izzako/sundanese-pixelgpt huggingface dataset:
Transportasi séjén utamana "mobil dina rel nu miring" sarta sarta kurang efisien keur mobil nu dipaké
Pamakaéan magnetik levitasi dimaksudkeun keur ngurangan béaya perawatan
Unggal gerakan dina sistim ieu merlukeun material anu saeutik
Ku sabab itu disebutna "tetapan padat"
Kauntungan séjénna nyaéta saeutik gesekan, halus sarta teu gandeng
Tempo oge: summary statistics, descriptive statistics
Daur cai (sacara husus dipikawanoh/katelah ogé daur hidrologis) nujul kana parobahan wujud antara cair, padet, jeung gas; sarta parobahan nu sinambung cai sajeroeun hidrosfir, antara atmosfir marcapada, lemah, cai lakop, cai taneuh, jeung tutuwuhan
Daurna bisa dibagi kana opat fase utama: "évaporasi", "présipitasi", infiltrasi, jeung "runoff"
Cai mangrupa hiji sanyawa kimiawi jeung molékul polar nu cair dina témperatur jeung tekenan baku ("standard temperature and pressure", STP)
Cai mibanda rumus kimiawi H2O, nu hartina hiji molekul cai diwangun ku dua atom hidrogén jeung hiji atom oksigén
Cai bisa kapanggih di ampir sakuliah tempat di Marcapada sarta dipikabutuh ku sakumna kahirupan
Aya kana 70%-na marcapada téh kalimpud ku cai
Cai geus kapanggih aya di sababaraha banda di Surya Mandala jeung di saluareunana dina rupa és
Pentingna cai pikeun kahirupan "terestrial" geus ngagiring kana panyangka yén ayana dina wujud cair di mana waé sagigireun di marcapada ieu bisa nyadiakeun habitat nu ngadukung pikeun kahirupan ékstraterestrial
Wujud padet cai dipikawanoh minangka és; wujud gasna katelah uap cai
Unit temperatur (tadina darajat Celsius, ayeuna Kélvin) ditangtukeun dina kontéks titik tripel cai, 273.16 K (0.01 °C) jeung 611.2 Pa, temperatur jeung tekenan nalika cai padet, cair, jeung gas araya dina kaayaan kasatimbangan
Cai mintonkeun sababaraha paripolah nu anéh pisan, kaasup kabentukna padetan cai nonkristalin ("glassy") "vitreous ice"
Dina hawa luhureun 647 K jeung tekenan luhureun 22.064 MPa, sakumpulan molekul cai ngalaman hiji kaayaan "superkritis", di mana guruntulan kawas-cairan ngambang di antara fase kawas-uap
Uap cai tiasa nyieun jadi lembap, salah sahiji produk pikeun nyerap kelembapan atawa molekul cai di udara nyaéta silica gel
Awak cai bisa mangrupa sagara, laut, situ, walungan, curug, kanal, balong, jeung sajabana
Tempo sumberdaya cai pikeun béja ngeunaan asupan cai bersih
Tempo ogé: cilaut, "fresh water", jeung "underwater"
Kandungan cai di Marcapada kira (jumlah asupan cai sadunya) aya 1,360,000,000 km³ (326,000,000 mil³) nu kabagi mangrupa: Sipat bipolar cai
Hiji ciri penting cai nyaéta sipat polarna
Cai minangka pangleyur
Cai ogé mangrupa hiji pangleyur nu hadé alatan polaritasna
Sipat pangleyur cai kacida pentingna dina biologi, sabab loba réaksi biokimiawi anu ngan bisa lumangsung dina kaayaan leyuran cai (kayaning réaksi dina sitoplasma jeung na getih)
Cai ogé dipaké dina angkutan molekul biologis
Nalika sanyawa ionik atawa polar asup kana cai, mangka bakal dikurilingan ku molekul cai
Ukuran molekul cai nu cukup leutik ngamungkinkeun molekul-molekul cai nyulusup sabudeureun hiji molekul "solute"
Sacara ngaluas, bahan-bahan ion jeung polar siga asam, alkohol, jeung garam téh gampang leyur dina cai
Sabalikna, bahan-bahan nonpolar siga lemak jeung minyak mah henteu
Molekul-molekul nonpolar cicing babarengan dina cai ku sabab molekul cai gaduh tanaga nu leuwih kuat pikeun ngiket hiji jeung nu séjénna daripada ngiketan jeung molekul nonpolar liwat iketan van der Waals
Hiji conto bahan ion nu bisa leyur téh garam dapur; natrium klorida, NaCl, dibagi kana Na+ katoda jeung Cl- anoda, masing-masing dikurilingan ku molekul-molekul cai
Jadina ion-ion ieu bisa gampang diubah ti kristalna jadi leyuran
Hiji conto bahan non-ion nu bisa leyur téh gula meja
Cai nyatukeun iketan dipolar hidrogen jeung kawasan dipolar molekul gula, mangpukeun gula diubah kana bentuk leyuran
Kohési jeung tegangan lakop
Beungkeut hidrogén nu kuat ngajadikeun cai mibanda kakohésifan nu luhur jeung, konsékuénsina, tegangan lakop
Ieu dibuktikeun lamun saeutik cai dicampurkeun jeung bahan teu leyur, caina bakalan ngumpul dina wujud tétésan
Wujud ieu téh penting dina pangangkutan cai di jero xilem nyusuran batang dina tanaman; iketan antarmolekul nu kuat nahan jeung nyatukeun jalur cai, ngahindarkeun tegangan nu dipikasebab ku tarikan transpirasi
Cairan nu séjén nu miboga tegangan nu leuwih leutik gaduh kamungkinan besar pikeun "rip", ngabentuk ruangan hampa udara jeung ngajadikeun pembuluh xilem teu operatif
Cai "murni" sabenerna mangrupa insulator nu alus (konduktor goréng), nu hartina "teu" ngalirkeun listrik
Ku sabab cai boga sipat pangleyur hadé, mimindengna cai téh ngandung "solute" nu leyur di jerona, utamana uyah
Mun cai mibanda pangotor nu karitu, nya jadi bisa listrik leuwih hadé, sabab pangotor kayaning uyah ngandung ion bébas dina leyuran cai di mana listrik bisa ngalir
Cai bisa dibeulah jadi unsur-unsur panyusunna, hidrogén jeung oksigén, ku jalan ngalirkeun arus
Prosés ieu disebut "éléktrolisis"
MOlekul cai sacara alami peupeus jadi ion H+ jeung OH- nu dibetot ka katoda jeung anoda
Na katoda, dua ion H+ nyokot éléktron jadi gas H2
Na anoda, opat ion OH- ngagabung sarta ngaleupaskeun gas O2, cai molekular, jeung opat éléktron
Gas ngabulukbuk kana beungeut cai, nu saterusna bisa dikumpulkeun
Sacara kimiawi, cai téh amfotérik: bisa meta minangka hiji asam atawa basa
Kadang istilah "asam hidroksida" dipaké nalika cai meta minangka asam dina hiji réaksi kimiawi
Dina pH 7 (nétral), kadar ion hidroksida (OH-) sarua jeung ion hidronium (H3O+) atawa ion hidrogén (H+)
Mun kasatimbangan kaganggu, leyuran jadi asam (kadar ion hidronium leuwih luhur) atawa basa (kadar ion hidroksida leuwih luhur)
Cai bisa meta minangka asam atawa basa dina hiji réaksi
Nurutkeun sistim Brønsted-Lowry, asam ditangtukeun minangka spésiés nu nyumbang proton (ion H+) dina hiji réaksi, sedengkeun alkali minangka nu narima proton
Nalika réaksi jeung asam nu leuwih kuat, cai meta minangka alkali, sarta bakal meta minangka asam mun réaksi jeung asam nu leuwih lemah
Pikeun conto, cai bakal nampa hiji H+ ti HCl dina kasatimbangan: HCl + H2O → H3O+ + Cl- Di dieu cai meta minangka alkali, ku jalan narima ion H+
Asam nyumbangkeun ion H+, tah, cai bisa milampah hal ieu, kawas dina réaksi jeung NaOH: NH3 + H2O → NH4+ + OH- pH dina prakték
Téorina, cai murni pH-na 7
Ari prakna, cai murni hésé pisan dialana
Cai nu diantepkeun nembrak bakal nyerep karbon dioksida, ngahasilkeun leyuran asam karbonat, nu pH-na kira 5.7 (Kendall, 1916)
Nilai pH dina cai nginum dikawasa ku industri pikeun nyumponan kisaran pH cai anu diidinan
Kusabab nilai cai tiasa nangtoskeun naha cai nginum éta sehat atanapi henteu
Salaku conto, upami nilai pH cai nginum langkung ti 7 (cai basa), cai nginum bakal nyayogikeun panyakit gastrointernal upami diinum sacara terus-terusan
Asam dina burih gaduh pH nilai anu saé pikeun ngancurkeun sesa dahareun
Upami nilai pH robih ku sabab konsumsi cai basa, écés éta bakal nyababkeun masalah
Samentara éta, upami pH cai nginum cai teuing (cai asam), éta ngagaduhan potensi pikeun ngarusak huntu bahkan nyababkeun kanker
Standar pH cai minum nu ditangtukeun ku Peraturan Menteri Kesehatan Nomor : 416/MEN.KES/PER/IX/1990 Tentang Syarat-syarat Dan Pengawasan Kualitas Air
Tiap industri AMDK, PDAM, depot cai nginum kedah minuhan peraturan éta
Pikeun ngukur pH nilai cai, industri nganggo pH meter air
pH meter mangrupi alat ukur laboratorium pikeun ngukur nilai pH atanapi tingkat kaasaman larutan (pH meter cai) atawa tanah (pH meter tanah)
Harga pH meter rupa-rupa gumantung kana kamampuan pH meter éta
Diantara kamampuan anu ditinga ku pangguna poténsial boh rumah tangga sareng industri nyaéta katepatan sareng résolusi pengukuran Ngamurnikeun cai
Ngamurnikeun cai perlu pikeun rupa-rupa kaperluan industri, pon kitu ogé keur konsumsi
Manusa merlukeun cai nu teu loba teuing ngandung uyah atawa nu séjénna
Pangotor nu ilahar kapanggih di antarana bahan kimiawi atawa baktéri
Sababara zat bisa lempur dina cai, malah dibutuhkeun pikeun ningkatkeun rasa nu dirasakeun
Cai anu bisa diinum disebut cai nginum
Genep métode umum pikeun ngamurnikeun cai: Miceunan cai
Miceunan cai ngandung harti ngamomorékeun mangpaat cai, dipaké pikeun nu teu perlu
Misalna ngagunakeun cai inumeun (geus dimurnikeun) pikeun tujuan séjén
Mikasebab cai jadi keuna polusi bisa jadi kasilapan pamakéan cai nu pangbesarna
Bukti yén pangotor téh jadi batesan pamakéan cai, manéhna jadi pangotor dina hiji sumber cai, teu dipikangaruh ku sabaraha untung si pangotorna
Rék kumaha oge, dina sasabaraha kota, kawas Hong Kong, cai laut dipaké pikeun malidkeun piceunan dina toilet ku tujuan pikeun ngajimatkeun sumber-sumber cai bérésih
Cai mangrupa salah sahiji tina opat unsur klasik babarengan jeung seuneu, taneuh, jeung hawa, nu diajénan minangka ylem, atawa unsur dasar mayapada
Water was considered cold and moist
In the théory of the four bodily humours, water was associated with phlegm
Cai ogé mangrupa salah sahiji ti Opat Unsur dina Taoisme Cina, bareng jeung taneuh, seuneu, kai, jeung logam
Filosofi air oge mingaruhan urang ningali cai
Cai jeung masarakat Sunda
Cai geus dalit pisan jeung hirup kumbuh masarakat Sunda
Ieu bisa kabukti dina pamakéan kecap cai pikeun méré ngaran unggal patempatan
Pirang-pirang tempat nu aya di tatar Sunda, loba nu dimimtian ku kecap cai, nu satuluyna diringkes jadi ci
Ajén cai dina agama
Cai dianggap nyucikeun dina rupa-rupa agama, kayaning Islam, Yahudi, jeung Sikh
PIkeun conto, wudu dina Islam jeung baptis di garéja Kristen ngagunakeun cai bersih/murni
Nya kitu ogé dina ngamandian mayit pikeun Islam jeung Yahudi
Para kimiawan sakapeung ngaheureuykeun cai minangka dihidrogén monoksida atawa DHMO, ngaran kovalén sistimatis pikeun ieu molekul, hususna dina parodi of chemical reséarch that call for this "lethal chemical" to be banned
Dina taun 2004, kota Aliso Viejo, California ampir ngalarang cangkir "foam" satutasna katalungtik yén DHMO geus dipaké dina produksina (tempo )
Ngaran asam sistimatis pikeun cai nyéta asam hidroksida ("hydroxic acid" atawa "hydroxilic acid"), najan istilah ieu jarang dipaké
Sarupa jeung éta, ngaran alkali sistimatis pikeun cai nyéta hidrogén hidroksida ("hydrogen hydroxide") – boh ngaran asam atawa alkali pikeun cai mémang aya sabab cai bisa meta minangka asam atawa alkali, gumantung kakuatan asam atawa alkali lawan réaksina (amfotér)
Hukum jeung ngokolakeun cai
World Water Development Report UNESCO (WWDR, 2003) tina World Water Assessment Program nunjukkeun yén 20 taun ka hareup dunya bakal nyanghareupan an unprecedented lack of drinking water
Jumlah cai nu bisa aya pikeun masarakat ditaker nurun nepi ka 30%
Nu jadi sabab nyaéta kontaminasi, pamanasan global, jeung masalah politis
40% pangeusi dunya kakurangan cai pikeun higiéne nu minimal
Leuwih ti 2,2 juta urang maot dina taun 2000 alatan kasakit nu patali jeung konsumsi cai nu kacemar
Taun 2004, sumbangan WaterAid Inggris ngalaporkeun yén unggal 15 detik aya saurang budak nu maot alatan kasakit nu patali jeung cai, padahal éta kasakit kagolongkeun babari dicegahna
Laporan ieu nunjukkeun ayana jurang dina kasadiaan cai: ti 10 m³ per jalma per taun di Kuwait nepi ka 812.121 m³ di Guiana Prancis
Najan kitu, nagara beunghar kawas Kuwait moal hésé dina ngayakeunana
Kaén jeung pakéan
Sababaraha rupa kaén kayaning anduk sacara husus dijieun pikeun nyerep cai
Sababaraha pakéan dijieun pikeun ngajaga tina cai (conto jas hujan), atawa pikeun digunakeun dina cai ("swimsuit")
Paraméter statistik nyaéta paraméter indeks tina kulawarga sebaran probabiliti
di antara kulawarga paraméterisasi distribusi nyaéta sebaran normal, sebaran Poisson, sebaran binomial, jeung sebaran eksponensial
Kulawarga sebaran normal mibanda dua paraméter, nyaéta mean jeung varian: lamun dina kasus husus, sebaran dipikanyaho sacara pasti
Kulawarga sebaran chi-kuadrat, di bagéan séjén, ngan mibanda hiji paraméter, nyaéta tingkat kabébasan
Dina kaputusan statistik, paraméter kadang-kadang dicokot tina data nu teu ka observasi, sarta dina ieu kasus statistikawan kudu narik kasimpulan dumasar kana observasi sebaran variabel random nurut kana sebaran probabiliti dina patarosan, atawa leuwih pastina nangtukeun dumasar kana sampel random nu cokot tina populasi nu keur ditalungtik
Dina kaayaan séjén, paramater bisa pasti sacara alami tina prosedur sampling atawa tipe prosedur statistik nu dipaké (contona, jumlah tingkat kabebasan dina tes chi-kuadrat Pearson)
Dina tiori probabiliti jeung statistik, sebaran beta nyaéta probability distribution kontinyu dina probability density function nu dihartikeun dina interval [0, 1]: formula_1 nu mana "a" jeung "b" mangrupa paraméter nu kudu leuwih gedé ti nol
Lamun "angger" kaasup sacara eksplisit, densiti ditempokeun saperti: formula_2 nu mana Γ jeung B nyaéta fungsi gamma jeung fungsi beta
Kasus husus sebaran beta, lamun "a" = 1 jeung "b" = 1, nyaéta sebaran seragam standar
Nilai ekspektasi jeung varian beta variabel random "X" nu mibanda paraméter "a" jeung "b" dirumuskeun ku: formula_3 formula_4 Di bagéan séjén, lamun nilai ekspektasi jeung varian beta variabel random "X" dipikanyaho, paraméter "a" jeung "b" diitung maké rumus,k
: formula_5 formula_6 nu mana 0 &lt; E("X") &lt; 1 jeung 0 &lt; var("X") &lt; E("X") (1 − E("X"))
Tes Pearson's chi-kuadrat (χ2) salah sahiji variasi tina tes chi-kuadrat – procedure statistik nu hasilna di-"evaluasi" dumasar kana sebaran chi-kuadrat
Tes ieu mimiti dipaluruh ku Karl Pearson
It tests a null hypothesis that the relative frequencies of occurrence of observed events follow a specified frequency distribution
The events are assumed to be independent and have the same distribution, and the outcomes of éach event must be mutually exclusive
A simple example is the hypothesis that an ordinary six-sided die is "fair", i.e., all six outcomes occur equally often
Péarson's chi-square is the original and most widely-used chi-square test
Chi-square is calculated by finding the difference between éach observed and théoretical frequency for éach possible outcome, squaring them, dividing éach by the théoretical frequency, and taking the sum of the results
The number of degrees of freedom is equal to the number of possible outcomes, minus 1: formula_1 where formula_2 = an observed frequency; formula_3 = an expected (theoretical) frequency, asserted by the null hypothesis; formula_4 = the number of possible outcomes of each event
Péarson's chi-square is used to assess two types of comparison: tests of goodness of fit and tests of independence
A test of goodness of fit establishes whether or not an observed frequency distribution differs from a théoretical distribution
A test of independence assesses whether paired observations on two variables, expressed in a contingency table, are independent of éach other – for example, whether péople from different regions differ in the frequency with which they report that they support a political candidate
A chi-square probability of 0.05 or less is commonly interpreted by applied workers as justification for rejecting the null hypothesis that the row variable is unrelated (that is, only randomly related) to the column variable
The alternate hypothesis is not rejected when the variables have an associated relationship
For example, to test the hypothesis that a random sample of 100 péople has been drawn from a population in which men and women are equal in frequency, the observed number of men and women would be compared to the théoretical frequencies of 50 men and 50 women
If there were 45 men in the sample and 55 women, then formula_5 If the null hypothesis is true (i.e., men and women are chosen with equal probability in the sample), the test statistic will be drawn from a chi-square distribution with one degree of freedom
Though one might expect two degrees of freedom (one éach for the men and women), we must take into account that the total number of men and women is constrained (100), and thus there is only one degree of freedom (2 − 1)
Alternatively, if the male count is known the female count is determined, and vice-versa
Consultation of the chi-square distribution for 1 degree of freedom shows that the probability of observing this difference (or a more extreme difference than this) if men and women are equally numerous in the population is approximately 0.3
This probability is higher than conventional criteria for statistical significance, so normally we would not reject the null hypothesis that the number of men in the population is the same as the number of women
The approximation to the chi-square distribution bréaks down if expected frequencies are too low
It will normally be acceptable so long as no more than 10% of the events have expected frequencies below 5
Where there is only 1 degree of freedom, the approximation is not reliable if expected frequencies are below 10
In this case, a better approximation can be had by reducing the absolute value of éach difference between observed and expected frequencies by 0.5 before squaring; this is called Yates' correction for continuity
In cases where the expected value, E, is found to be small (indicating either a small underlying population probability, or a small number of observations), the normal approximation of the multinomial distribution can fail, and in such cases it is found to be more appropriate to use the G-test, a likelihood ratio-based test statistic
Where the total sample size is small, it is necessary to use an appropriate exact test, typically either the binomial test or (for contingency tables) Fisher's exact test; but note that this test assumes fixed and known marginal totals
The null distribution of the Péarson statistic with "j" rows and "k" columns is approximated by the chi-square distribution with ("k" − 1)("j" − 1) degrees of freedom
This approximation arises as the true distribution, under the null hypothesis, if the expected value is given by a multinomial distribution
For large sample sizes, the central limit theorem says this distribution tends toward a certain multivariate normal distribution
In the special case where there are only two cells in the table, the expected values follow a binomial distribution, formula_6 where "p" = probability, under the null hypothesis, "n" = number of observations in the sample
In the above example the hypothesised probability of a male observation is 0.5, with 100 samples
Thus we expect to observe 50 males
If "n" is sufficiently large, the above binomial distribution may be approximated as by Gaussian (normal) distribution and thus the Péarson test statistic approximates a chi-squared distribution, formula_7 Let "O1" be the number of observations from the sample that are in the first cell
The Péarson test statistic can be expressed as formula_8 which can in turn be expressed as formula_9 By the normal approximation to a binomial this is the square of one standard normal variate, and hence is distributed as chi-square with 1 degree of freedom
Note that the denominator is one standard deviation of the Gaussian approximation, so can be written formula_10 So as consistent with the méaning of the chi-square distribution, we are méasuring how probable the observed number of standard deviations away from the méan is under the Gaussian approximation (which is a good approximation for large "n")
The chi-square distribution is then integrated on the right of the statistic value to obtain the probability that this result or worse were observed given the modél
Similar arguments as above léad to the desired result
(TODO: details) éach cell (except the final one, whose value is completely determined by the others) is tréated as an independent binomial variable, and their contributions are summed and éach contributes one degree of freedom
A more complicated, but more widely used form of Péarson's chi-square test arises in the case where the null hypothesis of interest includes unknown paraméters
For instance we may wish to test whether some data follows a normal distribution but without specifying a mean or variance
In this situation the unknown paraméters need to be estimated by the data, typically by maximum likelihood estimation, and these estimates are then used to calculate the expected values in the Péarson statistic
It is commonly stated that the degrees of freedom for the chi-square distribution of the statistic are then "k" − 1 − "r", where "r" is the number of unknown paraméters
This result is valid when the original data was multinomial and hence the estimated paraméters are efficient for minimizing the chi-square statistic
More generally however, when maximum likelihood estimation does not coincide with minimum chi-square estimation, the distribution will lie somewhere between a chi-square distribution with "k" − 1 − "r" and "k" − 1 degrees of freedom (See for instance Chernoff and Lehmann 1954)
Sababaraha ahli matematika maké istilah fungsi karakteristik sarua jeung "fungsi indikator"
The indicator function of a subset "A" of a set "B" is the function with domain "B", whose value is 1 at éach point in "A" and 0 at éach point that is in "B" but not in "A"
In probability theory, the characteristic function of any probability distribution on the real line is given by the following formula, where "X" is any variabel acak with the distribution in question: formula_1 Here "t" is a real number, E lambang nilai ekspektasi and "F" is the cumulative distribution function
The last form is valid only when "f"—the probability density function—exists
The form preceding it is a Riemann-Stieltjes integral and is valid regardless of whether a density function exists
If "X" is a vector-valued random variable, one takes the argument "t" to be a vector and "tX" to be a dot product
A characteristic function exists for any random variable
More than that, there is a bijection between cumulative probability functions and characteristic functions
In other words, two probability distributions never share the same characteristic function
Given a characteristic function φ, it is possible to reconstruct the corresponding cumulative probability distribution function "F": formula_2 In general this is an improper integral; the function being integrated may be only conditionally integrable rather than Lebesgue-integrable, i.e
the integral of its absolute value may be infinite
Characteristic functions are used in the most frequently seen proof of the central limit theorem
Characteristic functions can also be used to find moments of random variable
Provided that "n"-th moment exists, characteristic function can be differentiated "n" times and formula_3 Related concepts include the moment-generating function and the probability-generating function
The characteristic function is closely related to the Fourier transform: the characteristic function of a distribution with density function "f" is proportional to the inverse Fourier transform of "f"
Tes chi-kuadrat nyaéta hypothesis test nu mana tes statistik mibanda sebaran chi-kuadrat lamun null hipotesisna bener
Ieu kaasup: " please add tests, history, etc. "
Dina matematik, fungsi gamma nyaéta fungsi nu leuwih lega tina konsép faktorial kana wilangan kompleks
Lambang Γ("z") dumasar ka Adrien-Marie Legendre
Lamun bagéan réal tina wilangan kompleks "z" positip, mangka integral formula_1 pasti konvergen
ngagunakeun integral parsial, bisa ditembongkeun yén formula_2 Sabab Γ(1) = 1, dina kaitan ieu ngakibatkeun yen formula_3 keur sakabéh wilangan natural "n"
Ieu bisa dipaké keur ngalegaan Γ("z") jadi fungsi meromorpik dihartikeun keur sakabar wilangan kompleks "z" ial "z" = 0, −1, −2, −3, ... ku analisa kontinyu
Hal nu leuwih lega ilaharna dumasar salaku fungsi gamma
Notasi alternatip nu kadangkala dipaké nyaéta fungsi Pi, nu dina watesan fungsi gamma nyaéta formula_4 Kadangkala ogé manggihkeun formula_5 nu mangrupa hiji fungsi sakabehna, dihartikeun keur sakabéh wilangan kompleks
yén π("z") mangrupa sakabéh nu diperlukeun anu teu mibanda kutub, mangka Γ("z") teu mibanda nol
Bisa ogé nilai keur fungsi gamma dina non-integer nyaéta formula_6 Fungsi gamma mibanda hiji kutub orde 1 dina "z" = −"n" keuw sakabéh wilangan alami "n"; sesana dibérékeun ku formula_7 Bentuk kakali fungsi gamma saterusna nyaéta valid keur sakabéh wilangan kompleks "z" nu lain integer non-positip: formula_8 nu mana γ mangrupa konstanta Euler-Mascheroni
TeoremaBohr-Mollerup nangtukeun yén antara sakabéh fungsi dilegaan ku fungsi faktorial kana wilangan riil positip, ngan lamun fungsi gamma mangrupa log-convex
Kaitan jeung fungsi sejen
Dina integral di luhur, nu ngahartikeun fungsi gamma, watesan integralna geus ditangtukeun
Fungsi gama nu teu lengkep mangrupa fungsi nu ditangtukeun ku nuturkeun wates luhur atawa handap tina integral jadi variabel
Turunan logaritma fungsi gamma disebutna fungsi digamma
Dina teori probabiliti jeung statistik, sebaran eksponensial nyaéta sebaran probailiti kontinyu nu mibanda probability density function (pdf) formula_1 nu mana λ &gt; 0 mangrupa paraméter sebaran
Cumulative distribution function diberekeun ku formula_2 Nilai ekspektasi jeung simpangan baku variabel random eksponensial duaana nyaéta 1/λ (sarta varianna nyaéta 1/λ2.)
Sebaran eksponensial dipaké keur modél proses Poisson, nu mana kaayaanna obyek awal dina tetapan A bisa robah kana tetapan B nu mibanda konstanta probabiliti per satuan waktu λ. Waktu nu robah dina tetapan sabenerna dijelaskeun ku variabel random eksponensial nu mibanda paraméter λ. Sanajan kitu, integral ti 0 ka "T" dina "f" mangrupa probabiliti nu obyekna dina tetapan B nyaéta waktu "T"
Sebaran eksponensial bisa ditempo salaku lawan tina sebaran geometrik, nu ngajelaskeun wilangan Bernoulli trial penting keur prosés diskrit ka robahna tetapan
Beda jeung sebaran eksponensial nu ngajelaskeun waktu keur prosés kontinyu kana robahna tetapan
Conto variabel nu ngadeukeutan sebaran eksponensial nyaéta: Sipat penting tina sebaran eksponensial nyaéta kurang memori
Ieu hartina yén variabel random "T" kasebar eksponsial, probabiliti kondisional nurut kana formula_3 Ieu hartina yén probabiliti kondisional yén perlu ngadagoan, contona, leuwih ti 10 detik samemeh datang mimiti, diberekeun yén waktu datang teu kajadian sanggeus 30 detik, teu beda tina probabiliti mimiti nu merlukeun waktu ngadagoan leuwih ti 10 detik keur nu datang mimiti
Ieu sok salah harti ku siswa nu nyokot pangajaran probabiliti: kanyataanna yén P("T" &gt; 40 | "T" &gt; 30) = P("T" &gt; 10) "lain" hartina yén kajadian "T" &gt; 40 sarta "T" &gt; 10 hal nu bebas
Kasimpulanna: "memorlessness" sebaran probabiliti waktu ngadagoan "T" salili datang mimiti hartina formula_4 "Lain" hartina formula_5 Ieu kudu bebas
Dua kajadian ieu "heunteu" bebas
Generating variabel ku sebaran eksponensial
Diberekeun variabel random "Y" nu mibanda sebaran seragam dina interval (0;1], variabel formula_6 ngabogaam sebaran eksponensia; nu mibanda paraméter λ
Dina tiori probabiliti jeung statistik, sebaran gamma nyaéta probability distribution kontinyu
Probability density function bisa digambarkeun di watesan fungsi gamma: formula_1 nu mana "k" &gt; 0 nyaéta "parameter bentuk" jeung θ &gt; 0 nyaéta "parameter skala" sebaran gamma
Cumulative distribution function bisa ditembongkeun dina watesan incomplete gamma function, formula_2 Nilai ekspektasi sarta varian tina variabel random gamma "X" nyaéta: formula_3 Lamun formula_4 mibanda sebaaran gamma mibanda paraméter formula_5 jeung θ, sarta formula_6 mibanda sebaran gamma mibanda paramater formula_7 jeung θ, mangka formula_8 mibanda sebaran gamma mibanda paraméter formula_9 jeung θ. Lamun "k" sarua jeung 1, sebaran gamma mangrupa sebaran eksponensial mibanda paraméter
gamma mangrupa sebaran eksponensial mibanda paraméter θ. Jumlah "n" variabel eksponensial, sakabéhna mibanda paraméter θ nu sarua, mangrupa variabel gamma nu mibanda paraméter "n" jeung θ. Lamun "k" mangrupa integer, sebaran gamma mangrupa Erlang distribution (keur ngahargaan ka A.K
Erlang) sarta sebaran probabiliti waktu tunggu tina nu-"k" "datang" dina hiji-dimensi Poisson process nu mibanda intensitas 1/θ
Lamun "k" mangrupa satengah-integer sarta θ = 2, mangka sebaran distribution mangrupa sebaran chi-kuadrat nu mibanda "2 k" tingkat kabébasan
Sebaran gamma mangrupa sebaran probabiliti infinitely divisible
Hateup nyaéta bagéan pangluhurna tina imah nu nutupan wangunan
Hateup datar mindeng ditutupan ku tér jeung karihkil tur disadiakuen saluran keur nyalurkeun cihujan jeung salju
Hateup bentuk lianna diwangun pikeun ngucurkeun cai sacara alami, kaasup: Di nagara séjén, Amerika utamana
Hateup imah téh sok dipulas maké tér bahanna hateup sorangan dijieun aya tina kai , beusi galvanis, batu , aya ogé anu maké kenténg
Kadieunakeun hateup téh aya ogé anu ngagunakeun "panel surya", aya dua mangpaat sagigireun ngiuhan imah ogé bisa ngahasilkeun listrik pikeun kabutuhan rumah tangga
Hateup imah tradisional Sunda
Hateup dina wangunan imah tradisional Sunda mibanda ciri anu mandiri, aya sababaraha ngaran hateup anu remen dipaké kayaning: Sababaraha sistem konstruksi ngabagi beurat hateup kana pinding/dinding wangunan tur mageuhan éta hateup kana struktur imah
Éfék ukuran ngajelaskeun sabaraha gedé hubungan antara dua variabel
Informasi ieu penting dina panalungtikan ilmiah
Efek size bisa dipaké henteu ngan sakadar keur ngayahokeun naha panalungtikan aya efekna tapi ogé ukuran masing-masing efek
Efek ukuran ogé ngabantu dina situasi praktis, upamana keur nyieun kaputusan
Contona, lamun mahluk jomantara turun ka dunya, sabaraha lila waktu nu diperlukeun keur ngayakinkeun yen, sacara rata-rata, lalaki leuwih jangkung ti awewe
Jawabanna pakait jeung efek ukuran dina béda jangkung antara awewe jeung lalaki
Lamun efek ukuranna gedé, gampang keur nangtukeun yén lalaki leuwih jangkung
Lamun béda ukuranna leutik, mangka perlu waktu (sarta sampel nu leuwih loba) keur mastikeun yén lalaki, sacara rata-rata, leuwih jangkung tinimbang awewe
Konsép efek ukuran mucunghul ogé dina basa sapopoe
Upamana, program keur ngurangan beurat awak nu ngabalukarkeun leungitna beurat 30 pon
Dina hal ieu, 30 pon nunjukkeun efek ukuran
Conto séjénna yén program ngajar nu dipiharep bakal ningkatkeun hiji niley mata pangajaran
Naek ieu tingkatan disebut ogé efek ukuran tina program
Dina statistik inferensial, efek ukuran nyaéta ukuran bédana kayakinan statistik
Efek ukuran, nu digambarkeun ku N jeung nilai kritis alpa nangtukeun "power" dina tes hipotesa statistik
Dina meta-analysis, efek ukuran ilahar dipaké salaku ukuran nu bisa ngitung bédana panalungtikan sarta dikombinasikeun keur sakabéh kasus analisa
Tipe efek ukuran
Korelasi Pearson "r"
Korelasi Péarson's "r" salah sahiji métodeu nu panglobana dipaké keur nangtukeun efek ukuran
Bisa dipaké waktu data mayeng atawa biner, sabab kitu Péarson "r" nyaéta bisa disebutkeun ukuran éfék anu pang serbaguna
Ieu téh ukuran éfék penting mimiti nu diwangun dina statistika, sarta diwanohkeun ku Karl Péarson
Péarson's "r" bisa béda-béda gedéna ti -1,00 nepi ka 1,00, kalawan -1,00 némbongkeun hubungan négatif anu sampurna, 1.00 némbongkeun hubungan positif anu sampurna, sarta enol anu henteu némbongkeun hubungan dua variabel
Hal séjénna mindeng dipaké keur ngukur hubungan dua variabel nyaéta kuadrat atawa "r", mindeng disebut ""r"-kuadrat" atawa koefisien katangtuan, nyaéta ukuran bagian varian dibagi sarua ku dua variabel sarta béda-béda ti enol nepi ka 1,00
Cohen's "d" nyaéta pamarekanukuran éfék nu luyu pikeun digunakeun di konteks uji-t. "d" dihartikeun salaku béda antara dua mean dibagi ku simpangan baku keur dua méan eta
Mangka, formula_1 numana mean"i" jeung SD"i" nyaéta mean jeung simpangan baku keur grup "i", keur "i" = 1, 2
Unggal panalungtik nyarankeun cara nu béda keur ngagambarkeun hasil tina efek ukuran, tapi nu loba dipaké nyaéta ti Cohen (1992) nu mana 0.2 nembongkeun efek nu leutik, 0.5 sedeng sarta 0.8 nu gedé
Sabab kitu, dina conto nalungtik jangkung mahluk jomantara lalaki jeung awewe, data (ti 1000 lalaki jeung 1000 awewe ti sampel nu dianggap ngawakilan di Inggris) bisa: Efek ukuran (make Cohen's "d") bakal sarua jeung 1.99
Niley ieu kacida gedéna sarta mahluk jomantara taya masalah dina nangtukeun béda jangkung ieu
Salah sahiji cara keur ngurangan kasalahan nyaéta ku cara ngagunakeun simpangan baku, nu mana dina sababaraha kasus nembongkeun hasil leuwih hadé (upamana dina kasus uji coba terapi)
Cara séjénna nyaéta lobana sampel sarta sampel nu teu sarua teu dipaké dina waktu keur ngitung - dumasar kana hasil panalungtikan Hedges
Hedges and Olkin (1985) noted that one could adjust effect size estimates by taking into account the sample size
The problem with Cohen's "d" is that the outcome is héavily influenced by the denominator in the equation
If one standard deviation is larger than the other then the denominator is weighted in that direction and the effect size is more conservative
However, surely it makes more sense to put stock in the larger sample size
Hedges' "ĝ" incorporates sample size by both computing a denominator which looks at the sample sizes of the respective standard deviations and also makes an adjustment to the overall effect size based on this sample size
The formula for Hedges' "ĝ" (as used by software such as the Effect Size Generator) is formula_2 Cohen's formula_3
Cohen's formula_3 is the appropriate effect size méasure to use in the context of an F-test for multiple correlation or multiple regression
The formula_3 effect size méasure for multiple regression is defined as: formula_6 where formula_7 is the squared multiple correlation
The formula_3 effect size méasure for hierarchical multiple regression is defined as: formula_9 where formula_10 is the variance accounted for by a set of one or more independent variables "A", and formula_11 is the combined variance accounted for by "A" and another set of one or more independent variables "B"
By convention, formula_3 effect sizes of 0.02, 0.15, and 0.35 are considered small, medium, and large, respectively (Cohen, 1988)
The odds ratio is another useful effect size
It is appropriate when both variables are binary
For example, consider a study on spelling
In a control group, two students pass the class for every one who fails, so the odds of passing are two to one (or more briefly 2/1 = 2)
In the tréatment group, six students pass for every one who fails, so the odds of passing are six to one (or 6/1 = 6)
The effect size can be computed by noting that the odds of passing in the tréatment group are three times higher than in the control group (because 6 divided by 2 is 3)
Therefore, the odds ratio is 3
However, odds ratio statistics are on a different scale to Cohen's d. So, this '3' is not comparable to a Cohen's d of '3'
"Statistical power analysis for the behavioral sciences (2nd ed.)"
Hillsdale, NJ: Erlbaum Cohen, J
A power primer
"Psychological Bulletin, 112 (1)," 155-159
Lipsey, M.W., &amp; Wilson, D.B
Sage: Thousand Oaks, CA
Software Further Explanations
Dina statistik, skor standar ("z") nyaéta kuantitas "tak-berdimensi" nu asalna tina "subtraksi" sample mean tina individu skor (atah) sarta dibagi ku bédana simpangan baku: formula_1 Nilai "z" ngagambarkeun lobana simpangan baku antara skor atah jeung méan; nilai z negatip lamun skor atah sahandapeun méan, positip lamun saluhureunna
Sebutan séjén keur skor standar nyaéta skor-z
prosés konversina kadangkala disebut standarisasi
Konversi ka skor standar bisa dijieun ku ngabandingkeun jeung ngombinasikeun ukuran skala
Contona, nilai ujian dua siswa tina kelas nu béda bisa dibandingkeun ku konversi unggal skor siswa dumasar kana skor méan jeung simpangan baku manéhna di kelasna
Siswa nu mibanda skor standar pangluhurna nunjukkeun hal nu hadé, tinimbang lamun skor kotorna handap
Lamun data dikombinasikeun atawa di-skala, elimanisasi standarisasi kajadian dina "pemberat" ku sabab bédana méan jeung simpangan baku
Ieu hal penting dina linear regression waktu data mangrupa sampel méan tinimbang observasi pribadi
Skor standar mangrupa loba dipaké keur data nu kasebar normal, sanajan teu bisa disebutkeun yén urang teu merlukeun sarat dina ngagunakeun informasi ngeunaan data skewed
Standar skor ogé diperlukeun dina skor percentile rank sebaran normal
Standarisasi dina matematik statistik
Dina statistik matematis, variabel acak "X" mangrupa standarisasi dipaké dina (populasi) méan jeung simpangan baku téoritis: formula_2 nu mana μ = E("X") mangrupa mean sarta σ² = Var("X") varian ti probability distribution "X"
Lamun variabel acak dina ieu kaayaan mangrupa sample mean: formula_3 mangka versi standarisasi nyaéta formula_4
Sacara umum, regresi nyaéta pindah ka arah tukang
Danie G. Krige, nepi ka kiwari Profésor di Universitas Witwatersrand, Républik Afrika Kidul, salah saurang ahli géologi di Afrika Kidul nu ngawanohkeun géostatistik
Téhnik kriging dumasar kana ngaran manéhna
Pagawéan émpirisna keur ngévaluasi sumberdaya mineral [1] dirumuskeun dina taun 1960-an ku ahli rékayasa Perancis Georges Matheron
A statistical approach to some basic mine valuation problems on the Witwatersrand
J. of Chem., Metal, and Mining Soc
of South Africa, Vol
prosés Gauss (Ing
"Gaussian process") mangrupa prosés stokastik {"X""t"}"t", nu mana unggal kombinasi linear (terhingga) tina "X""t", mangrupa sebaran normal
Konsép ieu maké ngaran Carl Friedrich Gauss sabab sebaran normal kadangkala disebut ogé "sebaran Gaussian distribution", sanajan Gauss lain nu mimiti nalungtik ieu distribusi
Catetan yén sababaraha pangarang (contona B. Simon dina rujukan di handap ieu) ogé nganggap yén variabel "X""t" miboga méan sarua jeung nol
Alternatipna, ieu prosés Gauss iff keur susunan terhingga ditempokeun ku "t"1, ..., "t""k" formula_1 mangrupa nilai-vektor variabel random Gauss
ngagunakeun fungsi karakteristik variabel random, bisa dirumuskeun sipat Gauss saperti:{"X""t"}"t" mangrupa Gaussian iff keur unggal susunan terhingga nunjukkeun "t"1, ..., "t""k" nu mana riil positip σ"l j" jeung riil μ"j" mangka formula_2 Angka σ"l j" jeung μ"j" nempokeun bakal jadi variabel kovarian jeung méan dina ieu prosés
Prosés Wiener leuwih luas di-pelajari tinimbang prosés Gauss
prosés Gauss bisa dipaké salaku fungsi prior probability distribution dina inferensi Bayes
Nilai kaputusan kontinyu nu mibanda prior prosés Gaussian dipikanyaho salaku régrési prosés Gauss
Dina matematik, fungsi nyaéta hiji "hubungan," saperti unggal unsur tina susunan mangrupa gabungan tina susunan unsur unik séjénna (nu mungkin sarua)
Konsép fungsi jadi dasar pikeun sababaraha widang matematik sarta sakabéh élmu kuantitatif
Watesan fungsi, mapping, map, transformation sarta operator mangrupa hal nu ilaharna meh sarua
Essentially, a function is a "rule" that assigns a unique output to éach given input
Here are some examples of functions: The "rule" defining a function can be specified by a formula, a relationship, or simply a table listing the outputs against inputs
The most important féature of a function is that it is deterministic, always producing the same output from the same input
In this way, a function may be thought of as a "machine" or a "black box", converting a valid input into a unique output
The input is often called the "argument" of the function, and the output the "value" of the function
A very common type of function occurs when the argument and the function value are both numbers, the functional relationship is expressed by a formula, and the value of the function is obtained by direct substitution of the argument into the formula
Consider for example formula_1 which assigns to any number "x" its square
A straightforward generalization is to allow functions depending on several arguments
For instance, formula_2 is a function which takes two numbers "x" and "y" and assigns to them their product, "xy"
It might seem that this is not réally a function as we described above, because this "rule" depends on two inputs
However, if we think of the two inputs together as a single "pair" ("x", "y"), then we can interpret "g" as a function—the argument is the ordered pair ("x", "y"), and the function value is "xy"
In the sciences, we often encounter functions that are not given by (known) formulas
Consider for instance the temperature distribution on éarth over time: this is a function which takes location and time as arguments and gives as output the temperature at that location at that time
We have seen that the intuitive notion of function is not limited to computations using single numbers and not even limited to computations; the mathematical notion of function is still more general and is not limited to situations involving numbers
Rather, a function links a "domain" (set of inputs) to a "codomain" (set of possible outputs) in such a way that every element of the domain is associated to precisely one element of the codomain
Functions are abstractly defined as certain relations, as will be seen below
Because of this generality, the function concept is fundamental to virtually every branch of mathematics
As a mathematical term, "function" was coined by Leibniz in 1694, to describe a quantity related to a curve, such as a curve's slope or a specific point of a curve
The functions Leibniz considered are today called differentiable functions, and they are the type of function most frequently encountered by nonmathematicians
For this type of function, one can talk about limits and derivatives; both are méasurements of the change of output values associated to a change of input values, and these méasurements are the basis of calculus
The word function was later used by Euler during the mid-18th century to describe an expression or formula involving various arguments, e.g
"f"("x") = sin("x") + "x"3
During the 19th century, mathematicians started to formalize all the different branches of mathematics
Weierstrass advocated building calculus on arithmetic rather than on geometry, which favoured Euler's definition over Leibniz's (see arithmetization of analysis)
By broadening the definition of functions, mathematicians were then able to study "strange" mathematical objects such as continuous functions that are nowhere differentiable
These functions were first thought to be only théoretical curiosities, and they were collectively called "monsters" as late as the turn of the 20th century
However, powerful techniques from functional analysis has shown that these functions are actually more common than differentiable functions
Such functions have since been applied to the modélling of physical phenomena such as Brownian motion
Towards the end of the 19th century, mathematicians started trying to formalize all of mathematics using set theory, and they sought to define every mathematical object as a set
Dirichlet and Lobachevcky independently and almost simultanéously gave the modérn "formal" definition of function (see formal definition below)
In this definition, a function is a special case of a relation
In most cases of practical interest, however, the differences between the modérn definition and Euler's definition are negligible
The notion of function as a rule for computing, rather than a special kind of relation, has been formalized in mathematical logic by méans of the lambda calculus
Formally, a function "f" from a set "X" of input values to a set "Y" of possible output values (written as "f" : "X" → "Y") is a relation between "X" and "Y" which satisfies: For éach input value "x" in the domain, the corresponding unique output value "y" in the codomain is denoted by "f"("x")
A more concise expression of the above definition is the following: a function from "X" to "Y" is a subset "f" of the cartesian product "X" × "Y", such that for éach "x" in "X", there is a unique "y" in "Y" such that the ordered pair ("x", "y") is in "f"
The set of all functions "f" : "X" → "Y" is denoted by "YX"
Note that "|YX| = |Y||X|" (refer to Cardinal numbers)
A relation between "X" and "Y" that satisfies condition (1) is a multivalued function
Every function is a multivalued function, but not every multivalued function is a function
A relation between "X" and "Y" that satisfies condition (2) is a partial function
Every function is a partial function, but not every partial function is a function
In this encyclopedia, the term "function" will méan a relation satisfying both conditions (1) and (2), unless otherwise stated
Consider the following three examples: Domains, codomains, and ranges
"X", the set of input values, is called the domain of "f", and "Y", the set of possible output values, is called the codomain
The range of "f" is the set of all actual outputs {"f"("x") : "x" in the domain}
Beware that sometimes the codomain is incorrectly called the range because of a failure to distinguish between possible and actual values
An endofunction is a function whose domain and range are identical
In computer science, the datatypes of the arguments and return values specify the domain and codomain (respectively) of a subprogram
So the domain and codomain are constraints imposed initially on a function; on the other hand the range has to do with how things turn out in practice
Injective, surjective and bijective functions
Several types of functions that are very useful have special names: Images and preimages
The "image" of an element "x"∈"X" under "f" is the output "f"("x")
The image of a subset A⊂"X" under "f" is the subset of "Y" defined by "f"(A) := {"f"(x) : x in A}
Notice that the range of "f" is the image "f"("X") of its domain
In our function above, the image of {2,3} under "f" is "f"({2, 3}) = {c, d} and the range of "f" is {a, c, d}
Note that with this definiton, the direct image "f" becomes a function whose domain is the set of all subsets of "X" (also known as the power set of "X") and whose codomain is the power set of "Y"
Note that the same notation is used for the original function "f" and its direct image
This is a common convention; the intended usage must be inferred by context
The "preimage" (or "inverse image") of a set B ⊂ Y under "f" is the subset of X defined by "f" −1(B) := {x in "X" : "f"(x)∈B}
In our function above, the preimage of {a, b} is "f" −1({a, b}) = {1}
Note that with this definiton, "f" −1 becomes a function whose domain is the power set of "Y" and whose codomain is the power set of "X"'
Some consequences that follow immediately from these definitions are: These are valid for arbitrary subsets "A", "A"1 and "A"2 of the domain and arbitrary subsets "B", "B"1 and "B"2 of the codomain
The results relating images and preimages to the algebra of intersection and union work for any collections of subsets, not just for pairs of subsets
Graph of a function
The graph of a function "f" is the set of all ordered pairs("x", "f"("x")), for all "x" in the domain "X"
There are théorems formulated or proved most éasily in terms of the graph, such as the closed graph theorem
If "X" and "Y" are réal lines, then this definition coincides with the familiar sense of graph
Below is the graph of a cubic function: This function is surjective but not injective
Note that since a relation on the two sets "X" and "Y" is usually formalized as a subset of "X"×"Y", the formal definition of function actually identifies the function "f" with its graph
Most commonly used types of mathematical functions involving addition, division, exponents, logarithms, multiplication, polynomials, radicals, rationals, subtraction, and trigonometric expressions
They are sometimes collectively referred as elementary functions -- but the méaning of this term varies among different branches of mathematics
Example of non-elementary functions (or special functions) are Bessel functions sarta fungsi gamma
"n"-ary function: function of several variables
Functions in applications are often functions of several variables: the values they take depend on a number of different factors
From a mathematical point of view all the variables must be made explicit in order to have a functional relationship - no 'hidden' factors are allowed
Then again, from the mathematical point of view, there is no qualitative difference between functions of one and of several variables
A function of three réal variables is just a function that applies to triples of réal numbers
The following paragraph says this in more formal language
If the domain of a function is a subset of the Cartesian product of n sets then the function is called an "n-ary function"
For example, the relation "dist" has the domain R × R and is therefore a binary function
In that case "dist"((x,y)) is simply written as "dist"(x,y)
Another name applied to some types of functions of several variables is operation
In abstract algebra, operators such as "*" are defined as binary functions; when we write a formula such as "x"*"y" in this context, we are implicitly invoking the function *("x","y"), but writing it in a convenient infix notation
An important théoretical paradigm, functional programming, takes the function concept as central