About: Trapezoidal distribution

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In probability theory and statistics, the trapezoidal distribution is a continuous probability distribution whose probability density function graph resembles a trapezoid. Likewise, trapezoidal distributions also roughly resemble mesas or plateaus. The non-central moments of the trapezoidal distribution are

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rdfs:label	Trapezverteilung (de) Trapezoidal distribution (en)
rdfs:comment	Die Trapezverteilung ist eine stetige Wahrscheinlichkeitsverteilung auf einem kompakten Intervall. (de) In probability theory and statistics, the trapezoidal distribution is a continuous probability distribution whose probability density function graph resembles a trapezoid. Likewise, trapezoidal distributions also roughly resemble mesas or plateaus. The non-central moments of the trapezoidal distribution are (en)
name	Trapezoidal (en)
foaf:depiction
dcterms:subject	Continuous distributions
Wikipage page ID	40750679 (xsd:integer)
Wikipage revision ID	1093188246 (xsd:integer)
Link from a Wikipage to another Wikipage	Probability distribution Mesa Multimodal distribution Uniform distribution (continuous) Upper and lower bounds Value (mathematics) Maxima and minima Geometry Mode (statistics) Moment (mathematics) Bates distribution Statistics Plateau Symmetry Central limit theorem Irwin–Hall distribution Linearity Normal distribution Probability density function Probability Probability theory Continuous distributions Trapezoid Differentiable function Poisson distribution Special case Classification of discontinuities Event (probability theory) Triangular distribution dbr:Generalized_trapezoidal_distribution
sameAs	Trapezoidal distribution Trapezoidal distribution Trapezoidal distribution Trapezoidal distribution Trapezoidal distribution
dbp:wikiPageUsesTemplate	dbt:Math dbt:Mvar dbt:ProbDistributions dbt:Reflist dbt:Short_description dbt:Probability_distribution
thumbnail	wiki-commons:Special:FilePath/Trapezoidal_PDF.png?width=300
type	density (en)
has abstract	Die Trapezverteilung ist eine stetige Wahrscheinlichkeitsverteilung auf einem kompakten Intervall. (de) In probability theory and statistics, the trapezoidal distribution is a continuous probability distribution whose probability density function graph resembles a trapezoid. Likewise, trapezoidal distributions also roughly resemble mesas or plateaus. Each trapezoidal distribution has a lower bound a and an upper bound d, where a < d, beyond which no values or events on the distribution can occur (i.e. beyond which the probability is always zero). In addition, there are two sharp bending points (non-differentiable discontinuities) within the probability distribution, which we will call b and c, which occur between a and d, such that a ≤ b ≤ c ≤ d. The image to the right shows a perfectly linear trapezoidal distribution. However, not all trapezoidal distributions are so precisely shaped. In the standard case, where the middle part of the trapezoid is completely flat, and the side ramps are perfectly linear, all of the values between c and d will occur with equal frequency, and therefore all such points will be modes (local frequency maxima) of the distribution. On the other hand, though, if the middle part of the trapezoid is not completely flat, or if one or both of the side ramps are not perfectly linear, then the trapezoidal distribution in question is a , and more complicated and context-dependent rules may apply. The side ramps of a trapezoidal distribution are not required to be symmetric in the general case, just as the sides of trapezoids in geometry are not required to be symmetric. The non-central moments of the trapezoidal distribution are Special cases of the trapezoidal distribution include the uniform distribution (with a = b and c = d) and the triangular distribution (with b = c). Trapezoidal probability distributions seem to not be discussed very often in the literature. The uniform, triangular, Irwin-Hall, Bates, Poisson, normal, bimodal, and multimodal distributions are all more frequently discussed in the literature. This may be because these other (non-trapezoidal) distributions seem to occur more frequently in nature than the trapezoidal distribution does. The normal distribution in particular is especially common in nature, just as one would expect from the central limit theorem. (en)
cdf image	300 (xsd:integer)
parameters	* - lower bound * - level start * - level end * - upper bound (en)
pdf image	300 (xsd:integer)
gold:hypernym	Distribution
prov:wasDerivedFrom	wikipedia-en:Trapezoidal_distribution?oldid=1093188246&ns=0
page length (characters) of wiki page	5636 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Trapezoidal_distribution
is Link from a Wikipage to another Wikipage of	List of probability distributions Bates distribution Triangular distribution Stochastic empirical loading and dilution model
is foaf:primaryTopic of	wikipedia-en:Trapezoidal_distribution

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