izzako/sundanese-pixelgpt huggingface dataset:
Dina statistik, tes-"G" nyaéta tes rasio likelihood atawa maximum likelihood nu loba dipaké dina statistical significance sarta saméméhna disarankeun maké tes chi-kuadrat
Ilaharna maké tes chi-kuadrat keur "goodness of fit" tina hiji sebaran sarta keur kabébasan dina "contingency table" nu dina kanyataanna dideukeutan ku "log-likelihood ratio" keur tes G ieu
Perkiraan ieu diwanohkeun ku Karl Péarson alatan perluna waktu lila keur ngitung "log-likelihood"
Ku mecenghulna kalkulator sarta komputer pribadi éléktronik, hal ieu henteu jadi masalah deui
Tes-G mucunghul tur loba dipaké, saprak direkomendasikan di édisi 1994 dina sababaraha buku teks statistika ku Sokal sarta Rohlf
Rumus umum keur tes statistik chi-kuadrat Péarson's nyaéta formula_1 nu mana O nyaéta frékuénsi observasi dina sel, E nyaéta ekspektasi frékuénsi dina null hipotesa, sarta jumlah dina sakabéh sel
Rumus pakait nu ilahar dipaké keur "G" nyaéta formula_2 nu mana ln ngalambangkeun logaritma alami (log dina "e") sarta jumlah dina sakabéh sel
Dina null hipotesa yén hasil frekuesni observasi tina nyokot sampel sacara acak tina hiji sebaran ditangtukeun ku ekspektasi frékuénsi nu dipikanyaho, sebaran "G" meh sarua jeung chi-kuadrat, nu mana jumlah wilangan tingkat kabebasan saperti dina tes chi-kuadrat
Keur sampel nu meh sarua, tes-"G" jeung tes chi kuadrat bakal ngahasilkeun kasimpulan nu sarua
Sanajan kitu, pamarekankana téori sebaran chi-kuadrat keur tes-"G" leuwih hadé tina tes chi-kuadrat Péarson dina pasualan di mana keur sakabéh sel |"O" − "E"| &gt; "E", sarta dina sababaraha pasualan tes"G" geus ilahar dipaké
Keur sampel nu saeutik tes binomial keur "goodness of fit", sarta tes kapastian Fisher keur "contingency tables", leuwih hadé maké tes chi-kuadrat atawa tes-"G"
Latin square mangrupa tabel "n" × "n" nu dieusi ku "n" lambang nu béda dina sababaraha jalan mangka éta lambang pasti ngan aya sakali dina unggal baris jeung kolom
formula_1 formula_2 Latin squares salaku multiplication table dina quasigroup, ilahar dipaké dina desain percobaan
Ngaran Latin square asalna ti Leonard Euler nu ngagunakeun simbol ku hurup Latin
métodeu statistik Latin hypercube sampling diwangun sarta dikumpulkeun ku Ronald L. Iman, J. C. Helton, and J. E. Campbell, saparakanca keur nga-generate sebaran koleksi nu asup akal tina nilai paramater dina sebaran multidimensi
Paperna "An approach to sensitivity analysis of computer models, Part I
Introduction, input variable selection and preliminary variable assessment."
dina Journal of Quality Technology taun 1981
Dina statistik, téoréma Lehmann-Scheffé netepkeun yén unggal éstimator anu lengkep, cukup, sarta teu bias mangrupa éstimator teu bias nu "unik" tina nilai ekspektasi-na
Cara nu ilahar dipaké keur néangan nilai éstimator nyaéta ngagunakeuntéoréma Rao-Blackwell
Dina statistik modél linier bisa ditembongkeun ku nyebutkeun di mana Y mangrupa nx1 vektor kolom variabel random, X mangrupa matrik kuantitas nxp "dipikanyaho" (contona, bisa di-observasi sarta non-random), vektor baris pakait jeung statistical unit, β mangrupa px1 vektor paraméter (teu ka-observasi), sarta ε mangrupa nx1 vektor "error", nu teu pakait ka variabel random nu mibanda nilai ekspektasi 0 sarta varian σ2
Salawasna komponen vektor kasalahan nu dicokot bakal independent sarta kasebar normal
Anggap nilai X sarta Y ka observasi, statistikawan kudu nga-estimate β sarta σ2
Sacara tipikal paraméter β di-estimasi maké métodeu least squares
Tinimbang nyokot varian ε jadi σ2I, nu mana I mangrupa nxn matrik identitas, anggap varian mangrupa σ2M, nu mana M mangrupa matrik séjén nu dipikanyaho salian ti matrik identitas, mangka estimate β maké métodeu "generalized least squares", nu mana, ku ngaminimalkeun kuadrat residu, minimalkeun bentuk béda kuadrat dina residu—bentuk kuadrat dibérékeun ku matrik M−1
Lamun sakabéh diagonal dina matrik M sarua jeung 0, mangka estimasi normal β ku métodeu "weighted least squares", nu mibanda beurat sarua jeung diagonal asupan
Linear regression ordiner mangrupa topik nu raket pakait
Generalisasi model linier
Generalized linear models, tinimbang leuwih ilahar di mana f mangrupa "fungsi pakait"
Contona "model regresi Poisson", ku nuliskeun Fungsi pakait mangrupa fungsi logaritma natural
Observasi nu dipiboga xi sarta Yi keur i=1...,n, bisa nga-estimasi γ and δ ku métodeu maximum likelihood
Model linier general
General linear model (atawa multivariate regression model) mangrupa modél linier nu mibanda sababara ukuran dina unggal obyek
Unggal obyek diwakilan dina bentuk vektor
Prediksi linier mangrupa operasi matematik di mana nilai ka hareup tina digital signal mangrupa estimasi minangka fungsi linier sampel saméméhna
Dina digital signal processing prediksi linier ilahar disebut linear predictive coding (LPC) sarta bisa ditembongkeun minangka sub susunan filter theory
Dina system analysis (sub bagéan matematik), prediksi linier bisa ditempo minangka bagian mathematical modelling atawa optimization
Nu ilahar digambarkeun nyaéta formula_1 nu mana "x""n"′ mangrupa nilai prediksi tanda, "x""n"−"i" nilai saméméhna, sarta "a""i" koefisien prediktor
Generat kasalahan ku estimasi ieu nyaéta formula_2 nu mana "x""n" mangrupa nilai tanda sabenerna
Persamaan ieu valid keur sakabéh tipe (hiji-dimensi) prediksi linier
bédana kapanggih dina jalan paraméter "a""i" nu dipilih
Keur tanda multi-dimensi kasalahan biasana dihartikeun ku formula_3 nu mana formula_4 mangrupa vektor norm pilihan nu cocok
Nu ilahar dina optimasi paraméter formula_5 nyaéta kriteri root mean square nu mana disebut ogé kritéria autocorrelation
Dina métodeu ieu ngaminimalkeun nilai ekspektasi tina kuadrat kasalahan E(e2"n", ngahasilkeun persamaan formula_6 keur 1 ≤ "j" ≤ "p", di mana "R" mangrupa tanda autocorrelation "x""n", dihartikeun minangka formula_7 Dina kasus multi-dimensi pakait jeung ngaminimalkeun norma L2
Persamaan di luhur disebut persamaan normal atawa Yule-Walker
Dina bentuk matriks bisa sarua jeung formula_8 nu mana matrix autokorelasi "R" mangrupa Toeplitz matrix nu mibanda elemen "r""i","j" = "R"("i" − "j"), vektor "r" mangrupa vektor autokorelasi "r"j = "R"("j"), sarta vektor "a" mangrupa vektor paraméter
pamarekannu leuwih umum nyaéta ngaminimalkeun formula_9 nu mana umumna paraméter konstrain formula_5 mibanda formula_11 keur manggihkeun solusi trivial
Konstrain ieu ngahasilkeun prediktor nu sarua jeung di luhur ngan persamaan normal, mangka formula_12 nu mana indeks "i" antara 0 ka "p" sarta ukuran "R" nyaéta matriks ("p"+1) × ("p"+1)
Optimasi paraméter mangrupa topik luas sarta angka nu gedé mangrupa pendeketan séjén nu diusulkeun
métodeu autokorelasi leuwih ilahar sarta biasa digunakeun, contona, keur speech coding dina standar GSM
Solusi persamaan matriks "Ra" = "r" mangrupa prosés komputasi nu lumayan mahal
Gauss algorithm keur invers matrik bisa jadi mangrupa solusi heubeul tapi pamarekanieu teu epektip dipaké dina simetri "R" jeung "r"
Algoritma panggancangna ti Levinson recursion diusulkeun ku N. Levinson taun 1947, nu mangrupa solusi perhitungan bolak-balik
Pangahirna, Delsarte saparakanca ngusulkeun métodeu algoritma séjén nyaéta split Levinson recursion nu merlukeun satengah jumlah perkalian jeung pembagian
Ieu dipaké keur sipat simetri vektor paraméter diana tingkatan sub perhitungan
Dina statistik, lamun kulawarga densiti sebaran diparaméterisasi ku paraméter nilai -skalar atawa -vektor μ mangrupa bentuk "f"μ("x") = "f"("x" − μ) mangka μ disebut paraméter lokasi, sabab ieu nilai nangtukeun "lokasi" tina sebaran probabiliti
Kurva Lorenz diwangun ku Max O. Lorenz salaku grapik nu ngagambarkeun kateusajajaran pangala
Kurva bisa dipaké ogé keur ngukur kateusajajaran aset atawa sebaran séjénna
Dina diskusi panghasilan pribadi, urang remen nyebutkeun yen, "duapuluh persen sahandapeun sakabeh rumahtangga mibanda sapuluh persen total panghasilan"
Kurva Lorenz dumasar kana ieu "pernyataan"; unggal titik dina kurva ngagambarkeun unggal "pernyataan"
Kurva Lorenz mangrupa grafik nu nembongkeun, di handap x% rumahtangga, persentase y% total panghasilan no dipibanda
Persentase rumah tangga di plot dina sumbu x, persentasi panghasilan dina sumbu y. Sebaran panghasilan persis sarua di masarakat bakal jadi hiji di mana unggal jalma mibanda panghasilan nu sarua
Dina kasus ieu, handapeun N% masarakat bakal salawasna mibanda N% panghasilan
Mangka sebaran nu persis sarua digambarkeun ku garis lempeng y=x; bisa disebut yén ieu garis mangrupa garis persis sarua
Sebaran nu persis teusarua, sacara jelas, nyaéta saurang boga kabeg penghasilan sarta nu séjénna teu boga nanaon
Dina kasus eta, kurva bakal dina y=0 keur sakabrh x&lt;100, sarta y=100 waktu x=100
Garis dina kurva ieu disebut garis kateusaruaan sampurna
Catetan yén dumasar kana panghasilan (atawa naon baé nu bakal diukur) teu bisa negatip, mangka teu mungkin keur kurva Lorenz naek di saluhureun garis sarua sampurna, atawa nurun sahandapeun garis teusarua sampurna
Kurva kudu naek sarta konkav
Kurva Lorenz dipeke keur ngitung koefisien Gini, nu mana daerah antara garis sampurna jeung kurva, salaku persentasi daerah antara garis sarua sampurna jeung garis teu sarua sampurna
Tipikal kurva Lorenz bisa ditempo di handap ieu:
Dina statistik, téori kaputusan sarta ékonomi, loss function nyaéta fungsi nu metakeun hiji kajadian (sacara teknis hiji unsur dina rohangan sampel) kana wilangan riil keur ngagambarkeun biaya ekonomi atawa hanjelu pakait jeung hiji kajadian
"Loss functions" sacara tipikal digambarkeun dina watesan "keuangan" dumasar kana ukuran biaya nu mungkin, contona kalahiran jeung "kematian" dina widang public health
"Loss functions" are complementary to utility functions which represent benefit and satisfaction
Typically, for utility "U", loss is equal to "k"-"U", where "k" is some arbitrary constant
"Loss function" satisfies the definition of a random variable so we can establish a cumulative distribution function and an nilai ekspektasi
However, more commonly, the "loss function" is expressed as a function of some other random variable
For example, the time that a light bulb operates before failure is a random variable and we can specify the loss, arising from having to cope in the dark and/or replace the bulb, as a function of failure time
For a continuous random variable, "X" with probability density function "f"("x") and "loss function", λ("x"), the "expected loss" is: formula_1 Minimum "expected loss" is widely used as a criterion for choosing between prospects
It is closely related to the criterion of maximum "expected utility"
Loss functions in Bayesian statistics
One of the consequences of Bayesian inference is that in addition to experimental data, the loss function does not in itself wholly determine a decision
What is important is the relationship between the loss function and the prior probability
So it is possible to have two different loss functions which léad to the same decision when the prior probability distributions associated with éach compensate for the details of éach loss function
Combining the three elements of the prior probability, the data, and the loss function then allows decisions to be based on maximising the subjective expected utility, a concept introduced by Leonard J
He also argued that using non-Bayesian methods such as minimax, the loss function should be based on the idéa of regret, i.e
the loss associated with a decision should be the difference between the consequences of the best decision that could have been taken had the underlying circumstances been known and the decision that was in fact taken before they were known
Hukum Zipf-Mandelbrot (oge dipikanyaho minangka hukum Pareto-Zipf) nyaéta power-law distribution dina ranked data, dipaké sanggeus Harvard linguistic professor George Kingsley Zipf (1902-1950) nu ngusulkeun dina teks regularity, sarta mathematician Benoit Mandelbrot (lahir November 20, 1924), no nga-generalisir
Distribution kecap dirangking ku frequency-na dina random corpus text mangrupa power-law distribution umum, dipikanyaho minangka Zipf's law
Lamun hiji plot rangking frequency kecap dikandung dina corpus nu gedé tina data teks ka jumlah kajadian atawa frequencies sabenerna, meunangkeun power-law distribution, mibanda exponent raket ka hiji (tapi tempo Gelbukh jeung Sidoro 2001)
Koreksi Yates keur kontinyu, atawa "tes chi-kuadrat Yates", ngatur rumus keur uji kuadrat-chi Pearson nu ngurangan 0.5 tina unggal nilai dina tabel kontingensi 2 X 2
Rumus ieu dipaké lamun dina hiji sel dina tabel ngabogaan nilai ekspektasi kurang ti 5
Sumber séjén nyebutkeun yén koreksi ieu kudu dipaké lamun ekspektasi frekuensi kurang ti 10
An urn problem is an idéalized thought experiment in which some objects of réal interest (such as atoms, péople, cars, etc.)
are represented as colored balls in an urn or other container
One pretends to draw (remove) one or more balls from the urn; the goal is to determine the probability of drawing one color or another, or some other properties
Basic urn model
In this basic urn modél in probability theory, the urn contains "x" white and "y" black balls; one ball is drawn randomly from the urn and its color observed; it is then placed back in the urn, and the selection process is repéated
Possible questions that can be answered in this modél are: Other models
Many other variations exist: Historical remarks
Urn problems have been a part of the theory of probability since at léast the publication of the "Ars conjectandi" by Jakob Bernoulli (1713)
Bernoulli's inspiration may have been lotteries, elections, or games of chance which involved drawing balls from a container
It has been asserted that "Elections in medieval and renaissance Venice, including that of the doge, often included the choice of electors by lot, using balls of different colors drawn from an urn."
Bernoulli himself, in "Ars conjectandi", considered the problem of determining, from a number of pebbles drawn from an urn, the proportions of different colors
This problem was known as the "inverse probability" problem, and was a topic of reséarch in the eighteenth century, attracting the attention of Abraham de Moivre and Thomas Bayes
Dina statistik, kaasup dina jajal pamanggih sarta survey mirip, margin kasalahan nyaéta jari-jari interval kapercayaan—ilaharna 90% interval kapercayaan—keur populasi nu saimbang
Contona, tempo jumlah nu resep mangrupa hal nu saimbang keur pamilih nu milu ngajawab "enya" dina referendum
Sampel random pamilih tina populasi dicokot sarta manggihkeun yén 60% pamilih dina sampel bakal milih "enya"
Mangka estimasi saimbang tina sakabéh populasi nu bakal milih "enya" dicokot jadi 60%
Lamun 3% margin kasalahan dilaporkeun, hartina yén prosedur nu dipaké bakal 3% sarimbang jeung nu bakal diestimasi, 90% kali
Akibatna interval ti 57% ka 63% mangrupa 90% interval kapercayaan keur proporsi pamilih tina sakabéh populasi bakal ngajawab "enya"
Jari-jari interval nyaéta 3%; ieu nu disebut margin kasalahan
Kumaha cara ngitung margin kasalahan
Anggap "n" mangrupa jumlah pamilih dina sampel
Anggap ogé dicokot sacara random sarta bébas tina sakabéh pamilih
Ieu ngaharepkeun optimis, tapi angger kudu carincing dina nyokot sampel ngarah méré gambaran nu sabenerna
Anggap "p" mangrupa proporsi pamilih dina sakabéh populasi bakal ngajawab "enya"
Mangka jumlah pamilih "X" dina "sampel" nu bakal milih "enya" mangrupa variabel acak nu mibanda sebaran binomial nu paraméter-na "n" jeung "p"
Lamun "n" cukup gedé, mangka "X" ngadeukeutan sebaran normal nu mibanda nilai ekspektasi "np" sarta varian "np"(1 - "p")
Mangka formula_1 ngadeukeutan sebaran normal nu mibanda nilai ekspektasi 0 sarta varian 1
Nempo kana tabel persentase sebaran normal mangka nunjukkeun yén P(-1.645 &lt; Z &lt; 1.645) = 0.9, atawa, dina basa séjén, di dinya aya 90% kamungkinan kajadian
Mangka formula_2 Ieu sarua jeung formula_3
Dina statistik, méan kuadrat kasalahan tina estimator "T" dina paraméter nu teu ka-observasi θ nyaéta formula_1 dina hal ieu, mangrupa nilai ekspektasi kuadrat "kasalahan"
"Kasalahan" nyaéta jumlah nu mana éstimator béda jeung jumlah nu keur di-estimasi
Méan kuadrat kasalahan nyukupan identitas formula_2 di mana formula_3 dina hal ieu, the bias nyaéta lobana nu mana nilai ekspektasi tina éstimator béda keur jumlah nu teu ka-observasi nu keur di-estimasi
Anggap formula_4 dina hal ieu, ukran sampel random "n" tina populasi sebaran normal
Dua éstimators σ2 kadangkala dipaké (atawa nu séjénna): formula_5 nu mana formula_6 mangrupa "sampel mean"
Kahiji tina éstimator ieu nyaéta éstimator maximum likelihood, sarta bias, dina hal ieu, bias teu sarua jeung nol, tapi mibanda varian nu leuwih leutik tinimbang nu kadua, anu teu bias
Varian leutik tina akibat séjén keur bias, mangka méan kuadrat kasalahan tina bias éstimator leuwih leutik tinimbang éstimator unbiased
Dina statistika, tes nilai tengah atawa tes median mangrupa kasus husus dina uji kuadrat-chi Pearson
Tes null hypothesis nu median tina population tina dua samples digambarkeun identik
Data unggal sampe dibagi kana dua grup, hiji grup ngandung nilai data nu leuwih luhur tina median, sarta grup séjénna ngandung nilai data dina median atawa sahandapeunnana
Tes chi-kuadrat Péarson dipaké keur nangtukeun frékuénsi observasi dina unggal grup nu béda tina ekspektasi frékuénsi nu asalna tina kombinasi dua grup sebaran
Statistical power dina tes ieu kadangkala ditingkatkeun ku maké nilai séjén tinimbang median nu dihartikeun tina grup - hal ieu, ku maké nilai nu ngabagi grup kana nilai grup nu ampir sarua tinimbang median-na
Tes kacida kapakena waktu sebaran data béda tina normal, contona waktu raw score dina klasifikasi teu teratur kana "rentang pendekatan" nu dijieun
Ku kitu, ieu biasa dipaké salaku léngkah awal dina exploratory analysis
Dina tiori probabiliti, memorylessness nyaéta sipat penting sebaran probabiliti: sebaran eksponensial sarta sebaran geometrik
Suppose "X" is a discrete random variable whose values lie in the set { 0, 1, 2, ... } or in the set { 1, 2, 3, ... }
The probability distribution of "X" is memoryless precisely if for any "x", "y" in { 0, 1, 2, ... } or in { 1, 2, 3, ... }, (as the case may be), we have formula_1 It can réadily be shown that the "only" probability distributions that enjoy this discrete memorylessness are geometric distributions
These are the distributions of the number of independent Bernoulli trials needed to get one "success", with a fixed probability "p" of "success" on éach trial
Example and motivation for the name "memorylessness"
For example, suppose a die is thrown as many times as it takes to get a "1", so that the probability of "success" on éach trial is 1/6, and the random variable "X" is the number of times the die must be thrown
Then "X" has a géometric distribution, and the conditional probability that the die must be thrown at léast four more times to get a "1", given that it has alréady been thrown 10 times without a "1" appéaring, is no different from the original probability that the die would be thrown at léast four times
In effect, the random process does not "remember" how many failures have occurred so far
A frequent misunderstanding
Memorylessness is often misunderstood by students taking courses on probability: the fact that P("X" &gt; 16 | "X" &gt; 12) = P("X" &gt; 4) does "not" méan that the events "X" &gt; 16 and "X" &gt; 12 are independent; i.e., it does "not" méan that P("X" &gt; 16 | "X" &gt; 12) = P("X" &gt; 16)
To summarize: "memorlessness" of the probability distribution of the number of trials "X" until the first success méans formula_2 It does "not" méan formula_3 Continuous memorylessness
Suppose that rather than considering the discrete number of trials until the first "success", we consider continuous waiting time "T" until the arrival of the first phone call at a switchboard
To say that the probability distribtuion of "T" is memoryless méans that for any positive real numbers "s" and "t", we have formula_4 The only difference between this and the discrete version is that instéad of requiring "s" and "t" to be positive (or, in some cases, nonnegative) integers, thus achieving discreteness, we allow them to be réal numbers that are not necessarily integers
It can be shown that the only probability distributions that enjoy this continuous memorylessness are the sebaran eksponensial
Statistik matematis ngagunakeuntiori probabiliti sarta cabang séjén matematik pikeun ngulik statistik tina jihat matématis murni
Jadi, pikeun conto, hiji conto acak dituliskeun sabagé runtuyan variabel acak, formula_1 nu masing-masing nuturkeun hiji sebaran probabiliti nu tangtu (ilaharna dianggap independent and identically distributed|kasebar bebas sarta identik)
Sample mean digambarkeun salaku fungsi tina variabel, formula_2 sarta mangrupa variabel acak tina hiji sebaran
Ku jalan ngagunakeun ieu cara, statistik matematik mangrupa salah sahiji usaha keur ngabuktikeun téori-téori nu loba dipaké dina statistik terapan
Dina téori probabilitas, sebaran binomial négatip nyaéta anggota tina kulawarga sebaran probabilitas diskrit
Dina statistik, léma Neyman-Péarson nangtukeun yén waktu ngagawekeun tes hipotesa antara dua titik hipotesa "H"0: "θ"="θ"0 sarta "H"1: "θ"="θ"1, mangka likelihood-ratio test nu nolak "H"0 dina ngadukung "H"1 waktu formula_1 leuwih ilahar salaku tes power ukuran "α"
Métode kaputusan statistik Non-parametrik (atawa sebaran-bébas) mangrupa prosedur matematik keur tes hipotesa statistik, teu siga dina statistik parametrik, taya asumsi ngeunaan sebaran frekuensi tina variabel nu ditaksir
Pamakéan nu ilahar ieu métodeu nyaéta dina tes chi-kuadrat
Pamakéan séjén nu maké métodeu non-parametrik kaasup Mann-Whitney U, Kruskal-Wallis one-way analysis of variance, median test, Spearman's ρ, sarta estimasi sebaran maké sebaran binomial
kabéhanna "mungkin" leuwih mibanda statistical power tinimbang tes parametrik waktu asumsi dina kaayaan tes parametrik teu nyugemakeun
Tempo ogé statistik parametrik
Dina statistik, rankits titik data tina susunan data nu ngandung jejer skalar sederhana nyaéta nilai ekspektasi tina order statistik dina standar sebaran normal corresponding to data points in a manner determined by the order in which the data points appéar
This is perhaps most réadily understood by méans of an example
If an i.i.d
sample of six items is taken from a kasebar normal population with nilai ekspektasi 0 and varian 1 and then sorted into incréasing order, the expected values of the resulting order statistics are: formula_1 Suppose the numbers in a data set are 65, 75, 16, 22, 43, 40
The corresponding ranks are 5, 6, 1, 2, 4, 3, i.e., the number appéaring first is the 5th-smallest, the number appéaring second is 6th-smallest, the number appéaring third is smallest, the number appéaring fourth is 2nd-smallest, etc
One réarranges the expected normal order statistics accordingly, getting the rankits of this data set: formula_2 A graph ploting the rankits on the horizontal axis and the data points on the vertical axis is a rankit plot or normal probability plot
Such a plot is necessarily nondecréasing
In large samples from a normally distributed population, such a plot will approximate a straight line
Substantial deviations from straightness are considered evidence against normality of the distribution
The word rankit was introduced by the statistician Chester Bliss (not to be confused with the politician Chester Bliss Bowles)
Dina statistik spasial, semivarian dijelaskeun ku formula_1 nu mana "z" mangrupa nilai data tina sabagian lokasi, "h" nyaéta jarak antara nilai data, sarta "n"("h") dianggap angka pasangan nilai data dibérékeun, spasi jarak tina bagian "h"
Pot semivarian ka jarak antara data nilai dipikanyaho salaku semivariogram, atawa keur gampang nyebutna variogram
Topik pakait: géostatistik Rujukan:
A series of méasurements of a process may be tréated as a deret waktu, and then trend estimation is the application of statistical techniques to maké and justify statements about trends in the data
Assuming the underlying process is a physical system that is incompletely understood, one may thereby construct a modél, independent of anything known about the physics of the process, to explain the behaviour of the méasurement
In particular, one may wish to know if the méasurements exhibit an incréasing or decréasing trend, that can be statistically distinguished from random behaviour
For example, take daily average temperatures at a given location, from winter to summer; or the global temperature series over the last 100 yéars
Particularly in that latter case, issues of homogeneity (is the series equally reliable throughout its length?)
For the moment we shall simplify the discussion and neglect those points
This page does not attempt a full mathematical tréatment, merely an exposition
Fitting a trend: least-squares
Given a set of data, and the desire to produce some kind of "model" of that data (modél, in this case, méaning a function fitted through the data) there are a variety of functions that can be chosen for the fit
But if there is no prior understanding of the data, the simplest function to fit is a straight line and thus this is the "default"
Continuing, once it has been decided to fit a straight line, there are various ways to do so, but the overwhelming default is the léast-squares fit, equivalent to minimisation of the "L"2 norm
See least squares
Thus, given a set of data points formula_1, and data values formula_2, one choses formula_3 and formula_4 so that formula_5 is minimised
This can always be done, in closed form
For the rest of this article, "trend" will méan the léast squares trend
It's what it méans in 99% of cases everywhere else
Now, we have a trend
But is it significant
And what do we méan by significant
Tren dina data random
saméméh urang nempo kana tren data riil, kudu ngarti heula tren dina data random
If we take a series which is known to be random - fair dice falls; or computer-generated random numbers - and fit a trend line through the data, the chances of a truly zero trend are negligible
But we would probably expect the trend to be "small"
If we take a series with a given degree of noise, and a given length (say, 100 points), and generate a large number of such series (say, 100,000 series), we can then calculate the trends from these 100,000 series, and empirically establish a distribution of trends that are to be expected from such random data - see diagram
Such a distribution will be normal (Central limit theorem except in pathological cases, since (in a slightly non-obvious way of thinking about it) the trend is a linéar combination of the formula_2) and (if the series genuinely is random) centered on zero
We may now establish a level of statistical certainty, formula_7, desired - 95% confidence is typical; 99% would be stricter, 90% rather looser - and say: what value, formula_8, do we have to choose so that formula_7% of trends are within formula_8
(complication: we may be interested in positive and negative trends - 2-tailed - or may have prior knowledge that only positive, or only negative, trends are of interest)
In the above discussion the distribution of trends was calculated empirically, from a large number of trials
In simple cases (normally distributed random noise being a classic) the distribution of trends can be calculated exactly
Suppose we then take another series with approximately the same variance properties as our random series
We do not know in advance whether it "really" has a trend in it, so we calculate the trend, formula_11, and discover that it is less than formula_8
Then we may say that, at degree of certainty formula_7, any trend in the data cannot be distinguished from random noise
However, note that whatever value of formula_7 we choose, then a given fraction, formula_15, of truly random series will be declared (falsely, by construction) to have a significant trend
Conversely, a certain fraction of series that "really" have a trend will not be declared to have a trend
Data as trend plus noise
To analyse a (time) series of data, we assume that it may be represented as trend plus noise: formula_16 where formula_3 and formula_4 are (usually unknown) constants and the formula_19's are independent randomly distributed "errors"
Unless something special is known about the formula_19's, they will be assumed to have a normal distribution
It is simplest if the formula_19's all have the same distribution, but if not (if some have higher variance, méaning that those data points are effectively less certain) then this can be taken into account during the léast squares fitting, by weighting éach point by the inverse of the variance of that point
In most cases, where only a single time series exists to be analysed, the variance of the formula_19's is estimated by fitting a trend, thus allowing formula_23 to be removed and léaving the formula_19's as residuals, and calculating the variance of the formula_19's from the residuals — this is often the only way of estimating the variance of the formula_19's
One particular special case of gréat interest, the (global) temperature time series, is known not to be homogenéous in time: apart from anything else, the number of wéather observations has (generally) incréased with time, and thus the error associated with estimating the global temperature from a limited set of observations has decréased with time
In fitting a trend to this data, this can be taken into account, as described above
Once we know the "noise" of the series, we can then assess the significance of the trend by making the "null hypothesis" that the trend, formula_3, is not significantly different from 0
From the above discussion of trends in random data with known variance, we know the distribution of trends to be expected from random (trendless) data
If the calculated trend, formula_3, is larger than the value, formula_8, then the trend is deemed significantly different from zero at significance level formula_7
Noisy time series, and an example
It is harder to see a trend in a noisy time series
For example, if the true series is 0, 1, 2, 3 all plus some independent normally distributed "noise" formula_19 of standard deviation formula_32, and we have a sample series of length 50, then if formula_33 the trend will be obvious; if formula_34 the trend will probably be visible; but if formula_35 the trend will be buried in the noise
If we consider a concrete example, the global surface temperature record of the past 140 yéars as presented by the IPCC: , then the interannual variation is about 0.2 °C and the trend about 0.6 °C over 140 yéars, with 95% confidence limits of 0.2 °C (by coincidence, about the same value as the interannual variation)
Hence the trend is statistically different from 0
This alone, however, tells us nothing about the physical causes of the temperature change
Goodness of fit (R-squared) and trend
The léast-squares fitting process throws out a value - r-squared - which is the square of the residuals of the data after the fit
It says what fraction of the variance of the data is explained by the fitted trend line
Is does not relate to the significance of the trend line - see graph
A noisy series can have a very low r2 value but a very high significance of fit
Often, filtering a series incréases r2 whilst making little difference to the fitted trend or significance
Real data is auto-correlated
The above discussion assumed the data could be represented as trend + noise, with the noise at éach data point being "independent"
This is important, as it makes an enormous difference to the éase with which the statistics can be analysed
réal (climate) data rarely fulfills this criterion
["This section in need of expansion: examples."]
Ogé katelah wates toléran (Ing
Pamakéan rentang toléran
Rentang toléran patali jeung rékayasa wates toléran
Sacara husus, rékayasa wates toléran nangtukeun niléy maksimum jeung minimum pikeun hiji produk sangkan bisa lumaku
Rékayasa wates toléran bisa ditangtukeun maké "Geometric Dimensioning and Tolerancing"
Rentang tolérans mangrupa dasar keur chart kontrol dina sababaraha rupa
Statistik interval tolérans (atawa watés) dihasilekun tina mroses data
Lobana ieu interval gumantung kana prosésna
Rentang toléran dihartikeun salaku kamampuan prosés keur nangtukeun nilai minimum jeung maksimum
Nilai wates dina ieu wewengkon mibanda bagéan nu sarimbag jeung sakabéh populasi sarta mibanda probabiliti atawa kapercayaan husus
Tempo The NIST/SEMATECH e-Handbook of Statistical Methods, 2004 July 17
Dina bagian Section 7.2.6.3 - Tolerance intervals for a normal distribution Tempo "Quality Control Handbook", Juran
métodeu Taguchi nyaéta métodeu statistik nu diwangun ku Genichi Taguchi keur ningkatkeun kualitas produksi pabrik
"Metoda Taguchi" mangrupa hal nu kontroversi keur statistikawan urang kulon
Prinsip Taguchi nu mangaruhan kana statistik nyaéta
Dina statistik, outlier nyaéta hiji observasi nu jauh tina data nu keur ditempo
Harti "jauh tina" di hal ieu nyaéta: kurang ti "Q1" − 1.5 × "IQR" atawa leuwih ti "Q3" + 1.5 × "IQR" nu mana "Q1" sarta "Q3" kuartil kahiji jeung katilu, sarta "IQR" interquartile range (sarua jeung "Q3" − "Q1")
Nilai ieu ngahartikeun yén hartina aya dina "jero pager", saluareun éta observasi bisa dingarananmild outlier
Outliers ekstrim nyaéta observasi ayana "saluareun pager": kurang ti "Q1" − 3 × "IQR" atawa leuwih ti "Q3" + 3 × "IQR" Dina kasus data kasebar normal, maké harti di luhur, ngan 1 tina 150 observasi bakal aya "mild outlier" sarta ngan 1 tina 425,000 aya "outlier ekstrim"
"Outliers" ilaharna merlukeun perhatian saprak nembongkeun masalah dina sampling atawa kumpulan data atawa transkrip
Alternatipna, outlier bisa jadi hasil, contona, respon nu teu umum kana "perlakuan" nu ditempo, nu jadi perhatian "peneliti"
Ahmad Hassan Zewail (Basa Arab: أحمد زويل) (wedal 26 Pébruari 1946) kimiawan urang Mesir, dilélér Hadiah Nobel widang Kimia taun 1999 pikeun karyana ngeunaan fémtokimia
Lahir di Damanhur (60 km kidul-wétaneun Iskandariah) sarta digedékeun di Disuq, anjeunna nampa gelar kahijina ti Universitas Iskandariah méméh pindah ka US pikeun ngaréngsékeun PhD-na di University of Pennsylvania
Sanggeus sababaraha karya posdoktorat di UC Berkeley, anjeunna dileler a faculty appointment di Caltech taun 1976, where he has remained since
In 1990 he was made the first "Linus Pauling Chair in Chemical Physics"
Karya penting Zewail nyaéta mitambeyan fémtokimia - ulikan réaksi kimiawi dina jangka waktu fémtodetik
ngagunakeun téhnik laser nu gancang (céntangan laser pondok kacida)
Taun 1999, Zewail jadi urnag Mesir katilu nu nampa Hadiah Nobel, nuturkeun Anwar Sadat (1978 in Péace) jeung Naguib Mahfouz (1988 widang Sastra)
Pangleler internasional séjénna di antarana Hadiah Wolf (1993) jeung Robert A. Welch Award (1997)
Taun 1999 anjeunna nampa panghargaan nagara pangluhurna, Grand Collar of the Nile
Ahmed H. Zewail
Kalsium mangrupa unsur kimiawi na tabel periodik nu lambangna Ca sarta wilangan atom 20
Kalsium is a soft grey alkaline earth metal nu dipaké salaku agén pangréduksi na ékstraksi thorium, zirconium, jeung uranium
Unsur ieu ogé mangrupa unsur kalima nu paling ngaleuyah na kulit Marcapada
Penting pikeun organisme hirup, utamana dina fisiologi sél
Kalsium téh unsur teuas nu dimurnikeun ku jalan éléktrolisis kalsium fluorida, nu mun kaduruk seuneuna konéng-héjo, sarta ngabentuk nitrida bodas mun keuna ku udara
Dina cai, kalsium bakal jadi kalsium hidroksida
Kalsium téh salah sahiji komponén penting katuangan, kurang asupanana bisa ngabalukarkeun gangguan formasi tulang jeung huntu
Tapi konsumsi kalsium gé ulah nepi ka loba teuing, sabab bisa ngabalukarkeun batu ginjal
Kalsium bisa diserep ku peujit mun aya Vitamin D. Pikeun leuwih lengkep ngeunaan Ca dina kahirupan, mangga aos kalsium dina biologi
(Latin calx, lime) Lime was prepared and used by the Romans as éarly as the 1st century, but calcium was not discovered until 1808
After léarning that Berzelius and Pontin prepared calcium amalgam by electrolyzing lime in mercury, Sir Humphry Davy was able to isolate the impure metal
Calcium is the fifth most abundant element in the éarth's crust (forming more than 3%) and is an essential part of léaves, bones, teeth, and shells
Due to its chemical réactivity with air and water, calcium is never found in nature unbound to Apatite is the fluorophosphate or chlorophosphate of calcium
Electrolysis of molten calcium chloride (CaCl2) can be used to isolate pure calcium
"Isolation" (* follow): cathode: Ca2+* + 2e- --&gt; Ca anode: Cl-* --&gt; ½Cl2 (gas) + e- Compounds
Quicklime (CaO) is used in many chemical refinery processes and is made by héating and carefully adding water to limestone
When CaO is mixed with sand it hardens into a mortar and is turned into plaster by carbon dioxide uptake
Mixed with other compounds, CaO forms an important part of Portland cement
When water percolates through limestone or other soluble carbonate rocks, it partially disolves part of the rock and causes cave formation and characteristic stalactites and stalagmites and also forms hard water
Other important calcium compounds are nitrate, sulfide, chloride, carbide, cyanamide, and hypochlorite
Kalsium boga genep isotop stabil, dua di antarana aya di alam: Ca-40 stabil jeung Ca-41 radioaktif nu umur-satengahna = 103.000 taun
97% unsur ieu aya dina wujud Ca-40
Ca-40 téh turunan tina luruhna K-40, nu ogé ngahasilkeun Ar-40
"Baca ogé": gangguan métabolisme kalsium
Rasio ganjil nyaéta ukuran statistik, bagéan penting dina statistika Bayes sarta régrési logistik
Rasio ganjil dihartikeun salaku rasio hiji kajadian ahéng dina hiji grup kana kaganjilan nu kajadian dina grup séjén, atawa estimasi data dumasar kana rasio
Grup ieu bisa awewe jeung lalaki, grup percobaan sarta grup kontrol, atawa klasifikasi nu ngabingungkeun
Maka lamun kamungkinan kajadian unggal grup "p" jeung "q" mangka rasio-ganjil nyaéta formula_1 Logaritma rasio ganjil mangrupa béda logit tina probabilitas
Régrési logistik loba dipaké dina widang kadokteran jeung panalungtikan élmu sosial, hartina "rasio-ganjil" ilahar dipaké geus ngagambarkeun sababaraha bentuk uji klinis, saperti uji kasus-kontrol, sarta dina panalungtikan survéy
Jajal pamanggih mangrupa surveys pamanggih maké sampling
Hal ieu dijieun keur ngagambarkeun pamanggih tina populasi ku méré patarosan ka sajumlah leutik anggota populasi sarta nga-ekstrapolasi jawaban kana grup nu leuwih gedé
Sakabéh jajal mibanda margin kasalahan, nu mangrupa fungsi tina jumlah anggota nu ngajajal
Margin kasalahan ngagambarkeun kamungkinan kasalahan dina prosés sampling, tapi teu ngagambarkeun sumber kasalahan, saperti ukuran kasalahan atawa kasalahan dina prosés data
Jajal nu mibanda sampel 500 anggota mibanda margi kasalahan 4.5% keur estimasi persentese tina sakabéh populasi
Margin kasalahan 4.5% hartina yén 95% tina waktu prosedur nu dipaké bakal méré estimasi dina 4.5% persentase nu keur di-estimasi
Saprak anggota nu milu dina jajal nolak, sampel jajal teu ngagambarkeun sampel dina populasi, sarta karakter matematikna ditandaan ku béda tina populasi
Margin kasalahan béda jeung persentase estimasi, sarta persentase estimasi tanda béda tina populasi, margin kasalahan dina hasil jajal teu ngagambarkeun populasi nu sabenerna
Milih kalimah sarta urutan patarosan dina jajal pamanggih kacida perlu, ieu bisa mangaruhan kana hasil jajal pamanggih
Thus comparisons between polls often boil down to the wording of the question
One way in which pollsters attempt to minimize this effect is to ask the same set of questions over time, in order to track changes in opinion
The most effective controls, used by attitude reséarchers, are: These controls are not widely used in the polling industry... Nonrepresentative samples
Another source of error is the deliberate or accidental use of nonrepresentative samples
For example, when home telephones were rare, telephone sampling had a built-in error because most of those surveyed were well-to-do
Péople asked to participate in opinion polls also have the right to refuse; this méans that the sample is self-selected and consequently a non-probability sample
The validity of the results and of the statistical techniques used to derive characteristics of the sample such as the margin of error are therefore highly questionable
There are many polling organizations
The most famous is the Gallup poll, créated by George Gallup
Other major polling organizations in the United States include: Quinnipiac Polls, run by the University of Connecticut, and started as a student project
The Pew Charitable Trusts conducts polls concentrating on media and political beliefs
The Harris Poll Nielsen Ratings, virtually always for television
All the major television networks, alone or in conjunction with the largest newspapers or magazines, in virtually every country with elections, operate polling operations, alone or in groups
The best-known failure of opinion polling to date in the United States was the prediction that Thomas Dewey would deféat Harry S. Truman in the 1948 Presidential election
Major polling organizations, including Gallup and the Roper Center, indicated a landslide victory for Dewey
Dina statistik, order statistik ka-"n" tina sampel saruna jeung nilai sampel ka-"n" pangleutikna
Contona, lamun nilai sampe nyaéta: 6, 9, 3, 8 mangka order statistik kadua nyaéta: "x"(2) = 6
Order statistik kahiji (atawa "order statistik pangleutikna") salawasna "minimum" tina sampel
Keur ukuran sampel "n", order statistik ka-"n" (atawa "order statistik panggedéna") nyaéta "maximum"
Dina notasi konvensional, ditulis: "x"1 = 6 "x"2 = 9 "x"3 = 3 "x"4 = 8 teu maké kurung() dina "subscripts", dumasar kana urutan data nu dikumpulkeun, sarta: "x"(1) = 3 "x"(2) = 6 "x"(3) = 8 "x"(4) = 9 make kurung () dina "subscripts", dumasar kana order statistik, dina hal ieu, data disusun dumasar kana naekna order
"Beda jeung quantiles..."
Dina statistik, overfitting nyaéta modél statistik keur nyocogkeun niley nu mibanda sababaraha paraméter
modél "absurd" sarta falsu bakal cocog sacara sampurna lamun ieu modél mibanda karudetan nu cukup dibandingkeun jeung jumlah data nu aya
Overfitting ilaharna diwangun ku susunan Occam's razor
Widang anyar nu keur ilahar dipaké dina konsép overfitting nyaéta "machine learning"
Ilaharna algorithm diajar nyaéta ngajarkeun ku ngagunakeun sababaraha susunan latihan, upamana ngagunakeun sababaraha kaayaan nu hasil ahirna geus dipikawanoh
Nu diajar nganggap yén ngaramalkeun yén hasil nu bakal kahontal bakal nembongkeun hasil nu bener lamun dipaké kana conto séjénna, ku sabab kitu kaayaan umum ieu teu katembong salila diajarkeun (dumasar kana "inductive bias")
Sanajan kitu, umumna dina kasus nu aya salila diajar ngabutuhkeun waktu nu lila atawa conto latihan nu kawilang langka, nu diajar bakal ngadeukeutkeun manéh kana sababaraha hal husus variabel acak salila diajar, nu taya hubungan baraya jeung fungsi target nu bakal kahontal
Dina prosés overfitting ieu, hasil nu ditembongkeun dina nu diajar masih alus sedengkeun hasil dina data nu teu katempo bakal leuwih goreng
Boh dina statistik jeung machine learning, dina usaha keur meunang hasil nu cocog, perlu ditambahkeun téhnik séjénna(upamana validasi silang, "early stopping"), nu bisa nembongkeun yén léngkah diajar saterusna lain dihasilkeun tina ka-ilaharan nu panghadéna
Dina "treatment learning", niley minimum nu ngadukung pangalusna nu dipaké keur nangtukeun niley nu cocog dina overfitting
Rangking persentil tina skor nyaéta perséntase skor panghandapna tina sebaran frekuensina
Conto, skor uji leuwih ti 90% tina skor nu dicokot tina uju maka bakal disebutkeun dina persentil ka-90
Rangking persentil ilaharna dipaké keur ngajelaskeun interpretasi skor dina uji standar
Lamun sebaran ieu kasebar normal, rangking persentil bisa dicokot tina skor standar
métodeu kaputusan statistik parametrik mangrupa prosedur matematik keur tes hipotesa statistik nu nganggap yén sebaran variabel bakal bisa ditaksir ku karakter nu ditempo
Analisa varian nganggap yén dina kaayaan sebaran normal sarta varian tina sebaran nu dibandingkeun dianggap sarua
Koefisien korelasi momen-produk Pearson dianggap normal
Kadangkala tenknik parametrik mangrupa hal nu kuat – hal ieu, ku nahankeun tetempoan kana power keur ngalacak béda atawa sarua waktu ieu asumsi kalanggar – sababaraha sebaran ngalanggar asumsi mangka ditandaan salaku statistik non-parametrik, alternatip nu leuwih ilahar dipaké keur ngalacak béda atawa sarua
Interpolasi Pareto mangrupa métodeu interpolasi nonlinier keur manggihkeun median tina susunan data
Ilahar dipaké dina widang ekonomi keur ngagambarkeun analisa panghasilan
Anggapan nu dipaké yén data nuturkeun kurva nu disebut sebaran Pareto
Median dirumuskeun ku formula_1 nu mana paraméter κ jeung θ dirumuskeun ku: formula_2 sarta formula_3 nu mana "a" = wates handap kategori nu ngandung median "b" = wates luhur kategori nu ngandung median "P""a" = proporsi sebaran nu katutup di handapeun wates handap "P""b" = proporsi sebaran nu katutup di handapeun wates handap
Dina matematik, sarta dina sabagéan statistik, the Pearson product-moment correlation coefficient ("r") is a méasure of how well a linear equation describes the relation between two variables "X" and "Y" méasured on the same object or organism
It is defined as the sum of the products of the skor standard of the two méasures divided by the degrees of freedom: formula_1 The result obtained is equivalent to dividing the covariance between the two variables by the product of their standard deviations
In general the quantity of a correlation coefficient is the square root of the coefficient of determination ("r2"), which is the ratio of explained variation to total variation: formula_2 where: Y = a score on a random variable "Y" Y' = corresponding predicted value of "Y", given the correlation of "X" and "Y" and the value of "X" formula_3 = mean of "Y" The
formula_3 = mean of "Y" The correlation coefficient adds a sign to show the direction of the relationship
The formula for the Péarson coefficient conforms to this definition, and applies when the relationship is linéar
The coefficient ranges from -1 to 1
A value of 1 shows that a linéar equation describes the relationship perfectly and positively, with all data points lying on the same line and with "Y" incréasing with "X"
A score of -1 shows that all data points lie on a single line but that "Y" incréases as "X" decréases
A value of 0 shows that a linéar modél is inappropriate – that there is no linéar relationship between the variables
The Péarson coefficient is a statistic which estimates the correlation of the two given random variables
The linéar equation that best describes the relationship between "X" and "Y" can be found by linear regression
If "X" and "Y" are both normally distributed, this can be used to "predict" the value of one méasurement from knowledge of the other
That is, for éach value of "X" the equation calculates a value which is the best estimate of the values of "Y" corresponding the specific value of "X"
We denote this predicted variable by "Y"
Any value of "Y" can therefore be defined as the sum of "Y" and the difference between "Y" and "Y": formula_4 The varian of "Y" is equal to the sum of the variance of the two components of "Y": formula_5 Since the coefficient of determination implies that "sy.x2" = "sy2"(1 − "r2") we can derive the identity formula_6 The square of "r" is conventionally
The square of "r" is conventionally used as a méasure of the strength of the association between "X" and "Y"
For example, if the coefficient is .90, then 81% of the variance of "Y" is said to be explained by the changes in "X" and the linéar relation between "X" and "Y"
"r" is a statistik parametrik
It assumes that the variables being assessed are normally distributed
If this assumption is violated, a non-parametric alternative such as Spearman's ρ "may" be more successful in detecting a linéar relationship
Dina statistik jeung téori probabilitas, sebaran Poisson nyaéta sebaran probabilitas diskrét (dipanggihkeun ku Siméon-Denis Poisson (1781-1840) sarta dipublikasikeun, babarengan jeung téori probabilitas, taun 1838 dina makalahna "Recherches sur la probabilité des jugements en matiéres criminelles et matiére civile") dumasar kana variabel acak "N" nu diitung, di antara nu séjénna, wilangan kajadian diskrit (kadang kala disebut "datang") nu dicokot salila interval time nu panjang dibéré
Probabilitas nu mana kajadian "k" pasti ("k" salila natural number kaasup 0, "k" = 0, 1, 2, ...) nyaéta: formula_1 nu mana: Proses Poisson
Kadangkala formula_6 dijadikeun "laju", dina hal ieu, wilangan rata-rata kajadian per satuan waktu