Probability distribution fitting: Difference between revisions

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''Skew distributions to the left''
 
When the smaller values tend to be farther away from the mean than the larger values, one has a skew distribution to the left (i.e. there is negative skewness), one may for example select the ''square-normal distribution'' (i.e. the normal distribution applied to the square of the data values), the inverted (mirrored) Gumbel distribution, the [[Dagum distribution]] (mirrorredmirrored Burr distribution), or the [[Gompertz distribution]], which is bounded to the left.
 
== Techniques of fitting ==
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*''Parametric methods'', by which the [[parameter]]s of the distribution are calculated from the data series.<ref>H. Cramér, "Mathematical methods of statistics" , Princeton Univ. Press (1946)</ref> The parametric methods are:
**[[method of moments (statistics)|method of moments]]
**[[Maximum spacing estimation|maximum spacing estimation]]
**method of [[L-moment]]s<ref>{{cite journal | last=Hosking | first=J.R.M. | year=1990 | title=L-moments: analysis and estimation of distributions using linear combinations of order statistics | journal=Journal of the Royal Statistical Society, Series B | volume=52 | pages=105–124 | jstor=2345653}}</ref>
**[[Maximum likelihood]] method<ref>{{cite journal | last = Aldrich | first = John | title = R. A. Fisher and the making of maximum likelihood 1912–1922 | year = 1997 | journal = Statistical Science | volume = 12 | issue = 3 | pages = 162–176 | doi = 10.1214/ss/1030037906 | mr = 1617519 | ref = citeref Aldrich1997}}</ref>
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[[File:GEVdistrHistogr+Density.png|thumb|220px|Histogram and probability density of a data set fitting the [[GEV distribution]] ]]
 
 
==Goodness of fit==
 
By ranking the [[goodness of fit]] of various distributions one can get an impression of which distribution is acceptable and which is not.
 
 
==Histogram and density function==
 
From the [[cumulative distribution function]] (CDF) one can derive a [[histogram]] and the [[probability density function]] (PDF).
 
 
== See also ==