Lapultság

Az X valószínűségi változó lapultsága vagy lapultsági mutatója (esetenként csúcsossága vagy csúcsossági együtthatója) lényegében azt fogalmazza meg, hogy a valószínűségi változó sűrűségfüggvényének "csúcsossága" vagy "lapossága" hogyan viszonyul a normális eloszláséhoz. A precíz matematikai megfogalmazás a következő: az m várható értékű X valószínűségi változó lapultsága az

${\frac {\mathbf {E} \left[(X-m)^{4}\right]}{(\mathbf {E} \left[(X-m)^{2}\right])^{2}}}-3$

kifejezés értékével egyenlő, ahol E[·] a várható értéket jelöli. Úgy is fogalmazhatjuk, hogy a lapultság a negyedik centrális momentum és a variancia négyzetének a hányadosánál pont hárommal kisebb szám.

A lapultságot a magyar szakirodalom nem egységesen jelöli: időnként β₂-vel, máskor γ₂-vel.

Szemléletesen úgy jellemezhetjük ezt a mutatót, hogy

normális eloszlás esetén β₂ = 0
normális eloszlás "haranggörbe"-szerű sűrűségfüggvényénél "csúcsosabb" sűrűségfüggvényű eloszlások esetén β₂ > 0,
annál "laposabb" sűrűségfüggvényű eloszlások esetén β₂ < 0.

Források

Fazekas I. (szerk.) (2000): Bevezetés a matematikai statisztikába. Kossuth Egyetemi Kiadó, Debrecen.
Hunyadi L. - Vita L. (2006), Statisztika közgazdászoknak, KSH, ISBN 963-215-742-7
Michelberger P. – Szeidl L. – Várlaki P. (2001): Alkalmazott folyamatstatisztika és idősor-analízis. Typotex Kiadó, Budapest.
Vargha A. (2000): Matematikai statisztika pszichológiai, nyelvészeti és biológiai alkalmazásokkal. Pólya Kiadó, Budapest.

Read other articles:

كرة القدم في دورة الألعاب العربية 1965

يفتقر محتوى هذه المقالة إلى الاستشهاد بمصادر. فضلاً، ساهم في تطوير هذه المقالة من خلال إضافة مصادر موثوق بها. أي معلومات غير موثقة يمكن التشكيك بها وإزالتها. (ديسمبر 2018) مسابقة كرة القدم في دورة الألعاب العربية 1965تفاصيل المسابقةالبلد المضيفالجمهورية العربية المتحدةالتوار...

العلاقات العراقية اللاتفية

العلاقات العراقية اللاتفية العراق لاتفيا العراق لاتفيا تعديل مصدري - تعديل العلاقات العراقية اللاتفية هي العلاقات الثنائية التي تجمع بين العراق ولاتفيا.[1][2][3][4][5] مقارنة بين البلدين هذه مقارنة عامة ومرجعية للدولتين: وجه المقارنة الع�...

Arab Indonesian cuisine

Cuisine of the people of Arab Indonesians This article is part of the series onIndonesian cuisineMasakan Indonesia National dishes Gado-gado Nasi goreng Rendang Satay Soto Tumpeng Regional and cultural cuisines Acehnese Arab Balinese Banjarese Batak Betawi Chinese Gorontalese Indian Indo Javanese Madurese Makassarese Malay Minahasan Minangkabau Palembangese Peranakan Sundanese Ingredients Bumbu Condiments Peanut sauce Sambal Santan Types of food Foods Dishes Noodles Soups Desserts Snacks Kue ...

إيغور يغوروف

إيغور يغوروف معلومات شخصية الميلاد 4 نوفمبر 1968 (العمر 55 سنة)نيجني نوفغورود مركز اللعب وسط الجنسية روسيا الاتحاد السوفيتي معلومات النادي النادي الحالي نادي ينيسي كراسنويارسك [لغات أخرى]‏ (director) مسيرة الشباب سنوات فريق 1975–1984 DYuSSh-8 Gorky المسيرة الاحترافية1 سنوات فر�...

SMK Negeri 2 Bawang

Artikel ini tidak memiliki referensi atau sumber tepercaya sehingga isinya tidak bisa dipastikan. Tolong bantu perbaiki artikel ini dengan menambahkan referensi yang layak. Tulisan tanpa sumber dapat dipertanyakan dan dihapus sewaktu-waktu.Cari sumber: SMK Negeri 2 Bawang – berita · surat kabar · buku · cendekiawan · JSTOR SMK Negeri 2 Bawang adalah sebuah Sekolah Menengah Kejuruan di Kabupaten Banjarnegara. Lokasi SMK Negeri 2 Bawang adalah di jalan r...

Alar Karis

Alar Karis Presiden EstoniaPetahanaMulai menjabat 11 Oktober 2021Perdana MenteriKaja KallasPendahuluKersti KaljulaidPenggantiPetahanaDirektur Museum Nasional EstoniaMasa jabatan9 April 2018 – 7 September 2021PendahuluTõnis LukasPenggantiKertu Saks Informasi pribadiLahir26 Maret 1958 (umur 66)TartuPartai politikIndependenSuami/istriSirje Karis (m. 1977)Anak3Alma materEstonian University of Life SciencesSunting kotak info • L • B...

Carolingian Empire

Frankish empire in Western and Central Europe (800–887) Carolingian EmpireImperium Romanum, Universum Regnum, Romanorum sive, Francorum Imperium, Imperium Christianum (Latin)800–887The Carolingian Empire at its greatest extent in 814 Frankish realms and marches Tributary states CapitalMetz,[1] AachenOfficial languagesMedieval LatinCommon languagesFrankishOld FrenchOld Low GermanOld High GermanOld DutchOld FrisianGallo-Italic languagesOld Occi...

趙家驤

追晉陸軍二級上將趙家驤將軍个人资料出生1910年大清河南省衛輝府汲縣逝世1958年8月23日(1958歲—08—23)（47—48歲） † 中華民國福建省金門縣国籍中華民國政党中國國民黨获奖青天白日勳章（追贈）军事背景效忠中華民國服役國民革命軍中華民國陸軍服役时间1924年－1958年军衔二級上將（追晉）部队四十七師指挥東北剿匪總司令部參謀長陸軍�...

National Defence University of Malaysia

Military university in Malaysia This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed.Find sources: National Defence University of Malaysia – news · newspapers · books · scholar · JSTOR (May 2017) (Learn how and when to remove this template message) National Defence University of MalaysiaUniversiti Pertahanan Nasional MalaysiaS...

Eberhard III de Wurtemberg

Pour les articles homonymes, voir Eberhard de Wurtemberg (homonymie). Pour les autres membres de la famille, voir Maison de Wurtemberg. Eberhard III de WurtembergEberhard III de Wurtemberg et son conseilFonctionComte de WurtembergTitre de noblesseComteBiographieNaissance 1364StuttgartDécès 16 mai 1417GöppingenSépulture Église collégiale de StuttgartNom dans la langue maternelle Eberhard III. von WürttembergFamille Maison de WurtembergPère Ulrich du WurtembergMère Élisabeth de ...

الصين في الألعاب الأولمبية الصيفية 2012

يفتقر محتوى هذه المقالة إلى الاستشهاد بمصادر. فضلاً، ساهم في تطوير هذه المقالة من خلال إضافة مصادر موثوق بها. أي معلومات غير موثقة يمكن التشكيك بها وإزالتها. (فبراير 2016) الصين في الألعاب الأولمبية علم الصين رمز ل.أ.د. CHN ل.أ.و. اللجنة الأولمبية الصينية موقع الويبwww.o...

Nottingham West (UK Parliament constituency)

Parliamentary constituency in the United Kingdom, 1955–1983 Nottingham WestFormer Borough constituencyfor the House of Commons1955–1983SeatsoneCreated fromNottingham Central and Nottingham North WestReplaced byNottingham South and Nottingham North[1]1885–1950Seatsone Nottingham West was a borough constituency in the city of Nottingham. It returned one Member of Parliament (MP) to the House of Commons of the Parliament of the United Kingdom. The constituency was created for the 1...

Maurice A. Donahue

American politician Maurice A. DonahueDonahue, circa 1960-1968President of the Massachusetts SenateIn office1964–1971Preceded byJohn E. PowersSucceeded byKevin B. HarringtonMember of the Massachusetts Senate from the 2nd Hampden DistrictIn office1951–1971Preceded byWilliam E. NolanSucceeded byRoger L. Bernashe Personal detailsBorn(1918-09-21)September 21, 1918Holyoke, MassachusettsDiedJanuary 13, 1999(1999-01-13) (aged 80)Political partyDemocraticRelationsMartin J. Dunn (nephew)[...

Division of Chifley

Australian federal electoral division Australian electorate ChifleyAustralian House of Representatives DivisionDivision of Chifley in New South Wales, as of the 2016 federal electionCreated1969MPEd HusicPartyLaborNamesakeBen ChifleyElectors121,385 (2022)Area126 km2 (48.6 sq mi)DemographicOuter metropolitan The Division of Chifley is an Australian electoral division in the state of New South Wales. Chifley is located in outer western Sydney. It includes Rooty Hill, Doonside...

Renormalization

Method in physics used to deal with infinities Renormalization and regularization RenormalizationRenormalization group On-shell scheme Minimal subtraction scheme RegularizationDimensional regularization Pauli–Villars regularization Lattice regularization Zeta function regularization Causal perturbation theory Hadamard regularization Point-splitting regularization vte Quantum field theoryFeynman diagram History Background Field theory Electromagnetism Weak force Strong force Quantum mechanic...

Brotherhood of Railroad Trainmen

Former railroad union in the U. S. Brotherhood of Railroad Brakemen redirects here. Not to be confused with Brakemen's Brotherhood. Brotherhood of Railroad TrainmenMerged intoUnited Transportation UnionFoundedJune 1883Dissolved1 January 1969HeadquartersCleveland, OhioLocationInternational The Brotherhood of Railroad Trainmen (BRT) was a labor organization for railroad employees founded in 1883. Originally called the Brotherhood of Railroad Brakemen, its purpose was to negotiate contracts...

Lega Basket Serie A

Top men's basketball league in Italy Basketball leagueLega Basket Serie AFounded1920; 104 years ago (1920)First season1920–21CountryItalyFederationLega BasketConfederationFIBA EuropeNumber of teams16Level on pyramid1Relegation toSerie A2Domestic cup(s)Coppa ItaliaSupercupSupercoppaInternational cup(s)EuroLeagueEuroCupChampions LeagueEurope CupCurrent championsOlimpia Milano (31st title) (2023–24)Most championshipsOlimpia Milano (31 titles)All-time top scorerAntonello Riv...

Gioachino Rossini

Italian opera composer (1792–1868) Rossini redirects here. For other uses, see Rossini (disambiguation). Rossini as a young man, c. 1810–1815 Gioachino[n 1] Antonio Rossini[n 2] (29 February 1792 – 13 November 1868) was an Italian composer who gained fame for his 39 operas, although he also wrote many songs, some chamber music and piano pieces and some sacred music. He set new standards for both comic and serious opera before retiring from large-scale composition w...

Five points determine a conic

Principle in geometry In Euclidean and projective geometry, five points determine a conic (a degree-2 plane curve), just as two (distinct) points determine a line (a degree-1 plane curve). There are additional subtleties for conics that do not exist for lines, and thus the statement and its proof for conics are both more technical than for lines. Formally, given any five points in the plane in general linear position, meaning no three collinear, there is a unique conic passing through them, w...

Rudolf Hilferding

Austro-German economist, pediatrician, journalist, Marxist theoretician and politician Rudolf HilferdingHilferding in 1928Minister of Finance(Weimar Republic)In office13 August 1923 – October 1923Preceded byAndreas HermesSucceeded byHans LutherIn office29 June 1928 – 21 December 1929Preceded byHeinrich KöhlerSucceeded byPaul Moldenhauer Personal detailsBorn(1877-08-10)10 August 1877Leopoldstadt, Vienna, Austria-HungaryDied11 February 1941(1941-02-11) (aged 63)Paris...