decay to a different state, the number of atoms in the original state follows exponential decay as long as the remaining number of atoms is large. If an object at one temperature is exposed to a medium of another temperature, the temperature difference between the object and the medium follows exponential decay (in the limit of slow processes; equivalent to "good" heat conduction inside the object, so that its temperature remains relatively uniform throught its volume). en.wikipedia.org /wiki/Exponential_decay   (1091 words)

 1.3.6.6.7. Exponential Distribution Maximum likelihood estimation for the exponential distribution is discussed in the chapter on reliability (Chapter 8). The exponential distribution is primarily used in reliability applications. The exponential distribution is used to model data with a constant failure rate (indicated by the hazard plot which is simply equal to a constant). www.itl.nist.gov /div898/handbook/eda/section3/eda3667.htm   (318 words)

 Exponential Distribution   (Site not responding. Last check: 2007-10-22) The exponential distribution (continuous) is commonly used to model interarrival times of customers to some system when the arrival rate is approximately constant over the time period of interest. An exponential distribution with mean = m is a gamma distribution with mean = m and shape = 1. An exponential distribution with mean = m is a Weibull distribution with shape = 1 and scale = m. www.caciasl.com /docs/sp412/webhelp/SPHelp/exponential_distribution.html   (157 words)

 1.3.6.6.12. Double Exponential Distribution Since the general form of probability functions can be expressed in terms of the standard distribution, all subsequent formulas in this section are given for the standard form of the function. The double exponential survival function can be computed from the cumulative distribution function of the double exponential distribution. The formula for the inverse survival function of the double exponential distribution is www.itl.nist.gov /div898/handbook/eda/section3/eda366c.htm   (264 words)

 Hyper Exponential Distribution   (Site not responding. Last check: 2007-10-22) The hyper exponential distribution (continuous) is a mixture of two exponential distributions. Specifically, a hyper exponential distribution with parameters mean1, mean2, and probability1 takes on values from an exponential distribution with parameter mean1 with a probability of probability1 and takes on values from an exponential distribution with parameter mean2 with a probability of 1 - probability1. A hyper exponential distribution with probability1 = 1 is an exponential distribution with parameter mean1. www.caciasl.com /docs/sp412/webhelp/SPHelp/hyperexponential_distribution.html   (110 words)

 Overview of Exponential Distribution Characteristics In reliability engineering the exponential distribution has been found to adequately model the failure rate of electronics during their useful life [1]. The cumulative distribution function (area under PDF curve) is obtained by integrating the PDF as shown in Figure 2 and given by Equation 2. For the exponential distribution, the hazard function, or instantaneous failure rate, is constant over time, as shown in Figure 4. www.quanterion.com /FAQ/Exponential_Dist.htm   (209 words)

 Exponential Distribution The exponential distribution is a very commonly used distribution in reliability engineering. The exponential distribution is used to describe units that have a constant failure rate. The conditional reliability function for the 1-parameter exponential distribution is given by: www.weibull.com /AccelTestWeb/exponential_distribution.htm   (243 words)

 Exponential Distribution The exponential distribution is closely related to the poisson distribution. Because of this behavior, the exponential distribution is usually used to model the mean time between occurrences, such as arrivals or failures, and the poisson distribution is used to model occurrences per interval, such as arrivals, failures or defects. Because of this, the exponential distribution exhibits a lack of memory. www.engineeredsoftware.com /nasa/exponential.htm   (323 words)

 Gamma Distribution When used to describe the sum of a series of exponentially distributed variables, the shape factor represents the number of variables and the scale factor is the mean of the exponential distribution. A chi-squared distribution is a gamma distribution in which the shape parameter set to the degrees of freedom divided by two and the scale parameter set to two. The Erlang distribution is used to model the total interval associated with multiple Poisson events, The shape parameters represents the number of events and the scale parameter the average interval between events. www.brighton-webs.co.uk /distributions/gamma.asp   (487 words)

 Limitations of the Exponential Distribution for Reliability Analysis The exponential distribution models the behavior of units that fail at a constant rate, regardless of the accumulated age. It shows that the Weibull distribution models the behavior better, while the exponential distribution overestimates the initial failure rate and significantly underestimates the rate in later stages of life. Additionally, prior efforts and standards that extensively utilized the exponential distribution should be commended for introducing and formalizing the reliability methods that formed the basis of more advanced analysis techniques and for applying more rigorous scientific approaches within the field. www.reliasoft.com /newsletter/4q2001/exponential.htm   (1586 words)

 The Exponential/Gamma Distribution The Poisson distribution gives the probability of a certain number of events in a time period when we know the average number of events in the same time period. The distribution of the so-called "waiting times" is called the exponential distribution (when we are waiting for a single event) and the gamma (or Erlang) distribution (when we are waiting for more than one event). The lengths have an exponential distribution with mean 3 ft. I need a cable that is 5 ft long. www.nadn.navy.mil /MathDept/courses/pre97/sm230/gamma.htm   (1357 words)

 exponential distribution | TutorGig.co.uk Encyclopedia   (Site not responding. Last check: 2007-10-22) The exponential distributions can alternatively be parameterized by a scale parameter μ = 1/λ. But if we focus on a time interval during which the rate is roughly constant, such as from 2 to 4 PM during work days, the exponential distribution can be used as a good approximate model for the time until the next phone call arrives. This follows from the form of the quantile function given above and yields a convenient way to produce exponentially distributed values using a random number generator on a computer, for instance to conduct simulation experiments. www.tutorgig.co.uk /ed/exponential_distribution   (1363 words)

 Probability Distributions (Statistics Toolbox) The exponential distribution is special because of its utility in modeling events that occur randomly over time. Parameter estimation is the process of determining the parameters of the exponential distribution that fit this data best in some sense. For exponentially distributed lifetimes, the probability that an item will survive an extra unit of time is independent of the current age of the item. www-rohan.sdsu.edu /doc/matlab/toolbox/stats/prob_d14.html   (360 words)

 Probability Distributions   (Site not responding. Last check: 2007-10-22) The Gamma Distribution is a general distribution covering many special cases, including the Chi-squared distribution and Exponential distribution. The Log-Normal Distribution is useful when the raw data are highly skewed whereas the natural log of the data are normally distributed. The Beta Distribution is a continuous distribution bounded between 0 and 1. www.stat.vt.edu /~sundar/java/applets/Distributions.html   (494 words)

 Distributions in Continuous Systems The normal distribution, or Gaussian distribution, is a symmetrical distribution commonly referred to as the bell curve. The Exponential distribution arises in the calculations of reliability. It is similar to the Poisson distribution with www.efunda.com /math/distributions/dist_continuous.cfm   (108 words)

 Distributions   (Site not responding. Last check: 2007-10-22) The exponential distribution is a special case of the gamma distribution where a=1 and B = 1/lambda. To generate an exponential distribution with a mean "m" from a uniform distribution "u" on (0,1) use -m ln(u). The probability distribution of a narrow band noise process n(t) was formulated by Rice in papers published in the Bell Laboratories Journal, 1944 and 1945. local.wasp.uwa.edu.au /~pbourke/other/distributions   (901 words)

 September 22 Lecture   (Site not responding. Last check: 2007-10-22) Because, as we've seen, for reasonable size samples, the empirical cdf is a good approximation to the population cdf, using the empirical cdf to generate samples is essentially equivalent to generating samples from the original population. As a result, the bootstrap distribution of a statistic should be a good approximation of the sampling distribution of that statistic. In short, the bootstrap distribution of a statistic should be a reasonable approximation of the sampling distribution of that statistic, if the sample sizes are reasonably large. www.unc.edu /courses/2003fall/biol/145/001/docs/lectures/Sep22.html   (1076 words)

 2.2.1 Exponential distribution   (Site not responding. Last check: 2007-10-22) One of the most studied continuous distributions is the exponential distribution. An important property of the exponential distribution is the memoryless property. is the parameter that characterizes the distribution, and www.cs.wm.edu /~riska/PhD-thesis-html/node8.html   (100 words)

 Ocean *4413# ~ Exponential Gamma Distribution Box - Computer Forms. The distribution is two-sided, that is, it is defined from -infinity to +infinity. For this reason it may be a convenient alternative to the normal distribution in the case of skewed empirical data. Extreme value distribution for the exponential gamma distribution itself may be derived in terms of a new exponential gamma distribution as outlined in Paragraph 4.3.2 (v) (call *4325*# for text and *432*1# for equations). research.dnv.com /ocean/cc/g/w41/f30.htm   (348 words)

 Mis-Application of the Exponential Distribution   (Site not responding. Last check: 2007-10-22) For the exponential distribution parameter estimation when censored data is encountered is a relatively simple task. The exponential distribution is not very useful in modeling data in the real world. The exponential distribution is only useful for items that have a constant failure rate. www.engineeredsoftware.com /rma_exponential.asp   (310 words)

 Survival/Failure Time Analysis The major distributions that have been proposed for modeling survival or failure times are the exponential (and linear exponential) distribution, the Weibull distribution of extreme events, and the Gompertz distribution. Basically, this model assumes that the survival time distribution is exponential, and contingent on the values of a set of independent variables (zi). The Chi-square goodness-of-fit value is computed as a function of the log-likelihood for the model with all parameter estimates (L1), and the log-likelihood of the model in which all covariates are forced to 0 (zero; L0). www.statsoft.com /textbook/stsurvan.html   (2842 words)

 The Exponential Distribution The exponential distribution is a commonly used distribution in reliability engineering. Mathematically, it is a fairly simple distribution, which many times leads to its use in inappropriate situations. The exponential distribution is used to model the behavior of units that have a constant failure rate (or units that do not degrade with time or wear out). www.weibull.com /LifeDataWeb/the_exponential_distribution.htm   (77 words)

 The Positive solution is well-represented by a mixture of an EC distribution is well-represented by the convolution of an EC distribution This necessitates the second approach of using the convolution of an EC distribution and an exponential distribution. www.cs.cmu.edu /People/osogami/thesis/html/node57.html   (370 words)

 Exponential - Wikipedia, the free encyclopedia The term exponential may refer to any of several topics in mathematics: There is also a record label called Exponential. This is a disambiguation page: a list of articles associated with the same title. en.wikipedia.org /wiki/Exponential   (89 words)

 Excel Instructions - Exponential Distribution   (Site not responding. Last check: 2007-10-22) Excel cannot directly generate data from an exponential; however, the following procedure can be used to obtain random observations from an exponential distribution. The first step is to create a set of uniform random numbers between 0 and 1, see Uniform for more information. An example, one sample of 5 observations from a exponential distribution with a mean of 3: www.statsclass.com /excel/misc/exp_dist.html   (112 words)

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