Entry
Math: Probability: Distribution: Definition: What is definition of a statistical distribution?
Dec 28th, 2004 12:22
Knud van Eeden,
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--- Knud van Eeden --- 24 December 2004 - 07:24 pm -------------------
Math: Probability: Distribution: Definition: What is a definition of a
statistical distribution?
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Definition of a statistical distribution:
The 'distribution' of a variable is a description of the relative
number of times each possible outcome will occur in a number of trials.
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This function is usually defined in the form of a table
(which you then e.g. can show in a graph)
---------------------------------------------------..----------------
x1 | x2 | x3 | xN
---------------------------------------------------..----------------
frequency( x1 ) | frequency( x2 ) | frequency( x3 ) | frequency( xN )
---------------------------------------------------..----------------
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You further make sure that you standardize the frequency, by scaling
the results by dividing by the total of possible outcomes, or otherwise
the total area under the curve. So that you get a percentage between 0
and 1 and if you add them all together you get 1, in line with the
maximum value 1 for a probability.
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Further are negative y values not possible in the graph, because
a probability is per definition always between 0 and 1, and negative
probabilities, or thus negative y-values in the probability graph
are not possible so.
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This scaled function describing the 'distribution' is called the:
'probability function'
or also the
'probability density function'
or also the
'density function'
or also the
'probability distribution function'
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The function describing the probability that a given value or any value
smaller than it will occur is called the:
'distribution function'
or also the
'cumulative probability function'
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Book: see also:
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[book: Lipschutz, Seymour - Probability - McGraw-Hill (Schaum) - p.
75 'Random variables']
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[book: Spiegel, Murray R. - Probability and statistics - McGraw-Hill
(Schaum series) - p. 41 'Continuous probability functions']
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[book: Weisstein, Eric W. - CRC concise encyclopedia of mathematics -
ISBN 0-8493-9640-9 - p. 475 'Distribution']
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Internet: see also:
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Statistical Distributions: Continuous Distributions (81) / Discrete
Distributions (19) / General Distributions (14) / Limit Theorems (13)
http://mathworld.wolfram.com/topics/StatisticalDistributions.html
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Probability distributions
http://en.wikipedia.org/wiki/Category:Probability_distributions
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Math: Probability: Distribution: Link: Overview: Can you give an
overview of links?
http://www.faqts.com/knowledge_base/view.phtml/aid/32917/fid/815
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