Fungsi sebaran kumulatif: Béda antarrépisi
Konten dihapus Konten ditambahkan
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
:<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'', ''b''<nowiki>]</nowiki>
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, '≤' 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.
== 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
===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
==Complementary cumulative distribution function==<!-- This section is linked from [[Power law]] -->
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==Inverse==
If the cdf ''F'' is strictly
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]
[[Kategori:Statistika]]
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