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Topic: Triangular distribution

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Probability distribution

Probability distribution

	Triangular distribution - Wikipedia, the free encyclopedia
		In probability theory and statistics, the triangular distribution is a continuous probability distribution with lower limit a, mode c and upper limit b.
		The Triangular Distribution is typically used as a subjective description of a population for which there is only limited sample data, and especially in cases where the relationship between variables is known but data is scarce (possibly because of the high cost of collection).
		The Triangular distribution, along with the Beta distribution, is also widely used in project management (see PERT and CPM) to model events which take place within an interval defined by a minimum and maximum value.
	en.wikipedia.org /wiki/Triangular_distribution (350 words)

	Probability distribution - Wikipedia, the free encyclopedia
		A probability distribution is a special case of the more general notion of a probability measure, which is a function that assigns probabilities satisfying the Kolmogorov axioms to the measurable sets of a measurable space.
		The rectangular distribution is a uniform distribution on [-1/2,1/2].
		The triangular distribution on [a, b], a special case of which is the distribution of the sum of two uniformly distributed random variables (the convolution of two uniform distributions).
	en.wikipedia.org /wiki/Probability_distribution (1449 words)

	2.5.4.1. Standard deviations from assumed distributions
		The triangular distribution leads to a less conservative estimate of uncertainty; i.e., it gives a smaller standard deviation than the uniform distribution.
		The calculation of the standard deviation is based on the assumption that the end-points, ± a, of the distribution are known and the mode of the triangular distribution occurs at zero.
		The calculation of the standard deviation is based on the assumption that the end-points, ± a, encompass 99.7 percent of the distribution.
	www.itl.nist.gov /div898/handbook/mpc/section5/mpc541.htm (299 words)

	Beta distribution - Wikipedia, the free encyclopedia
		The Dirichlet distribution is the multivariate generalization of the beta distribution.
		Beta distributions are used extensively in Bayesian statistics, since beta distributions provide a family of conjugate prior distributions for binomial distributions.
		For this reason, the Beta distribution - along with the triangular distribution - is used extensively in PERT, CPM and other project management / control systems to describe the time to completion of a task.
	en.wikipedia.org /wiki/Beta_distribution (408 words)

	[No title] (Site not responding. Last check: 2007-10-20)
		In another embodiment, the distributed heat sources comprise radiant heat sources, such as, for example, optical fiber arrays which are disposed about the flow sensor conduit in such a manner as to direct radiant energy onto the conduit and produce the desired triangular temperature distribution along the heated length of the conduit.
		The desired sharp peak of the triangular temperature distribution profile may be described mathematically as an isolated discontinuity in the temperature gradient at the junction of the distributed heat sources.
		The distributed heat sources 214,216 deliver heat at each point along the sensor conduit in the amount needed at each point to replace heat lost due to conduction and radiation from the outer and inner surfaces of the sensor conduit, which loss is a function of the local temperature.
	www.wipo.int /cgi-pct/guest/getbykey5?KEY=01/75400.011011&ELEMENT_SET=DECL (5586 words)

	Computation - Operations Research Models and Methods
		The probability distribution of the sum is the triangular distribution with a mode of 7.
		After identifying a distribution and defining appropriate parameters, the random variable information is placed on the worksheet with the rectangular construction as in the example.
		The orientation of the distribution data is determined by the Orient frame of the dialog.
	www.me.utexas.edu /~jensen/ORMM/computation/unit/rvadd/adding.html (943 words)

	Computation - Operations Management/Industrial Engineering
		The distribution is shown by the heavy line and the cumulative distribution is shown by the dotted line.
		The triangular distribution results are on the left and the traditional results are on the right.
		For the triangular distribution, the critical path has an expected value of 61 and the project is late by 2.
	www.me.utexas.edu /~jensen/ORMM/omie/computation/unit/project/uncertainty.html (1394 words)

	[No title] (Site not responding. Last check: 2007-10-20)
		Thus, 20% uncertainty is associated with a triangular distribution having a maximum and a minimum of 1.50 and 0.72, respectively, which equal the 2.5% and 97.
		distribution to a corresponding triangular distribution, and wherein the processing element is capable of assigning a qualitative measure by assigning a qualitative measure of maturity to each triangular distribution.
		distribution to a corresponding triangular distribution, and wherein the second executable portion assigns a qualitative measure by assigning a qualitative measure of maturity to each triangular distribution.
	www.wipo.int /cgi-pct/guest/getbykey5?KEY=04/109457.041216&ELEMENT_SET=DECL (7030 words)

	Triangular Distribution
		The Triangular Distribution is typically used as a subjective description of a population for which there is only limited sample data.
		Despite being a simplistic description of a population, it is a very useful distribution for modeling processes where the relationship between variables is known, but data is scarce (possibly because of the high cost of collection).
		Triangular distributions are used in oil and gas exploration where data is expensive to collect and it is almost impossible to model the population being sampled accurately, thus subjectivity plays a greater role than in data rich sectors.
	www.brighton-webs.co.uk /distributions/triangular.asp (460 words)

	Random Number Generator - Triangular Distribution
		The Triangular distribution is often used when no or little data is available.
		The distribution is skewed to the left when the peak is closed to the minimum and to the right when the peak is closed to the maximum.
		It is a simple distribution that as its name implied, has a triangular shape.
	www.excel-modeling.com /examples/example_024.htm (176 words)

	Triangular distribution: Facts and details from Encyclopedia Topic (Site not responding. Last check: 2007-10-20)
		The erlang distribution is a probability distribution developed by agner krarup erlanga....
		The cantor distribution is the probability distribution whose cumulative distribution function is the cantor function....
		The matrix normal distribution is a probability distribution that is a generalization of the normal distribution....
	www.absoluteastronomy.com /encyclopedia/t/tr/triangular_distribution.htm (652 words)

	Triangular Distribution (Site not responding. Last check: 2007-10-20)
		The triangular distribution (continuous) is typically used as a rough model for the time required to perform some task when no real-world data are available.
		A triangular distribution takes on values in the finite interval [minimum, maximum] (minimum >= 0.0, mode > minimum, and maximum > mode), with values near the mode being most likely to occur.
		The mean of a triangular distribution is only equal to the mode when the distribution is symmetric.
	www.caciasl.com /docs/sp412/webhelp/SPHelp/triangular_distribution.html (109 words)

	Foundation engineering - Braced excavation
		My understanding is that the distribution of soil pressure for braced or tied back excavations have been measured in-situ on many projects and the distributions you indicate are the ones recommended by AASHTO and other official groups to most closely match actual expected conditions.
		Once the second brace is installed and the excavation continues, the actual pressure distribution becomes very funky and difficult to model, as loads shift from the upper brace to the lower brace to the toe.
		The distribution of the load is influenced by the deflection of the sheeting which is difficult to predict with sufficient accuracy to predict brace loaads.
	www.eng-tips.com /viewthread.cfm?qid=31934 (1082 words)

	Probability distribution - LearnThis.Info Enclyclopedia (Site not responding. Last check: 2007-10-20)
		The Bernoulli distribution, which takes value 1 with probability p and value 0 with probability q=1-p.
		The Poisson distribution, which describes the number of rare events that happen in a certain time interval.
		In physics it is usually called a Lorentzian, and it is the distribution of the energy of an unstable state in quantum mechanics.
	encyclopedia.learnthis.info /p/pr/probability_distribution.html (966 words)

	[No title]
		Triangular distribution's EV: The triangular distribution was using the incorrect formula to calculate an expected value during NON-simulation analysis.
		Triangular distribution: If a triangular distribution with a minimum value of 0 was used as a probability, simulation would stop if a zero value was returned.
		Distributions: For Distribute Children with discrete distribution, the variable value assigned at each branch is an integer (if appropriate).
	www.treeage.com /support-2003/suppbugs.htm (1593 words)

	[No title] (Site not responding. Last check: 2007-10-20)
		For example, the interarrival rates of telephone calls is often given by the exponential distribution, the times to travel from point A to point B by truck is normally distributed, the time for a ship to return to a port is exponential, the time between storms is exponential, etc.
		The normal distribution is a two parameter distribution and is specified by the mean and standard deviation.
		A triangular distribution with a minimum of 10, a maximum of 100 and a mode of 20 will be skewed to the left.
	oldwww.rasip.fer.hr /nastava/mis/gpss/knjiga/CHAP13.html (1701 words)

	Package Set 2
		A distribution is log-normally distributed when the natural log of the set of the random variables in that distribution is a normally distributed.
		Both distributions are symmetrical, both range in value from negative infinity to positive infinity, and both have a mean of zero and standard derivation of one.
		The Gamma distribution is most often used to describe the distribution of the amount of time until the nth occurrence of an event in a Poisson process.
	www.excel-modeling.com /index_008.htm (833 words)

	Triangular Distribution
		A triangular distribution is very simple: it is peaked somewhere in the middle and has a finite range.
		It is not usually equal to the mean unless the distribution is symmetric.
		A triangular distribution is useful when you have only a vague idea about the shape of the distribution, perhaps you only know the range and where the peak occurs.
	www.caciasl.com /products/webhelp/SPHelp/triangular_distribution.html (116 words)

	Triangular approximations for continuous random variables in risk analysis
		This paper examines further the problem of approximating the distribution of a continuous random variable based on three key percentiles, typically the median (50th percentile) and the 5% points (5th and 95th percentiles).
		Tukey mean approximation remains highly accurate for a range of unbounded distributions, although the accuracy in these cases can be improved by a slightly different 3:10:3 weighting of the 5%, 50% and 95% points.
		In addition, triangular approximations allow the underlying distribution function to be estimated by a triangular cdf.
	www.palgrave-journals.com /jors/journal/v53/n4/abs/2601330a.html (329 words)

	Inventory Modeling
		The methodology used to optimize inventory placement within the distribution network consisted of two modeling phases (stochastic simulation of the distribution network and statistical modeling using RSM) as well as a financial analysis.
		The stochastic simulation models were developed to create virtual models of the distribution network that could be experimented on without impacting our customers and were run in a relatively short period of time.
		The same process was used with experts in the warehouse and distribution centers to get triangular distributions for throughput times.
	www.intel.com /technology/itj/2005/volume09issue03/art07_inventorymodeling/p03_distribution.htm (933 words)

	(WO 01/75400) CONSTANT TEMPERATURE GRADIENT DIFFERENTIAL THERMAL MASS FLOW SENSOR (Site not responding. Last check: 2007-10-20)
		The sensor conduit is heated by a pair of distributed heat sources (214, 216) and a concentrated heat source (310) located between the distributed heat sources.
		The heater density of the sensor conduit increases linearly from the outer ends of the distributed heat sources towards the center of the heater length of the sensor conduit, and spikes to a substantially greater value at a point corresponding to the centrally located concentrated heat source.
		The temperature distribution function along the flow sensor tube is a substantially symmetric triangular function.
	wipo.int /cgi-pct/guest/getbykey5?KEY=01/75400.011011&ELEMENT_SET=DECL (213 words)

	Alternatives to the Triangular Distribution in Modeling Expert Opinion
		The Triangular distribution (M0477) is very popular for modeling a subjective estimate (M0019 discusses techniques and traps of subjective estimation) of some uncertain quantity in a Crystal Ball model: in Crystal Ball business risk models it is the most common distribution.
		The Triangular distribution has a mean equal to the average of its three parameters, i.e.
		The PERT distribution has a mean equal to (Min+4*Mode+Max)/6, in other words it is the average of all three parameters but with four time the weighting on the Mode.
	www.decisioneering.com /support/risktips/risktip-3.html (831 words)

	ExpertFit: Pitfalls in Input Modeling
		The variability of the probability distributions, rather than just their means, has a significant impact on the congestion level in most queueing-type (e.g., manufacturing) systems.
		The usual approach for modeling a source of randomness in the absence of data is to use a triangular distribution.
		Suppose, however, that the processing-time distribution is unknown and that we decide to approximate it by a triangular distribution, which is specified by its minimum, maximum, and most likely values.
	www.averill-law.com /ExpertFit-pitfalls-paper.htm (1683 words)

	RANDOM Functions
		is a seed for the distribution to use.
		is uniformly distributed on the range 0 to 1.
		is 1 the Weibull distribution is the same as the exponential distribution.
	www.vensim.com /documentation/html/22675.htm (786 words)

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