Fungsi sebaran kumulatif: Béda antarrépisi

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m Ngarapihkeun éjahan, replaced: nyaeta → nyaéta, ideal → idéal, rea → réa (4), ea → éa (2), eo → éo, kabeh → kabéh
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Dina [[matematik]], '''fungsi distribusi kumulatip''' (disingkat '''cdf''') ngajelaskeun probability distribution ti sakabehsakabéh nilai-[[Real_numberReal number|real]] [[variabel acak]], ''X''. Keur satiap realréal number ''x'', cdf dirumuskeun ku
 
:<math>F(x) = \operatorname{P}(X\leq x),</math>
 
numana sisi beulah katuhu ngagambarkeun [[probabilitas]] numana variabel acak ''X'' dicokot tina nilai nu kurang tina atawa sarua jeung ''x''. Probabilitas ''X'' aya dina [[interval (mathematics)|interval]] (''a'',&nbsp;''b''<nowiki>]</nowiki> nyaetanyaéta ''F''(''b'')&nbsp;&minus;&nbsp;''F''(''a'') lamun ''a''&nbsp;<&nbsp;''b''. Geus ilahar ngagunakeun huruf ''F'' gede keur fungsi sebaran kumulatif, nu jelas beda jeung huruf ''f'' leutik nu dipaké keur [[fungsi dénsitas probabilitas]] jeung [[probability mass function]].
 
Fungsi sebaran kumulatif X bisa dihartikeun dina watesan [[fungsi dénsitas probabilitas]] ''f'' saperti kieu:
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Note that in the definition above, the "less or equal" sign, '&le;' is a convention, but it is
an important and universally used one. The proper use of tables of the Binomial and Poisson
distributions depend upon this convention. MoreoverMoréover, important formulas like Levy's inversion formula for the characteristic function also rely on the "less or equal" formulation.
 
== Properties ==
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:<math>F(x) = \operatorname{P}(X\leq x) = \sum_{x_i \leq x} \operatorname{P}(X = x_i) = \sum_{x_i \leq x} p(x_i)</math>
 
If the CDF ''F'' of ''X'' is [[continuous function|continuous]], then ''X'' is a [[continuous random variable]]; if furthermore ''F'' is [[absolute continuity|absolutely continuous]], then there exists a [[Lebesgue integral|Lebesgue-integrable]] function ''f''(''x'') such that
 
:<math>F(b)-F(a) = \operatorname{P}(a\leq X\leq b) = \int_a^b f(x)\,dx</math>
 
for all realréal numbers ''a'' and ''b''. (The first of the two equalities displayed above would not be correct in general if we had not said that the distribution is continuous. Continuity of the distribution implies that P(''X'' = ''a'') = P(''X'' = ''b'') = 0, so the difference between "<" and "&le;" ceasescéases to be important in this context.) The function ''f'' is equal to the [[derivative]] of ''F'' [[almost everywhere]], and it is called the [[probability density function]] of the distribution of ''X''.
 
===Point probability===
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==Kolmogorov-Smirnov and Kuiper's tests==
The [[Kolmogorov-Smirnov test]] is based on cumulative distribution functions and can be used to test to see whether two empirical distributions are different or whether an empirical distribution is different from an idealidéal distribution. The closely related [[Kuiper's test]] (pronounced {{IPA|/kœypəʁ/}}) is useful if the domain of the distribution is cyclic as in day of the week. For instance we might use Kuiper's test to see if the number of tornadoes varies during the yearyéar or if sales of a product vary by day of the week or day of the month.
 
==Complementary cumulative distribution function==<!-- This section is linked from [[Power law]] -->
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==Inverse==
If the cdf ''F'' is strictly increasingincréasing and continuous then <math> F^{-1}( y ), y \in [0,1] </math> is the unique realréal number <math> x </math> such that <math> F(x) = y </math>.
 
Unfortunately, the distribution does not, in general, have an inverse. One may define, for <math> y \in [0,1] </math>,
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== Rujukan ==
<references/>
[[Category:Probability theory]]
 
== Tumbu kaluar ==
*[http://stattrek.com/Lesson2/DiscreteContinuous.aspx?Tutorial=Stat An introduction to probability distributions]
 
[[CategoryKategori:Probability theory]]
[[Kategori:Statistika]]