open-index/open-wikipedia-markdown huggingface dataset:
Curve fitting

In the philosophy of science, and science generally, and in statistics, the **curve fitting problem** is how to choose among an infinite number of curves that fit the graphically-represented data points, normally by finding a mathmatical expresion to créate the curve.

The simplest curve is said to be preferable. This is thought to be related to Occam's Razor in so far as there is a preference for simplicity among a family of curves just as there is a preference of simplicity among competing théories.

Commonly used procedures are least squares fitting, linear regression, and nonlinéar regression.  One of the difficulties in curve fitting is to choose the functional form of the data for paraméter optimization.  Computers are often used to perform curve fitting procedures. Computers do this by solving a system of equations to find the paraméters of the function that minimize the squared error. The gradient descent algorithm is often used for this purpose.

## Rujukan 
Audi, R., Ed. (1996) The Cambridge Dictionary of Philosophy. Cambridge, Cambridge University Press. curve fitting problem p.&nbsp;172-173.

## Tumbu kaluar
*LAB Fit Curve Fitting Software 2D and 3D fitting with Finder
*Curve Expert (shareware)  fits functions to data (limited to one dependant and one independent variable.) 
*Online curve and surface fitting
*TableCurve2D and TableCurve3D by Systat automates curve fitting
Validasi-silang

Dina statistik, **validasi-silang** nyaéta prakték ngabagi  sample tina data kana *subsampel* saperti analisa mangrupa rarangkay mimiti dina *subsamel* tunggal, saterusna subsampel diingkeun sina "lolong" *("blind")* in order for subsequent use in confirming and validating the initial analysis.

Cross-validation is important in guarding against testing hypotheses suggested by the data, especially where further samples are hazardous, costly or impossible (uncomfortable science) to collect.
Matriks kovarians

Dina statistik, **covariance matrix** nyaruakeun konsép varian tina hiji ka *n* dimension, dina basa séjén, bentuk nilai-scalar random variable ka nilai-vector random variables (tuple tina variabel random skalar).  Lamun *X* mangrupa nilai-skalar variabel random nu mibanda nilai ekspektasi &mu; mangka variance-na nyaéta

:\sigma^2={\rm var}(X)=E((X-\mu)^2)

Lamun *X* nyaéta hiji *n*-ku-1 nilai-vektor kolon variabel random whose expected value is an *n*-by-1 column vector &mu; then its variance is the *n*-by-*n* nonnegative-definite matrix

:\Sigma={\rm var}(X)=E((X-\mu)(X-\mu)^\top)

The entries in this matrix are the covariances between the *n* different scalar components of *X*.  Since the covariance between a scalar-valued random variable and itself is its variance, it follows that, in particular, the entries on the diagonal of this matrix are the variances of the scalar components of *X*.  This may appéar to be a property of this matrix that depends on which coordinate system is chosen for the space in which the random vector *X* resides.  However, it is true generally that if *u* is any unit vector, then the variance of the projection of *X* on *u* is *u*T&Sigma;*u*.  (This point is expanded upon somewhat at http://www.wikipedia.org/wiki/Talk:Covariance_matrix.  It is a consequence of an identity that appéars below.)

Nomenclatures differ.  Some statisticians, following the probabilist William Feller, call this the **variance** of the random vector *X*, because it is the natural generalization to higher dimensions of the 1-dimensional variance.  Others call it the **covariance matrix**, because it is the matrix of covariances between the scalar components of the vector *X*.

With scalar-valued random variables *X*, we have the identity
:{\rm var}(aX)=a^2{\rm var}(X)
if *a* is constant, i.e., not random.  If *X* is an *n*-by-1 column vector-valued random variable and *A* is an *m*-by-*n* constant (i.e., non-random) matrix, then *AX* is an *m*-by-1 column vector-valued random variable, whose variance must therefore be an *m*-by-*m* matrix.  It is
:{\rm var}(AX)=A\Sigma A^\top

This covariance matrix (though very simple) is a very useful tool in many
very different aréas. From it a transformation matrix can be derived
that allows one to completely decorrelate
the data or, from a different point of view, to find an optimal basis
for representing the data in a compact way.
This is called **PCA** (principal components analysis) in statistics and **KL-Transform**  (Karhunen-Loéve transform) in image processing.
Rasio korelasi

Dina statistik, **rasio korelasi** nyaéta ukuran hubungan antara dispersi statistik dina kategori individu jeung dispersi lintasan tina sakabéh populasi atawa sampel.

Upamana unggal observasi nyaéta yxi nu mana x nembongkeun kategori nu di-observasi sarta xi nyaéta ngaran tina bagian observasi.  Urang bakal nuliskeun nx keur jumlah observasi dina kategori x (teu pati penting keur nilai nu béda tina x) sarta 
:\overline{y_x}=\frac{\sum_i y_{xi}}{n_x} and \overline{y}=\frac{\sum_x n_x \overline{y_x}}{\sum_x n_x}
maka rasio korelasi &eta; (eta) dihartikeun salaku 
:\eta^2 = \frac{\sum_x n_x (\overline{y_x}-\overline{y})^2}{\sum_{xi} (y_{xi}-\bar{y})^2} nu bisa ogé ditulis saperti \frac{\sigma_{\overline{y}}^2}{\sigma_{y}^2}.

Hal ieu mangrupa catetan penting lamun hubungan antara nilai x \;\  jeung nilai \overline{y_x} linier (nu salawasna bener lamun ngan dua kamungkinan keur x) hal ieu bakal méré  hasil nu sarua saperti koefisien korelasi; maka lamun taya rasio korelasi bakal leuwih gedé dina besaran, sanajan angger teu leuwih ti 1 dina éta besaran. Hal ieu bisa dipaké keur mutuskeun hubungan non-linier.
Model

**modél** istilah nu biasa dipaké dina sababaraha widang:
* Dina élmu jeung téhnologi, **modél** hartina abstrak atawa téori nu ngagambarkeun hiji fénoména atawa kajadian; tempo modél. Keur modél dina kajadian husus, tempo **modél (ékonomi)**, **modél (makroékonomi)**, **modél statistik** jeung **modél matematika**.
* Dina Neuro-linguistic programming (NLP) modélling refers to the systematic unpacking and sequencing of the conscious and unconscious processes - see Modeling (NLP).
* In science, technology, and leisure for **modéls** as physical representations see model.
* For **modéls** in society, art, fashion, and cosmetics, see role model, model or supermodel.
* In world politics, **modél** refers to the *Movement for Democracy in Liberia* organization.
* In video games or computer modélling, a model is a fully-3D, polygonal object or character.
* In automobiles, a **modél** is a type of vehicle sold under a marque
Statistika bisbol

Bagéan nu katempo dina kaulinan baseball nyaéta ngumpulkeun statistik terus-terusan keur nangtukeun kasuksesan pamaen.  Dimimitian ku Henry Chadwick dina 19th century nu ngarancang konsép batting average dumasar kana panglaman dina cricket. Loba watesan nu dipaké keur kaulinan softball. Umumna abbreviation statistik nu dipaké dijelaskeun di handap ieu:

## Hitting statistics
* 1B - Single
* 2B - Double
* 3B - Triple
* AB - At bat
* BA - Batting average
* BB - Base on balls (also called a "walk")
* CS - Caught stealing
* EBH - Extra base hit  (Sometimes EB or XBH)
* FC - Fielder's choice
* G - Games played
* G/F - Ground ball fly ball ratio
* GIDP - Ground into Double play
* H - Hit
* HBP - Hit by pitch
* HR - Home run
* OBP - On base percentage
* OPS - On-base plus slugging
* PA - Plate appearance
* R - Run
* RBI - Run batted in
* SB - Stolen base
* SF - Sacrifice fly
* SH - Sacrifice hit
* SLG - Slugging percentage
* SO - Strike out (also abbreviated *K*)
* TB - Total bases

## Pitching statistics
* AVG - Opponents batting average
* BB - Base on balls (also called a "walk")
* BS - Blown save
* CG - Complete game
* ER - Earned run
* éra - Earned run average
* GIR - Games in relief
* GF - Games finished
* GP - Games pitched
* G/F - Ground ball fly ball ratio
* GS - Games started
* H/9 - Hits per nine innings
* HLD - Hold
* IBB - Intentional base on balls
* IRA - Inherited runs allowed
* IP - Innings pitched
* R/9 - Runs per nine innings
* SHO - Shutout
* SO - Strikeout (also abbreviated *K*)
* SO/9 - Strikeouts per nine innings
* SV - Save
* TBF - Total batters faced
* W - Win (also related: **winning percentage**)
* L - Loss
* W+S - Relief wins plus saves
* WHIP - Walks plus hits per inning pitched

## Fielding statistics
* A - Assist
* DP - Double play
* E - Error
* FP - Fielding percentage
* PB - Passed ball
* PO - Putout
* TC - Total chances
* TP - Triple play
* WP - Wild pitch

## Tempo oge
* Triple Crown in Major League Baseball
* MLB Most Valuable Player Award winners
* Cy Young Award winners
* MLB Rookie of the Year Award winners
* Gold Glove Award winners

## Watesan séjén
* Ball
* Strike
* Strike zone

## Rujukan
*sabermetrics
*Official Baseball Rules, Section 10 - Scoring  from http://www.mlb.com
*Find statistics for all of major léague history at http://www.Baseball-Reference.com/
Élmu bahan

**Élmu bahan** ngawengku bagian-bagian ti kimia, fisika, géologi, ogé biologi nu patali jeung sipat-sipat fisik, kimiawi, atawa biologis rupa-rupa bahan/matéri. Élmu ieu biasana dianggap salaku élmu terapan, sabab sipat-sipat nu diulik biasana dipatalikeun jeung tujuan industrial.

Élmu bahan ngawengku sakabéh opat kelas bahan nu masing-masing boga widang ulikanana séwang-séwangan: (1) logam jeung métalurgi, (2) keramika, semikonduktor, jeung bahan éléktronik lianna, (3) polimér, (4) komposit jeung biomaterial nu bisa asup kana kelas bahan 1 n.k. 4 tadi. Métalurgi jeung keramika mibanda sajarah nu panjang salaku disiplin rékayasa/téhnik, tapi ku sabab élmu nu jadi tatapakan disiplin ieu larap ka sakabéh kelas bahan, mangka élmu bahan dianggap salaku disiplin anu misah.

Élmu bahan aya patalina jeung rékayasa bahan, nu condong museur kana téhnik ngolah (casting, rolling, welding, cangkok ion, kamekaran kristal, thin-film deposition, sintering, glassblowing, jsb.), téhnik analitis (mikroskop éléktron, difraksi sinar-X, kalorimétri, mikroskopi inti (HEFIB) jsb.), rancang bahan, sarta untung/rugina dina produksi industrial.

## Sub-widang élmu bahan 
* Nanotéhnologi --- ngulik jeung nyipta bahan hasil rékayasa molekular (nanomaterial) nu strukturna dina ukuran nanométer.
* Kristalografi --- ngulik fisika kristal, kaasup
** defects in crystals, such as grain boundaries and dislocations, and their effects on physical properties;
** téhnik difraksi, pikeun idéntifikasi fase.
* Métalurgi --- ngulik logam
* Keramik
* Biomaterial
* Kimia bahan padet --- ngulik kimia nu lumangsung dina bahan padet
* Fisika bahan padet --- biasana dianggap ulikan pangaruh kuantum na bahan padet, kayaning semikonduksi atawa superkonduksi.
* Mékanika continuum --- ngulik padetan jeung cairan, kalawan asumsi yén éta bahan kaasup bahan kontinyu.

## Jejer nu patali dina fisika 
* Térmodinamik, pikeun stabilitas, transformasi, jeung diagram fase.
* Kinetik, dilarapkeun kana laju transformasi jeung difusi.

## Tempo ogé 
* Kala téhnologi bahan
* Kristal cair
Variabel random diskrit

Dina matematik, variabel random mangrupa **diskrit** lamun éta probability distribution ogé disckrit; **sebaran probibiliti diskrit** lamun satemenna dikarakterisasi ku probability mass function. Mangka *X* variabel random diskrit lamun

:\sum_u P(X=u) = 1

salaku *u* ngaliwatan susunan tina sakabéh nilai mungkin variabel random *X*.

Poisson distribution, Bernoulli distribution, sebaran binomial, geometric distribution, sarta negative binomial distribution dipikanyaho salaku sebaran probabiliti diskrit.

Lamun variabel random variable mangrupa diskrit mangka set sakabéh nilai mungkin bisa dianggap finite sarta countably infinite, sabab jumlah nu teu bisa diitung unggal positive real number positip (nagrupakeun wates handap pangleutikna tina sakabéh susunan jumlah parsial) salawasna kasebar nuju takhingga.
Fungsi Heaviside step

The Heaviside step function

**Fungsi Héaviside step**, ngaran nu dipaké keur ngahargaan ka Oliver Heaviside, nyaéta a fungsi diskontinyu nu mana nileyna nyaéta nol keur asupan negatip sarta hiji keur nu séjénna:
:H(x)=\left\{\begin{matrix} 0 : x 

The function is used in the mathematics of signal processing to represent a signal that switches on at a specified time and stays switched on indefinitely. Its derivative is formally the Dirac delta function.

It is the cumulative distribution function of a variabel acak which is almost surely 0. (See constant random variable.)

The Héaviside function is the integral of the Dirac delta function. The value of H(0) is of very little importance, since the function is often used within an integral. Some writers give H(0) = 0, some H(0) = 1. H(0) = 0.5 is often used, since it maximizes the symmetry of the function. This makés the definition:

:H(x)=\left\{\begin{matrix} 0 : x  0 \end{matrix}\right. 

This is sometimes notated by a subscript, as in H0.5(x), which méans that H(0) = 0.5. This notation is also used to represent a completely different concept, however; an x offset:

:H_c(x) = H(x - c)\,\!

where *c* is a positive offset in the *x*-dimension of the transition from 0 to 1. In other words, *H*3(*x*) = *H*(*x* − 3) would be zero until *x* = 3, and would transition to 1 for *x* > 3. The méaning of the subscript should be given in context.

The question of the Fourier transform of H is an interesting example for the théory of distributions. It is often stated that it is 1/x, up to a normalizing constant. But néar x=0 that cannot be justified: the definition must be given in terms of *principal value* limit, and the transform isn't to be tréated simply as a function. The corresponding convolution operator is the *Hilbert transform*.

Often an integral representation of the step function is useful,
:H(x)=-{1\over 2i\pi}\int_{-\infty}^\infty {d\tau \over \tau+i\epsilon} 
e^{-i\tau x},
in the limit \epsilon\to 0.

## Related topics 
* Step response
* Negative and non-negative numbers
Variabel acak kontinyu

Dumasar kasapukan, variabel acak *X* disebut **kontinyu** mun fungsi sebaran kumulatifna kontinyu. That is equivalent to saying that Pr[*X* = *a*] = 0 for all real numbers *a*, i.e.: the probability that *X* attains the value *a* is zero, for any number *a*.

While for a discrete random variable one could say that an event with probability zero is impossible, this can not be said in the case of a continuous random variable, because then no value would be possible.

This paradox is solved by réalizing that the probability that *X* attains a value in an uncountable set (for example an interval) can not be found by adding the probabilities for individual values.

By another convention, the term "continuous random variable" is reserved for random variables that have probability density functions. A random variable with the Cantor distribution is continuous according to the first convention, and according to the second, is neither continuous nor discrete nor a weighted average of continuous and discrete random variables.

In practical applications random variables are often either discrete or continuous.
Inverse transform sampling method

The **inverse transform sampling method** is a method of sampling a number at
random from any probability distribution, given its cumulative distribution function (cdf).

The problem that the inverse transform sampling method solves is as follows:

*Anggap X bakal jadi variabel acak nu mana sebaranna bisa dijelaskeun ku cdf d(*x*).
*We want to generate values of *x* which are distributed according to this distribution.

Many programming languages have the ability to generate pseudo-randomnumbers which are effectively distributed according to the standard sebaran seragam. If a random variable has that distribution, then the probability of its falling within any subinterval (*a*, *b*) of the interval from 0 to 1 is just the length *b* - *a* of that subinterval.

The inverse transform sampling method works as follows:
#Generate a random number from the standard uniform distribution; call this *u*.
#Compute the value for *x* which has the associated cdf value *u*; call this *x**chosen*.
#Take *x**chosen* to be the random number drawn from the distribution described by d(*x*).

The following diagram may help the réader to visualise how the method works:

**Sampling using the inverse transform method**

### Tempo ogé 
The rejection sampling method.
Ajén-P

Dina statistik, **nilai-p** tina variabel random T nyaéta probabilitas Pr(T ≤ tobserved) nu mana T bakal dianggap leuwih gedé atawa sarua jeung nilai observasi tobserved, dina kayaan null hypothesis dianggap bener.

Dina basa séjén, anggapan yén null hypothesis sederhana ditolak lamun tes statistic *T* leuwih gedé tinimbang nilai kritis *c*. Kira-kira dina sabagéan kasus T nu di-observasi sarua jeung tobserved. Mangka nilai-p tina T dina éta kasus probabiliti yén T bakal sarua atawa leuwih ti tobserved.

## Sumber Rujukan 
* Sellke, T., M.J. Bayarri, & J. Berger. 2001. Calibration of P-values for Testing Precise Null Hypotheses. *Am. Statistician* 55: 62-71.
Harold Jeffreys

*Sir* **Harold Jeffreys** (22 April 1891 - 18 March 1989) nyaéta saurang ahli matématika, statistika, géofisika sarta astronomi.

Anjeunna dibabarkeun Fatfield, County Durham, diajar di Armstrong College di Newcastle-upon-Tyne, bihari mangrupa bagéan ti University of Durham anu saterusna jadi University of Newcastle. Tamat ti dinya indit ka St. John's College, Cambridge sarta jadi pangajar dina taun 1914. Di Cambridge University anjeunna ngawulang matematik, saterusna geofisika sarta ahirna jadi *Plumian Professor of Astronomy*.

Anjeunna nikah jeung ahli matématika sarta fisika, Bertha Swirles (1903-1999), dina taun 1940 sarta babarengan nulis *"Methods of Mathematical Physics"*.

Salah sahiji kontribusina nyaéta sistem Bayesian pikeun ngadeukeutan probabilitas, sarta idena yén inti planét bumi mangrupa cairan. Anjeunna sinatria dina 1953. 

## Rujukan 
* Maria Carla Galavotti. "Harold Jeffreys' Probabilistic Epistemology: Between Logicism And Subjectivism". *British Journal for the Philosophy of Science*, 54(1):43-57 (March 2003). ''(A review of Jeffreys' approach to probability; includes remarks on R.A. Fisher, Frank P. Ramsey, and Bruno de Finetti. Also online: http://www3.oup.co.uk/phisci/hdb/Volume_54/Issue_01/default.html )''

## Tumbu kaluar
* Biografi MacTutor
* Biografi Para Pinunjul Hadiah Vetlesen - Sir Harold Jeffreys 
* Harold Jeffreys salaku Ahli Statistik
Sebaran frekuensi

Dina statistik, **sebaran frékuénsi** nyaéta daptar nilai variabel nu dicokot tina sampel. Daptar ieu ilaharna disusun dumasar kana kuantitas, nembongkeun jumlah waktu unggal nilai nu ngadeukeutan. Conto, lamun 100 urang dibagi kana lima bagéan sikep nilai sarta milih dina skala 1 nu nunjukkeun satuju kacida sarta 5 teu satuju kacida, sebaran frékuénsi bisa jadi saperti di handap ieu:

Tes hipotesa statistik nu kapanggih dina taksiran nilai nu béda sarta sarua antara distribusi frékuénsi. Taksiran ieu kaasup ukuran kacenderungan ka tengah atawa rata-rata, saperti mean jeung median, sarta ukuran variabiliti atawa dispersi statistik, saperti simpangan baku atawa varian.

Sebaran frékuénsi disebut mencong lamun nilai méan jeung median boga nilai nu béda. Kurtosis tina sebaran frékuénsi nyaéta ngumpulna skor dina méan, atawa nembongkeun posisi puncak sebaran sacara grafis&mdash;contona dina histogram. Lamun sebaran puncak sebaran leuwih ti sebaran normal disebut leptokurtic; lamun kurang disebutna platykurtic.
Momen (matematika)

:*Baca ogé momen (fisika).*

Konsép **momen** dina matematika diwangun tina konsép momen dina fisika.  Momen ka-*n* tina fungsi nilai-riil *f*(*x*) tina variabel riil nyaéta

:\mu'_n=\int_{-\infty}^\infty x^n\,f(x)\,dx.

**Masalah momen** nyiar karakterisasi runtuyan { &mu;&prime;*n* : *n* = 1, 2, 3, ... } nu mangrupa runtuyan momen sababaraha fungsi *f*.

Mun (aksara leutik) *f* mangrupa fungsi dénsitas probabilitas, mangka nilai integral di luhur disebut momen anu ka-*n* tina momen probability distribution.  Sacara umum, lamun (hurup gedé) *F* nyaéta fungsi distribusi kumulatip keur unggal distribusi probabiliti, nu teu mibanda fungsi density, mangka momen ka-*n* disitribusi probabiliti  ngagunakeun Riemann-Stieltjes integral

:E(X^n)=\int_{-\infty}^\infty x^n\,dF(x),

di mana *X* nyaéta variabel random nu mibanda sebaran ieu.

Momen tengah ka***n*** distribusi probabiliti variabel random *X* nyaéta

:\mu_n=E((X-\mu_1')^n).

Central momen kadua nyaéta varian.

The central momemts are cléarly translation-invariant, i.e., the *n*th central moment of *X* is the same as that of *X* + *c* for any constant *c* (in this context "constant" méans a *non-random* quantity).

The first moment and the second and third *central* moments are linéar in the sense that

:\mu_1(X+Y)=\mu_1(X)+\mu_1(Y)

and

:\operatorname{var}(X+Y)=\operatorname{var}(X)+\operatorname{var}(Y)

and

:\mu_3(X+Y)=\mu_3(X)+\mu_3(Y)

if *X* and *Y* are independent random variables (independence is not needed for the first of these three identities; for the second it can be wéakened to uncorrelatedness).

The central moments beyond the third lack this linéarity; in that respect they differ from the cumulants (the first three cumulants are the same as the first moment and the second and third *central* moments; the higher cumulants have a more complicated relationship with the central moments).

Like the cumulants, the factorial moments of a probability distribution are also polynomial functions of the moments.
Fungsi nu ngahasilkeun momen

Dina téori probabilitas jeung statistika, **fungsi nu ngahasilkeun momen** tina variabel acak *X* nyaéta
:M_X(t)=E\left(e^{tX}\right).
Fungsi ieu ngahasilkeun momen tina sebaran probabilitas:

:E\left(X^n\right)=M_X^{(n)}(0)=\left.\frac{\mathrm{d}^n}{\mathrm{d}t^n}\right|_{t=0} M_X(t).

Lamun *X* mibanda fungsi dénsitas probabilitas kontinyu *f*(*x*) mangka fungsi nu ngahasilkeun momen dibérékeun ku

:M_X(t) = \int_{-\infty}^\infty e^{tx} f(x)\,\mathrm{d}x
::: = \int_{-\infty}^\infty \left( 1+ tx + \frac{t^2x^2}{2!} + \cdots\right) f(x)\,\mathrm{d}x
::: = 1 + tm_1 + \frac{t^2m_2}{2!} +\cdots,

di mana m_i mangrupa momen ka-*i*.

Leupas tina sebaran probabilitas kontinyu atawa heunteuna, fungsi nu ngahasilkeun momen dibérékeun ku integral Riemann-Stieltjes

:\int_{-\infty}^\infty e^{tx}\,dF(x)

di mana *F* nyaéta fungsi sebaran kumulatif.

Konsép nu pakait kaasup fungsi karakteristik, fungsi nu ngahasilkeun probabilitas, jeung fungsi nu ngahasilkeun kumulan. Fungsi nu ngahasilkeun kumulan téh bentuk logaritma tina fungsi nu ngahasilkeun momen.
Téoréma De Finetti

Dina téori probabilitas, **téoréma de Finetti** nerangkeun kunaon observasi *bisa digantikeun* mangrupa *kondisional* bébas tina sababaraha (umumna) kuantitas teu ka-observasi nu mana epistemic probability sebaran bakal ditangtukeun.  Ieu ngaran keur ngahargaan ka Bruno de Finetti.
Régrési Deming

**Régrési Deming** nyaéta métodeu  linear regression nu nangtukeun garis panghadéna keur susunan data nu pakait. Régrési ieu béda jeung régrési liniér dina ngitung kasalahan boh dina sumbu-'x' jeung sumbu-'y'.

Keur conto, lamun data dina sumbu-x dipikanyaho henteu mibanda kasalahan, tapi dina sumbu-y mibanda kasalahan, (saperti dina estimasi populasi (y), dina waktu nu dipikanyaho (x)), mangka bisa maké régrési liniér sederhana.

Lamun duanana susunan data mibanda kasalahan, conto hubungan antara konsentrasi dua material dina getih, régrési Deming méré  hasil nu leuwih hadé.

Hal anu teu nguntungkeun dina régrési Deming nyaéta sacara matematis leuwih kompleks waktu dipaké ngitung. Ieu hartina dina ngalakukeun itungan, dina tulisan séjén, atawa dina nulis rumus keur spreadsheet, leuwih hese.
Statistika démografi

Di antara data-data nu perlu dipimilik ku pamingpin nasional nyaéta **statistika démografi** populasina. Catetan kalahiran, kapapaténan, kawin, imigrasi jeung émigrasi, sarta sénsus régulér populasina bisa nyadiakeun informasi nu jadi konci dina nyieun kaputusan ngeunaan kawijakan nasional.

Ringkesan data nu mangpaat pisan di antarana piramida populasi, nu nyadiakeun data ngeunaan sebaran kelamin jeung umur populasi dina wanda grafik nu basajan.

Ringkesan séjénna disebut tabel kahirupan. Tina *cohort* jalma-jalma nu lahir dina taun nu sarua, urang bisa nyusud sarta ngagambarkeun pangalaman hirup ti lahir nepi ka pupusna. For a given cohort, the proportion expected to survive éach yéar (or decade in an *abridged life table*) is presented in tabular or graphical form.

Nisbah lalaki jeung awéwé dumasar umur nunjukkeun balukar tina béda laju mortalitasna.

## Sumber rujukan
* Demographic statistics, ti Wikipédia basa Inggris, disalin ping 3 Séptémber 2004.

## Tumbu kaluar
* Keur conto, tempo laporan statistik dina  Malta 
* Population pyramid
* Life Table
Éstimasi dénsitas

Dina probabilitas jeung statistika,
**éstimasi dénsitas** hartina konstruksi tina éstimasi dumasar kana data observasi, nu teu kaobservasi dina kaayaan fungsi probabilitas dénsitas. Fungsi dénsitas nu teu kaobservasi dianggap salaku dénsitas dina sebaran populasi nu gedé; data umumna dianggap salaku sampel acak tina populasi.
jmpl|Éstimasi dénsitas
Aya sababaraha cara nu bisa dipaké keur ngitung éstimasi dénsitas, kaasup jandéla Parzen sarta téhnik rentang data clustering.

Ieu mangrupa gambaran éstimasi dénsitas.

## Rujukan 
* Trevor Hastie, Robert Tibshirani, and Jerome Friedman. *The Elements of Statistical Learning*. New York: Springer, 2001. ISBN 0-387-95284-5. *(See Chapter 6.)*
* D.W. Scott. *Multivariate Density Estimation. Theory, Practice and Visualization*. New York: Wiley, 1992.
* B.W. Silverman. *Density Estimation*. London: Chapman and Hall, 1986.
Dutch book

Dina judi **Dutch book** atawa **lock** nyaéta susunan ganjil sartataruhan nu pasti meunang, teu pakait jeung hasil tina judi.  Kaayaan ieu pakait jeung kamungkinan ku ayana kaahengan nu teu asup akal.

One example is where a bookmaker has offered odds and attracted bets which makes the result irrelevant; in this case the implied probabilities will add up to a number gréater than 1.

In this case, whichever horse wins, the bookmaker will pay out 200 (including returning the winning stake) and so maké a profit of 10.

If for some réason Horse 4 was withdrawn and the bookmaker was foolish enough not to adjust the other odds, the implied probabilities would add up to 0.95 and a gambler could lock in a profit of 10, by betting 100, 50 and 40 on the remaining three horses respectively.

Other forms of Dutch books can exist when incoherent odds are offered on exotic bets such as forecasting the order in which horses will finish.  With competitive fixed-odds gambling being offered electronically, gamblers can sometimes créate a Dutch book by selecting the best odds from different bookmakers, in effect by undertaking an arbitrage operation. The bookmakers should réact by adjusting the offered odds in the light of demand, so as to remove the potential profit.

In Bayesian probability, Frank Ramsey and Bruno de Finetti required personal degrees of belief to be coherent so that a Dutch book could not be made against them, whichever way bets were made; in other words their degrees of belief had to satisfy the axioms of probability.
Persamaan paramétrik

Dina matématik, **persamaan paramétrik** nyaéta hubungan éksplisit dua atawa leuwih variabel dina watesan hiji atawa leuwih paraméter bébas. Sacara abstraks, rélasi (hubungan) dijelaskeun dina wangun equation (persamaan), jeung nembongkeun ogé bayangan bentuk fungsi, sebutkeun, *R**n*. Sanajan kitu aya sababaraha hal anu leuwih akurat keur dihartikeun salaku *representasi parametrik*. Tempo ogé parameter, parametrization, regular parametric representation.

Contona, persamaan parabola sederhana,

:y=x^2,

bisa di-paraméterisasi ku ngagunakeun paraméter bébas t, sarta disusun di bentuk

:x=t,y=t^2.

Sanajan dina conto saméméhna ampir ngadeukeutan hal *trivial*, paraméter di handap ieu milu kana circle radius a:

:x\equiv a\cos t,y\equiv a\sin t.

Ahirna, bentuk géometri penting nu ampir teu mungkin keur ngajelaskeun persamaan tunggal tapi mibanda gambaran nu hadé dina bentuk persamaan parametrik :

:x\equiv a\cos t

:y\equiv a\sin t

:z\equiv bt

nu mana ngajelaskeun kurva tilu-dimensi, helix, nu mibanda radius *a* sarta ningkat ku 2 \pi b satuan per turn. (Catetan yén persamaan identik dina plane keur circle; kanyataanna, helix ngan sakadar 'a circle whose ends don't have the same *z*-value'.

Sababaraha gambaran di luhur umumna ditulis salaku

:r(t)\equiv(x(t),y(t),z(t))=(a\cos t,a\sin t, bt)

Cara ieu keu ngagambarkeun kurva sacara praktis tur efisien; contono, bisa integrate jeung differentiate saperti watesan kurva. Saterusna, bisa dijelaskeun velocity partikel nuturkeun pola paraméter di handap ieu:

:v(t)\equiv r'(t)=(x'(t),y'(t),z'(t))=(-a\sin t,a\cos t, b)

sarta acceleration nyaéta:

:a(t)\equiv r*(t)=(x*(t),y*(t),z*(t))=(-a\cos t,-a\sin t, 0)

Sacara umum, kurva parametrik ngaruppakeun fungsi hiji paraméter bébas (umumnya dilambangkeun ku t). Paraméterisasi permukaan, leuwih ilahar digunakeun saperti dina aplikasi vector calculus saperti Stokes' theorem, mangrupa pungsi 2 paraméter, leuwih ilahar (s,t) or (u,v).

Conto paraméter permukaan nyaéta (capless) cylinder dibérékeun ku

:r(u,v)\equiv(x(u,v),y(u,v),z(u,v))=(a\cos u,a\sin u, v)

Kanyataan yén gambaran silinder ieu mangrupa kajadian waktu hiji persamaan nu ditempo ngagambarkeun lingkatan dina bidang, nu diijinkeun keur dicokot tina  nilai *z*.
Kasalahan ekologis

**Kasalahan ékologis** nyaéta kasalahan nu remen kajadian dina interpretasi data statistik, lantaran kacindekan ngeunaan kaayaan individu dumasar kana kumpulan komponén statistik tina grup tempat ayana individu éta.

**Conto:** Betty meunang peunteun 'A' di sakolana. Di sakola Simon peunteun rata-rata matematikana 'B'. Kasalahan ekologis pikeun ngajadi lamun urang nyimpulkeun atawa nyindekkeun yén Betty leuwih pinter matematika tinimbang Simon. Kasimpulan anu teu tangtu bener.

Tempo ogé prosecutor's fallacy.
Analisa conjoint

**Analisa conjoint**, disebut modél komposisi multi-attribute, nyaéta téhnik statistik nu aslina tina mathematical psychology. Ayeuna dipaké di loba widang social science jeung applied science kaasup marketing, product management, jeung operations research.

*Tempo oge*: Conjoint analysis (in marketing)
Errors and residuals in statistics

Dina statistik, konsep **kasalahan** jeung **sesa** gampang silih bingungkeun.

***Kasalahan*** nyaéta hal nu salah; **kasalahan** nyaéta loba beda nu kapanggih tina nilai ekspektasi; saterusna bakal dumasar kana sakabéh populasi tina satuan statistik nu dipilih sacara acak. Nilai ekspektasi, nilai rata-rata tina populasi nu ditempo, sacara tipikil teu katempo. Lamun rata-rata jangkung lalaki nu umurna 21 taun nyaéta 5 kaki 9 inci, sarta kapilih sacara acak lalaki nu jangkungna 5 kaki 11 inci, mangka "kasalahan" nyaéta 2 inci; lamun sacara acak kapilih lalaki nu jangkungna 5 kaki 7 inci, mangka "kasalahan" nyaéta &minus;2 inci.  Istilah ieu diwangun tina ukuran kasalahan acak dina astronomi. Saperti dina ukuran jangkung lalaki tadi nu mana diukur tina rata-rata populasi, mangka beda antara jangkung lalaki jeung ukuran rata-rata mangrupa ukuran kasalahan.

**Sesa** nyaéta *estimasi* nu katempo tina kasalahan nu teu katempo. Pasualan nu gampang dina sampel acak jangkung lalaki *n*  nyaéta ukuranna. Rata-rata *sampel* dipaké keur ngira-ngira rata-rata *populasi*. Mangka:

*Beda antara unggal jangkung lalaki jeung rata-rata *populasi* nu teu katempo disebut *kasalahan*, sarta
*Beda antara jangkung lalaki jeung rata-rata *sampel* disebut *sesa*.

:***Sesa bisa katempo; kasalahan henteu***.

Catetan: jumlah sesa sarua jeung nol, mangka sesa *henteu mandiri*.  Jumlah kasalahan teu sarua jeung nol; kasalahan mangrupa variabel acak mandiri lamun dicokot tina populasi nu mandiri.

:'''*Kasalahan ilaharna masing-masing mandiri; sesa ilaharna *henteu* mandiri tinu sejen.*'*

## Conto
Lamun urang nganggap populasi nu kasebar normal mibanda méan &mu; sarta simpangan baku &sigma;, sarta individu nu dipilih bébas, mangka

:X_1, \dots, X_n\sim N(\mu,\sigma^2)

sarta sampel méan mangrupa sebaran variabel random:

:\overline{X}\sim N(\mu, \sigma^2/n).

Mangka *kasalahan* nyaéta

:\varepsilon_i=X_i-\mu,

sedengkeun *sesa* nyaéta

:\widehat{\varepsilon}_i=X_i-\overline{X}.

(Saperti nu ilahar dipaké, tanda "topi" di handapeun aksara &epsilon; nunjukkeun *estimasi* observasi tina kuantitas nu teu kaobservasi disebut &epsilon;.)

Jumlah kuadrat **kasalahan**, dibagi ku &sigma;2, mibanda sebaran chi-kuadrat mibanda *n* tingkat kebébasan:

:\sum_{i=1}^n \left(X_i-\mu\right)^2/\sigma^2\sim\chi^2_n.

Nilai ieu teu bisa kapanggih, sedengkeun kuadrat jumlah **sesa**, bisa kapanggih. Bagi ieu jumlah ku &sigma;2 nu mibanda sebaran chi-kuadrat ngan ku *n'' &minus; 1 tingkat kabébasan:

:\sum_{i=1}^n \left(\,X_i-\overline{X}\,\right)^2/\sigma^2\sim\chi^2_{n-1}.

Hal ieu bisa ditandaan yén variabel acak jeung sampel méan nembongkeun kamandirian sewang-sewangan. Ieu kanyataan sebaran normal jeung chi-kuadrat nembongkeun yén itungan bentuk dasar di luhur dumasar kana interval kapercayaan dina sebaran-t student.  Batalna &sigma; tina nu ngabagi jeung nu dibagi dina éta itungan nembongkeun yén aya kateujelasan nu nyababkeun ayana anggapan yén &sigma;2 teu méré  pangaruh nanaon.

## Tempo ogé
Studentized residual
Expectation-maximization algorithm

## Rujukan 
* Arthur Dempster, Nan Laird, and Donald Rubin. "Maximum likelihood from incomplete data via the EM algorithm". *Journal of the Royal Statistical Society*, Series B, 39(1):1–38, 1977.
* Radford Néal, Géoffrey Hinton. "A view of the EM algorithm that justifies incremental, sparse, and other variants". In Michael I. Jordan (editor), *Learning in Graphical Models* pp 355–368. Cambridge, MA: MIT Press, 1999.
Modél grafik

Dina tiori probabiliti sarta statistik, **modél grapik (GM)** ngagambarkeun kabebasan antara variabel random maké grafik nu mana unggal variabel random mangrupa hiji titik.

Dina kasus sederhana, stuktur jaringan modél nyaéta *directed acyclic graph* (DAG).  Mangka GM ngagambarkeun faktorisasi gabungan probabiliti sakabéh variabel random.  Leuwih pastina, lamun kajadian

:*X*1, ..., *X**n*,

mangka gabungan probabiliti

:*P*(*X*1, ..., *X**n*),

sarua jeung hasil kondisional probabiliti

:P(*Xi* | parents of *Xi*) for *i* = 1,...,*n*.

Dina basa séjén, faktor sebaran gabungan kana hasil kali sebaran kondisional.  Struktur grafik nunjukkeun kabébasan langsung antara variabel.  Unggal dua titik nu pakait henteu nurun/naek mangrupa kondisional bebas nu méré keun nilai keur indungna.
Kuadrat Graeco-Latin

**Kuadrat Graeco-Latin** *n*&times;*n* nyaéta tabel nu unggal sel-na mibanda pasangan simbol, susunan simbol tina unggal dua set unsur *n*. éach pair occurs exactly once in the table. éach symbol in the two, not necessarily distinct, sets occurs exactly once in éach row and exactly once in éach column. Kuadrat Graeco-Latin dipaké dina desain percobaan.

A 4&times;4 Graeco-Latin square on the sets {*A*, *B*, *C*, *D*} and {α, β, γ, δ} is:

The tabular arrangements of {*A*, *B*, *C*, *D*} (Latin characters) alone and {α, β, γ, δ} (Greek characters) alone éach forms a Latin square. éach pair from the two sets (i.e. every element of their cartesian product) occurs exactly once and we say that the two Latin squares are *orthogonal*.

## History
In the 1780s, Leonard Euler  demonstrated methods for constructing Graeco-Latin squares where *n* is odd or a multiple of 4. He further proved that no 2&times;2 square exists and conjectured that none existed for *n*=4*k*+2, where *k* is a natural number.

In 1901, Gaston Tarry demonstrated that there was no 6&times;6 square by enumerating all the possible arrangements of symbols. However, in 1959, Parker, Bose and Shrikhande constructed a 10&times;10 square.

In 1978, the French writer Georges Perec used the 10&times;10 square (believed then to be the only one possible) for the structure of constraints underlying his novel Life: A User's Manual.

## Tempo ogé
* Latin square
Rasio bencana

**Rasio bencana** dina analisa survival nyaéta kasimpulan tina beda antara dua kurva survival, ngagambarkeun nguranganna resiko kematian dina babandingan kontrol pencegahan, salila waktu nu diperhatikeun. Ieu mangrupa bentuk resiko relatip. modél proporsi regresi bencana (oge disebut modél regeresi Cox) nganggep yén resiko relatip kematian antara pencegahan jeung kontrol mangrupa hal nu angger dina interval waktu. modél ieu dipaké salaku algoritma komputer keur nyimpulkeun risiko kematian relatip kana interval waktu dina hiji gambar.

O(treatment) /E(treatment)  \over O(controls) /E(controls) 

nu mana O nyaéta jumlah observasi kematian dina grup husus, sarta E jumlah ekspektasi kematian, dumasar kana ieu kaayaan, tapi teu nyokot itungan tina unggal ekspektasi pencegahan.

## Tumbu kaluar
* http://www.graphpad.com/www/book/compsurv.htm 

## Rujukan
* Altman, DG.  Practical Statistics for Medical Reséarch. Chapman & Hall. London, 1991.  ISBN 0412276305.  pp383–4.
Kurva Hubbert

**Kurva Hubbert**, ngaran nu dipaké keur ngahargaan ka géofisikis M. King Hubbert, mangrupa derivatif tina kurva logistik.

Salah sahiji conto kurva Hubbert nya éta:

:
x = {e^{-t}\over(1+e^{-t})^2}={1\over2+2\cosh t}

Kurva Hubbert raket jeung susunan bentuk, sanajan asalna béda, probability density function tina sebaran normal. Kurva ieu asalna tina mode laju éxtraxi minyak bumi. Dumasar kana ieu modél, laju produksi minyak ditangtukeun ku laju sumur minyak anyar nu kapanggih; "penclut Hubbert (*Hubbert peak*]]" dina laju éxtraxi minyak bakal nuturkeun ku nurunna produksi minyak nepi ka béakna.

*Catetan: keur diskusi leuwih jéntré ngeunaan minyak bumi, tingali dina artikel penclut Hubbert.*
Independent components analysis

**Independent components analysis (ICA)** is a mathematical method for separating a signal into its most probable additive subcomponent supposing the statistical independence of the source signals. This assumption is correct in most cases so the blind ICA separation of a mixed signal gives very good results. It is also used for signals that are not supposed to be generated by a mixing for analysis purposes.

The statistical method revéal hidden factors (independent components), presuming their non-gaussianity.

It uses principal components analysis as a first step.
Apply whitening of the data, and then apply an iterative algorithm (such as an adaptive filter).

The ICA séarches for orthogonal components that are mutually statistically independent to describe the input data matrix (composed by the féatures vectors). This can allow the reconstruction of source signals from several corrupted mixtures theréof.

The method is important to blind signal separation, EEG analysis and FMRI analysis.

This concept can be extended to analyse non physical signals, for instance ICA has been aplied to discover discussions topics on a bag of news list archives.

Pakait jeung 
* PCA (principal component analysis)
* varimax rotation
* projecting pursuit
* Image processing
* Signal processing
Kaputusan statistik

** Kaputusan statistik ** nyaéta cabang tina statistik nu ngandung generalisasi tina sampel ka populasi, ngararangkay tes hipotesa, nangtukeun hubungan antar variabel, sarta nyieun prediksi.
Metoda inpormasi leherbotol

**métodeu  inpormasi leherbotol** mangrupa téhnik keur manggihkeun *perdagangan* nu hadé antara akurasi jeung kompresi waktu nyieun kasimpulan (contona clustering) variabel random **X** waktu dibérékeun joint sebaran probabiliti antara **X** jeung variabel observasi **Y**.

## Tempo oge
* Tiori inpormasi

## Tumbu kaluar
* Paper by N. Tishby, et. al
Interaction (statistics)

Dina statistik, **interaksi** nyaéta watesan dina model statistik nu mana efek dua variabel atawa leuwih teu bisa ditambahkeun sacara langsung.

Mangka, for a response *y* and two variables *x*1 and *x*2 an *additive* modél would be:

:y = ax_1 + bx_2 + \mbox{error},

- while,

:y = ax_1 + bx_2 + c(x_1\times x_2) + \mbox{error},

- is an example of a modél with an *interaction* between variables *x*1 and *x*2 (the word "errors" is not to be construed literally; it refers to a random variable by which *y* differs from the nilai ekspektasi of *y*).  See errors and residuals in statistics, and note that it is éasy to confuse errors with residuals, although the two are different.

Very often the interacting variables are categorical variables rather than réal numbers.  For example, members of a population may be classified by religion and by occupation.  If one wishes to predict a person's height based only on the person's religion and occupation, a simple *additive* modél, i.e., a modél without interaction, would add to an overall average height an adjustment for a particular religion and another for a particular occupation.  A modél with interaction, unlike an additive modél, could add a further adjustment for the "interaction" between that religion and that occupation.  This example may cause one to suspect that the word *interaction* is something of a misnomer.

The consequence of an *interaction* is that the effect of one variable depends on the value of another. This has implications in desain percobaan as it is misléading to vary one factor at a time.

réal-world examples of systems that manifest interactions include:

**Interaction* between adding sugar to coffee and stiring the coffee. Neither of the two individual variables has much effect on sweetness but a combination of the two does.
**Interaction* between adding carbon to steel and quenching. Neither of the two individually has much effect on strength but a combination of the two has a dramatic effect.

Genichi Taguchi contended that *interactions* could be eliminated from a system by appropriate choice of response variable and transformation. However George Box and others have argued that this is not the case in general.

### Bibliography
Box, G E P (1990) Do interactions matter? *Quality Engineering* vol 2, pp365–369
Interquartile range

Dina statistik deskriptif, **interquartile range (IQR)** nyaéta beda antara kuartil katilu jeung kahiji. Interquartile range leuwih nembongkeun nu sabenerna dina statistik tinimbang rentang, sarta ilaharna dipikaresep dina statistik.

Lamun 25% data kurang atawa sarua jeung kuartil kahiji sarta 25% leuwih gedé atau sarua jeung kuartil katilu, bedana nyaéta panjang interval kaasup satengahna tina data. Beda ieu kudu diukur tina satuan data nu sarua.

## Persentil jeung kuartil
Keur lobana sampel n mangka observasi x_1, x_2, .... x_n observasi diruntuykeun ti nu leutik kanu gedé. Tina runtuyan statistik ieu bisa kapanggih persentil sampel.

Lamun 0, **persentil sampel** nu ka-100p nujul kana np sampel observasi leuwih leutik tinimbang éta sarta (n+1)p sampel observasi leuwih gedé tinimbang eta. Salah sahiji cara keur narima ieu nyaéta nyokot sampel persentil nu ka-(100p) ku runtuyan statistik (n+1)p, tur (n+1)p minangka integer.

Lamun (n+1)p lain interger tur sarua jeung r ditambah sababaraha bagéan a/b mangka bakal manggih interpolasi linier antara y_r jeung y_{r+1}.
Mangka sampel persentil nu ka-100p dihartikeun minangka:

:\tilde{\pi}_p = y_r +(a/b)(y_{r+1}-y_r)

Persentil nu pasti mibanda ngaran husus. Persentil nu ka-50 disebutna **median** tina sampel. Persentil nu ka-25, 50, tur ka-75  disebut **kuartil** kahiji, kadua jeung katilu tina sampel. Hal ini nembongkeun **kasimpulan lima-wilangan** tina runtuyan data, nyaéta minimal, kuartil kahiji, median, kuartil katilu jeung kuartil maksimum.

Ayeuna **IQR** atawa **interquartile range** dihartikeun minangka:

:IQR = \tilde{r}_3-\tilde{r}_1.

## Conto
Itungan ieu maké data tina kaca quartile.

```
i    x[i]
     1    102
     2    105
    ----------- the first quartile, Q[1] = (105+106)/2 = 105.5
     3    106
     4    109
   ------------ the second quartile, Q[2] or median = 109.5
     5    110
     6    112
   ------------ the third quartile, Q[3] = (112+115)/2 = 113.5
     7    115
     8    118
```

Tina tabel eta, the **interquartile range** is 113.5 - 105.5 = 8

Tempo ogé: statistical dispersion, mean
Sekuen Halton

Dina statistika, **sekuen Halton** leuwih dipikanyaho minangka sekuen kuasi-random, mimiti diwanohkeun dina taun 1960 minangka alternatip tina sekuan wilangan pseudo-random.  Sekuen ieu dirarancang utamana keur dipaké dina simulasi integral Monte Carlo nu teu mibanda bentuk-raket dina usaha keur ngurangan varian.

Aslina, sekuen Halton dirarancang dumasa kana modél deterministik nu maké wilangan prima minangka dasarna. Sekuen Halton hiji-dimesi dumasar kana wilangan prima *p* (≥ 2) ngeusi dina rohangan 0-1 ku ngabagi kana bagéan *p*, sarta sacar sistematis dieusikan kana rohangan nu kosong, maka siklus panjang *p* nu disimpen unggal gambar dina unggal segmen. Panjang sekuen Halton *N* saterusna ngandung panjang siklus mimiti p-1, ditambahkeun kana *[N-(p-1)]DIV[p]* panjang siklus “lengkep” *p*, sarta, iwal dina kasus di mana *(N+1)MOD(p)=0*, ogé dina panjang siklus ahir “teu lengkep” final *(N+1)MOD(p)*.

Sacara resmi, φp *(i)*, unsur ka-*i* dina sekuen Halton dumasar kana wilangan prima *p*, ditangtukeun ku nyokot inverse interger radikal *i* dina dasar *p* ku ngagambarkeun ngaliwatan titik radikal, saperti:

di mana nilai *b0(i), ..., bL(i)*  ditangtukeun ku ngarengsekeun:

Unggal sekuen Halton standar diwangun dina dimensi handap, masalah pakait dicatet antara sekuen nu di-generate tina wilangan prima pangluhurna. Pasti, ieu nembongkeun risiko serius salila estimasi integral dimensi-luhur (misalna, -- *pamilihan model spasial, saperti lokasi atawa rute*).  Dina usaha keur nganyahokeun paripolah ieu, sababaraha métodeu  diusulkeun;  salah sahiji solusi nu kawentar nyaéta sekuen Halto (*make koefisien permutasi nu ditangtukeun samemehna digunakeun dina ngawangun sekuen standar*).
Fungsi survivor

**Fungsi survivor** atawa **fungsi reliabiliti** nyaéta sipat unggal variabel acak nu ngagambarkeun susunan kajadian, ilaharna pakait jeung paeh atawa gagalna sababaraha sistim, dumasar kana time. Ieu kawengku dina probabiliti nu mana sistim bakal nyalametkeun manéh salila waktu nu ditangtukeun. Watesan *fungsi reliabiliti* ilahar dipaké dina widang rékayasa sabalikna watesan *fungsi survivor* dipaké leuwih lega, kaasup dina hurip manusa.

## Harti
Anggap *X* mangrupa variabel bébas nu mibanda cumulative distribution function *F*(*t*) dina interval [0,&infin;). Maka *fungsi-survivor* atawa *fungsi-reliabiliti* nyaéta:

:R(t)=1-F(t).

## Sipat
Unggal fungsi *R*(*t*) bakal turun sacara angger.

Waktu, *t*=0, ngagambarkeun kaayaan mimiti, sacara tipikal dimimitian nu nalungtik atawa sistim mimiti dipaké. *R*(0) ilaharna satuan tapi bisa kurang keur ngagambarkeun probabiliti nu mana sistem gagal teu lila sanggeus operasi.

Sakali deui, lim*t*&rarr;&infin;*R*(*t*) ilaharna nol tapi bisa ogé leuwih gedé keur ngagambarkeun kahirupan dina jero sistim nu mungkin.

## Konsep pakait
Tempo oge:

*Hazard rate
*Cummulative hazard function
*Mean time to failure
*Mean residual life
Dinamika sistim

**Dinamika sistim** sahiji *pendekatan* keur dinamika dina populasi, system ekologi sarta ékonomi, nu ilaharna pakait raket. Dinamika sistem dipanggihkeun di awal taun 1960s ku Jay W. Forrester di MIT nu ngawangun MIT System Dynamics Group. Dina waktu nu sarua, manéhna mimiti maké nu nalungtik ngeunaan sistim salila manéhna gawe di rekayasa listrik keur sistim nu dipaké unggal poe. Naha nu dipaké sistim dinamik béda tina pamarekanséjén nu diajarkeun dina sistim kompleks nu dipaké di feedback loops. *Stocks* sarta *flows* mangrupa wangunan blok modél sistim dinamika. manéhna mantuan ngajelaskeun kumaha sistim pakait ku *feedback loops* nu dijieun nonlinearity remen kapanggih dina masalah kiwati. Perangkat lunak komputer dipaké keur simulasi model dinamika sistim nu keur ditalungtik. Running "what if" simulations to test certain policies on such a modél can gréatly aid in understanding how the system changes over time.

## Tumbu kaluar 
* MIT System Dynamics Group  
* The System Dynamics Society is an international, nonprofit organization devoted to encouraging the development and use of systems thinking and system dynamics around the world
* An Annotated Survey of the Essential System Dynamics Literature

### Perngkat lunak haratis 
* Simile (free for reséarch, educational and personal use)
* http://www.suite101.com/article.cfm/scientific_computing/85003 
* Vensim (free for educational and personal use)
* *Introduction to Social Macrodynamics*
* TRUE (free for educational and personal use)

### Mailing lists 
* System Dynamics Mailing List 
* Computer Simulation in Social Sciences