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Cumulative distribution function Distribuo Συνάρτηση κατανομής Функция распределения Função distribuição acumulada Funció de distribució Distribuční funkce Dystrybuanta 累积分布函数 Kumulativ fördelningsfunktion Funzione di ripartizione 累積分布関数 Функція розподілу ймовірностей Banaketa-funtzio Función de distribución Verteilungsfunktion 누적 분포 함수 Verdelingsfunctie دالة التوزيع التراكمي
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Έστω ένας χώρος πιθανότητας και μια πραγματική τυχαία μεταβλητή πάνω σε αυτόν. Η συνάρτηση με ονομάζεται συνάρτηση κατανομής (σ.κ., ή αθροιστική συνάρτηση κατανομής, α.σ.κ.) της τυχαίας μεταβλητής. Για μια διακριτή τυχαία μεταβλητή που παίρνει τιμές x1, x2, ... με πιθανότητα p(xi) = P(Χ=xi) η αντίστοιχη συνάρτηση κατανομής ισούται με Για μια συνεχή τυχαία μεταβλητή με συνάρτηση πυκνότητας πιθανότητας f η αντίστοιχη συνάρτηση κατανομής ισούται με Die Verteilungsfunktion ist eine spezielle reelle Funktion in der Stochastik und ein zentrales Konzept bei der Untersuchung von Wahrscheinlichkeitsverteilungen auf den reellen Zahlen. Jeder Wahrscheinlichkeitsverteilung und jeder reellwertigen Zufallsvariable kann eine Verteilungsfunktion zugeordnet werden. Anschaulich entspricht dabei der Wert der Verteilungsfunktion an der Stelle der Wahrscheinlichkeit, dass die zugehörige Zufallsvariable einen Wert kleiner oder gleich annimmt. Ist beispielsweise die Verteilung der Schuhgrößen in Europa gegeben, so entspricht der Wert der entsprechenden Verteilungsfunktion bei 45 der Wahrscheinlichkeit, dass ein beliebiger Europäer die Schuhgröße 45 oder kleiner besitzt. دالة التوزيع التراكمي (بالإنجليزية: Cumulative distribution function)‏ أو دالة التجزيئ في علم الإحصاء ونظرية الاحتمالات هي دالة تحدد ما هو احتمال أن تكون قيمة متغير عشوائي ما (س) أقل من أو تساوي قيمة معينة (د). أو بمعنى آخر، فإنها دالة تعطي توزيع الاحتمالات لمتغير عشوائي على أن تكون قيمته عددا حقيقيا. وينبغي عدم الخلط بين دالة التوزيع التراكمي ودالة الكثافة الاحتمالية أو الخاصة بالمتغيرات العشوائية المنفصلة. In probability theory and statistics, the cumulative distribution function (CDF) of a real-valued random variable , or just distribution function of , evaluated at , is the probability that will take a value less than or equal to . Every probability distribution supported on the real numbers, discrete or "mixed" as well as continuous, is uniquely identified by an upwards continuous monotonic increasing cumulative distribution function satisfying and . Den kumulativa fördelningsfunktionen beskriver en sannolikhetsfördelning för en slumpvariabel inom den matematiska statistiken. För en slumpvariabel X definierad på sannolikhetsrummet definieras den kumulativa fördelningsfunktionen FX(x) som . beskriver sannolikheten att X antar ett värde mindre än eller lika med x. Den kumulativa fördelningsfunktionen är monotont växande och högerkontinuerlig. Den har alltid egenskaperna * * * För en kontinuerlig slumpvariabel är F en kontinuerlig funktion. Om F dessutom är så gäller Функція розподілу ймовірностей (ФРІ) — в теорії ймовірностей це функція, яка повністю описує розподіл ймовірностей випадкової величини. Нехай — ймовірнісний простір, в якому — множина елементарних подій, — сукупність підмножин , що утворюють -алгебру, множини з називаються випадковими подіями, — міра на , що задовольняє умову . Функція , визначена рівністю , називається функцією розподілу ймовірностей або кумулятивною функцією розподілу ймовірностей випадкової величини ξ. Вираз в правій частині рівності є ймовірністю того, що випадкова величина набуває значень менших або рівних . 累积分布函数(英語:cumulative distribution function,CDF)或概率分布函数,简称分布函数,是概率密度函數的积分,能完整描述一個實随机变量X的概率分佈。 在標量連續分佈的情況下,它給出了從負無窮到的概率密度函數下的面積。 也用於指定的分佈。 Distribuo (distribu(ant)a funkcio) de hazarda variablo X estas ofte signifata per FX kaj estas difinata kial: alinome estas probableco, ke hazarda variablo X havos valoron malpli aŭ egalan al x. Ofte ĝi estas difinata kiel funkcio kiu plenumebla sub kondiĉo sed kun "<" anstataŭ "≤". distribuanta funkcio difinas probabla distribuo – du variabloj kiuj havas saman distribuo havas ankaŭ saman probabla distribuo.Tute, distribuo estas mezura funkcio kiu havas valorojn en , almenaŭ ofte oni uzas ankaŭ mallongan signifon F(x)=P(X≤x). Probabilitate-teorian, banaketa-funtzioa balio batetik beherako probabilitatea (balio hori barne) ematen duen funtzio bat da. Probabilitate-funtzioekin (zorizko eta dentsitate-funtzioarekin estu loturik dago: adibidez, dentsitate-funtzio batean, banaketa funtzioak x balio baterainoko azalera ematen du. Horrela, dentsitate-funtziotik (eta baita ere probabilitate-funtziotik zorizko aldagai diskretuetan) banaketa-funtzioa eratortzen da eta alderantziz. Matematikoki honela definitzen da, X zorizko aldagai baterako: Honela kalkulatzen dira probabilitateak banaketa-funtzioarekin: 累積分布関数(るいせきぶんぷかんすう、英: cumulative distribution function, CDF)や分布関数(ぶんぷかんすう、英: distribution function)とは、確率論において、確率変数 X の実現値が x 以下になる確率の関数のこと。連続型確率変数では、負の無限大から x まで確率密度関数を定積分したもの。 累積分布関数は同時確率分布でも条件付き確率分布でも定義される。 In statistica e teoria della probabilità, la funzione di ripartizione (o funzione cumulativa) è una funzione di variabile reale che racchiude le informazioni su un fenomeno (un insieme di dati, un evento casuale) riguardanti la sua presenza o la sua distribuzione prima o dopo un certo punto. En teoria de la probabilitat i estadística, la funció de distribució (també funció de distribució acumulada, o CDF pel seu acrònim en anglès cumulative distribution function) d'una variable aleatòria real, avaluada en , és la probabilitat que prengui un valor inferior o igual a . La funció de distribució determina totes les probabilitats relatives a la variable aleatòria. Les funcions de distribució són importants perquè són funcions ordinàries, en contrast amb les probabilitats, que són funcions de conjunts, i llavors les eines de l'Anàlisi matemàtica clàssica poden aplicar-se a estudiar les probabilitats corresponents a les variables aleatòries. Em teoria da probabilidade, a função distribuição acumulada (fda) ou simplesmente função distribuição, descreve completamente a distribuição da probabilidade de uma variável aleatória de valor real X. Para cada número real x, a fda é dada por: A probabilidade de que X se situe num intervalo ]a, b] (aberto em a e fechado em b) é F(b) − F(a) se a ≤ b. É convenção usar um F maiúsculo para a fda, em contraste com o f minúsculo usado para a função densidade da probabilidade e função massa de probabilidade. Para uma variável aleatória contínua: En la teoría de la probabilidad y en estadística, la función de distribución acumulada (FDA, designada también a veces simplemente como función de distribución o FD) o función de probabilidad acumulada asociada a una variable aleatoria real sujeta a cierta ley de distribución de probabilidad, es una función matemática de la variable real que describe la probabilidad de que tenga un valor menor o igual que .Intuitivamente, asumiendo la función como la ley de distribución de probabilidad, la FDA sería la función con la recta real como dominio, con imagen del área hasta aquí de la función , siendo aquí el valor x para la variable aleatoria real .La FDA asocia a cada valor x, la probabilidad del evento: «la variable toma valores menores o iguales a x».El concepto de FDA puede generalizars Dystrybuanta (fr. distribuer „rozdzielać, rozdawać” z łac. distribuo zob. dystrybucja) – funkcja rzeczywista jednoznacznie wyznaczająca rozkład prawdopodobieństwa (tj. miarę probabilistyczną określoną na σ-ciele borelowskich podzbiorów prostej), a więc zawierająca wszystkie informacje o tym rozkładzie. Dystrybuanty są efektywnym narzędziem badania prawdopodobieństwa, ponieważ są obiektami prostszymi niż rozkłady prawdopodobieństwa. W statystyce dystrybuanta rozkładu próby zwana jest dystrybuantą empiryczną i jest blisko związana z pojęciem rangi. Фу́нкция распределе́ния в теории вероятностей — функция, характеризующая распределение случайной величины или случайного вектора; вероятность того, что случайная величина X примет значение, меньшее х, где х — произвольное действительное число. При соблюдении известных условий (см. ) полностью определяет случайную величину. In de kansrekening en de statistiek is de verdelingsfunctie, ook aangeduid als cumulatieve (kans)verdelingsfunctie of cumulatieve distributiefunctie (cdf), van een reëelwaardige stochastische variabele de functie waarmee de verdeling van de stochastische variabele beschreven of vastgelegd wordt. De verdelingsfunctie bestaat altijd en voor elke gebeurtenis die de stochastische variabele betreft, kan daarmee de kans op die gebeurtenis bepaald worden. Populair gezegd worden alle kansen betreffende de stochastische variabele bepaald door de verdelingsfunctie. Distribuční funkce, funkce rozdělení (pravděpodobnosti) nebo (spíše lidově) (zleva) kumulovaná pravděpodobnost (anglicky Cumulative Distribution Function, CDF) je funkce, která udává pravděpodobnost, že hodnota náhodné proměnné je menší než zadaná hodnota (nerovnost může být i neostrá). Distribuční funkce jednoznačně určuje rozdělení pravděpodobnosti a ve spojitém případě je úzce spjatá s funkcí hustoty pravděpodobnosti. 확률론에서 누적분포함수(累積分布函數, 영어: cumulative distribution function, 약자 cdf)는 주어진 확률 변수가 특정 값보다 작거나 같은 확률을 나타내는 함수이다.
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En la teoría de la probabilidad y en estadística, la función de distribución acumulada (FDA, designada también a veces simplemente como función de distribución o FD) o función de probabilidad acumulada asociada a una variable aleatoria real sujeta a cierta ley de distribución de probabilidad, es una función matemática de la variable real que describe la probabilidad de que tenga un valor menor o igual que .Intuitivamente, asumiendo la función como la ley de distribución de probabilidad, la FDA sería la función con la recta real como dominio, con imagen del área hasta aquí de la función , siendo aquí el valor x para la variable aleatoria real .La FDA asocia a cada valor x, la probabilidad del evento: «la variable toma valores menores o iguales a x».El concepto de FDA puede generalizarse para modelar variables aleatorias multivariantes definidas en Probabilitate-teorian, banaketa-funtzioa balio batetik beherako probabilitatea (balio hori barne) ematen duen funtzio bat da. Probabilitate-funtzioekin (zorizko eta dentsitate-funtzioarekin estu loturik dago: adibidez, dentsitate-funtzio batean, banaketa funtzioak x balio baterainoko azalera ematen du. Horrela, dentsitate-funtziotik (eta baita ere probabilitate-funtziotik zorizko aldagai diskretuetan) banaketa-funtzioa eratortzen da eta alderantziz. Matematikoki honela definitzen da, X zorizko aldagai baterako: Honela kalkulatzen dira probabilitateak banaketa-funtzioarekin: Distribuční funkce, funkce rozdělení (pravděpodobnosti) nebo (spíše lidově) (zleva) kumulovaná pravděpodobnost (anglicky Cumulative Distribution Function, CDF) je funkce, která udává pravděpodobnost, že hodnota náhodné proměnné je menší než zadaná hodnota (nerovnost může být i neostrá). Distribuční funkce jednoznačně určuje rozdělení pravděpodobnosti a ve spojitém případě je úzce spjatá s funkcí hustoty pravděpodobnosti. Em teoria da probabilidade, a função distribuição acumulada (fda) ou simplesmente função distribuição, descreve completamente a distribuição da probabilidade de uma variável aleatória de valor real X. Para cada número real x, a fda é dada por: A probabilidade de que X se situe num intervalo ]a, b] (aberto em a e fechado em b) é F(b) − F(a) se a ≤ b. É convenção usar um F maiúsculo para a fda, em contraste com o f minúsculo usado para a função densidade da probabilidade e função massa de probabilidade. A função distribuição pode ser facilmente obtida a partir da função de probabilidade respectiva. No caso duma variável aleatória discreta: Para uma variável aleatória contínua: Note-se que na definição acima, o sinal "", '≤' poderia ser substituído por "menor" '<'. Isto produziria uma função diferente, mas qualquer uma das funções pode ser facilmente deduzida a partir da outra. Também se poderia mudar para um sinal maior e deduzir as propriedades desta nova função. A única coisa a lembrar é ajustar a definição ao sinal pretendido. Em países de língua inglesa, a convenção que usa a desigualdade fraca (≤) em vez da desigualdade estrita (<) é quase sempre usada. In statistica e teoria della probabilità, la funzione di ripartizione (o funzione cumulativa) è una funzione di variabile reale che racchiude le informazioni su un fenomeno (un insieme di dati, un evento casuale) riguardanti la sua presenza o la sua distribuzione prima o dopo un certo punto. Die Verteilungsfunktion ist eine spezielle reelle Funktion in der Stochastik und ein zentrales Konzept bei der Untersuchung von Wahrscheinlichkeitsverteilungen auf den reellen Zahlen. Jeder Wahrscheinlichkeitsverteilung und jeder reellwertigen Zufallsvariable kann eine Verteilungsfunktion zugeordnet werden. Anschaulich entspricht dabei der Wert der Verteilungsfunktion an der Stelle der Wahrscheinlichkeit, dass die zugehörige Zufallsvariable einen Wert kleiner oder gleich annimmt. Ist beispielsweise die Verteilung der Schuhgrößen in Europa gegeben, so entspricht der Wert der entsprechenden Verteilungsfunktion bei 45 der Wahrscheinlichkeit, dass ein beliebiger Europäer die Schuhgröße 45 oder kleiner besitzt. Ihre Bedeutung erhält die Verteilungsfunktion durch den Korrespondenzsatz, der besagt, dass jeder Verteilungsfunktion eine Wahrscheinlichkeitsverteilung auf den reellen Zahlen zugeordnet werden kann und umgekehrt. Die Zuordnung ist bijektiv. Dies ermöglicht es, anstelle der Untersuchung von Wahrscheinlichkeitsverteilungen als Mengenfunktionen auf einem komplexen Mengensystem mit Methoden der Maßtheorie die entsprechenden Verteilungsfunktionen zu untersuchen. Diese sind reelle Funktionen und somit über die Methoden der reellen Analysis leichter zugänglich. Als alternative Bezeichnungen finden sich unter anderem kumulierte Verteilungsfunktion, da sie die Wahrscheinlichkeiten, kleiner als zu sein, anhäuft, siehe auch kumulierte Häufigkeit. Weiterhin wird sie zur besseren Abgrenzung von ihrem höherdimensionalen Pendant, der multivariaten Verteilungsfunktion, auch als univariate Verteilungsfunktion bezeichnet. In Abgrenzung zum allgemeineren maßtheoretischen Konzept einer Verteilungsfunktion finden sich die Bezeichnungen als wahrscheinlichkeitstheoretische Verteilungsfunktion oder als Verteilungsfunktion im engeren Sinn. Die Entsprechung der Verteilungsfunktion in der deskriptiven Statistik ist die empirische Verteilungs- oder Summenhäufigkeitsfunktion. Функція розподілу ймовірностей (ФРІ) — в теорії ймовірностей це функція, яка повністю описує розподіл ймовірностей випадкової величини. Нехай — ймовірнісний простір, в якому — множина елементарних подій, — сукупність підмножин , що утворюють -алгебру, множини з називаються випадковими подіями, — міра на , що задовольняє умову . Функція , визначена рівністю , називається функцією розподілу ймовірностей або кумулятивною функцією розподілу ймовірностей випадкової величини ξ. Вираз в правій частині рівності є ймовірністю того, що випадкова величина набуває значень менших або рівних . Έστω ένας χώρος πιθανότητας και μια πραγματική τυχαία μεταβλητή πάνω σε αυτόν. Η συνάρτηση με ονομάζεται συνάρτηση κατανομής (σ.κ., ή αθροιστική συνάρτηση κατανομής, α.σ.κ.) της τυχαίας μεταβλητής. Για μια διακριτή τυχαία μεταβλητή που παίρνει τιμές x1, x2, ... με πιθανότητα p(xi) = P(Χ=xi) η αντίστοιχη συνάρτηση κατανομής ισούται με Για μια συνεχή τυχαία μεταβλητή με συνάρτηση πυκνότητας πιθανότητας f η αντίστοιχη συνάρτηση κατανομής ισούται με Фу́нкция распределе́ния в теории вероятностей — функция, характеризующая распределение случайной величины или случайного вектора; вероятность того, что случайная величина X примет значение, меньшее х, где х — произвольное действительное число. При соблюдении известных условий (см. ) полностью определяет случайную величину. In de kansrekening en de statistiek is de verdelingsfunctie, ook aangeduid als cumulatieve (kans)verdelingsfunctie of cumulatieve distributiefunctie (cdf), van een reëelwaardige stochastische variabele de functie waarmee de verdeling van de stochastische variabele beschreven of vastgelegd wordt. De verdelingsfunctie bestaat altijd en voor elke gebeurtenis die de stochastische variabele betreft, kan daarmee de kans op die gebeurtenis bepaald worden. Populair gezegd worden alle kansen betreffende de stochastische variabele bepaald door de verdelingsfunctie. Elke functie die opgevat kan worden als verdelingsfunctie van een stochastische variabele, wordt ook verdelingsfunctie genoemd. Het betreft dan een functie met de hieronder aangeduide eigenschappen. Distribuo (distribu(ant)a funkcio) de hazarda variablo X estas ofte signifata per FX kaj estas difinata kial: alinome estas probableco, ke hazarda variablo X havos valoron malpli aŭ egalan al x. Ofte ĝi estas difinata kiel funkcio kiu plenumebla sub kondiĉo sed kun "<" anstataŭ "≤". distribuanta funkcio difinas probabla distribuo – du variabloj kiuj havas saman distribuo havas ankaŭ saman probabla distribuo.Tute, distribuo estas mezura funkcio kiu havas valorojn en , almenaŭ ofte oni uzas ankaŭ mallongan signifon F(x)=P(X≤x). Distribuo ankaŭ havas ĝeneralan signifon. Distribui estas disdoni al ĉiu parton de io laŭ ties destino. Distribuo ( PIV2 ) do estas unuflanke ago distribui, aliflanke maniero en kiu io estas distribuita. 累積分布関数(るいせきぶんぷかんすう、英: cumulative distribution function, CDF)や分布関数(ぶんぷかんすう、英: distribution function)とは、確率論において、確率変数 X の実現値が x 以下になる確率の関数のこと。連続型確率変数では、負の無限大から x まで確率密度関数を定積分したもの。 累積分布関数は同時確率分布でも条件付き確率分布でも定義される。 累积分布函数(英語:cumulative distribution function,CDF)或概率分布函数,简称分布函数,是概率密度函數的积分,能完整描述一個實随机变量X的概率分佈。 在標量連續分佈的情況下,它給出了從負無窮到的概率密度函數下的面積。 也用於指定的分佈。 Dystrybuanta (fr. distribuer „rozdzielać, rozdawać” z łac. distribuo zob. dystrybucja) – funkcja rzeczywista jednoznacznie wyznaczająca rozkład prawdopodobieństwa (tj. miarę probabilistyczną określoną na σ-ciele borelowskich podzbiorów prostej), a więc zawierająca wszystkie informacje o tym rozkładzie. Dystrybuanty są efektywnym narzędziem badania prawdopodobieństwa, ponieważ są obiektami prostszymi niż rozkłady prawdopodobieństwa. W statystyce dystrybuanta rozkładu próby zwana jest dystrybuantą empiryczną i jest blisko związana z pojęciem rangi. Den kumulativa fördelningsfunktionen beskriver en sannolikhetsfördelning för en slumpvariabel inom den matematiska statistiken. För en slumpvariabel X definierad på sannolikhetsrummet definieras den kumulativa fördelningsfunktionen FX(x) som . beskriver sannolikheten att X antar ett värde mindre än eller lika med x. Den kumulativa fördelningsfunktionen är monotont växande och högerkontinuerlig. Den har alltid egenskaperna * * * För en diskret slumpvariabel som kan anta värdena x1, x2... är F diskontinuerlig i punkterna xi och har konstant värde däremellan, det vill säga, den har ett trappstegsliknande utseende. För en kontinuerlig slumpvariabel är F en kontinuerlig funktion. Om F dessutom är så gäller där f(t) är täthetsfunktionen (eller frekvensfunktionen) för variabelns fördelning. Sannolikheten för att en slumpvariabel ska anta värden större än a och mindre eller lika med b kan beräknas med: Tabell över värdena hos den kumulativa normalfördelningsfunktionen finns att läsa här. Andra fördelningar har andra tabeller. En teoria de la probabilitat i estadística, la funció de distribució (també funció de distribució acumulada, o CDF pel seu acrònim en anglès cumulative distribution function) d'una variable aleatòria real, avaluada en , és la probabilitat que prengui un valor inferior o igual a . La funció de distribució determina totes les probabilitats relatives a la variable aleatòria. Les funcions de distribució són importants perquè són funcions ordinàries, en contrast amb les probabilitats, que són funcions de conjunts, i llavors les eines de l'Anàlisi matemàtica clàssica poden aplicar-se a estudiar les probabilitats corresponents a les variables aleatòries. En el cas de les distribucions absolutament contínues, la funció de distribució en el punt és igual a l'àrea sota la funció de densitat de probabilitat de menys infinit a . Les funcions de distribució multidimensionals o multivariants serveixen per especificar les probabilitats dels vectors aleatoris o variables aleatòries multivariades. In probability theory and statistics, the cumulative distribution function (CDF) of a real-valued random variable , or just distribution function of , evaluated at , is the probability that will take a value less than or equal to . Every probability distribution supported on the real numbers, discrete or "mixed" as well as continuous, is uniquely identified by an upwards continuous monotonic increasing cumulative distribution function satisfying and . In the case of a scalar continuous distribution, it gives the area under the probability density function from minus infinity to . Cumulative distribution functions are also used to specify the distribution of multivariate random variables. 확률론에서 누적분포함수(累積分布函數, 영어: cumulative distribution function, 약자 cdf)는 주어진 확률 변수가 특정 값보다 작거나 같은 확률을 나타내는 함수이다. دالة التوزيع التراكمي (بالإنجليزية: Cumulative distribution function)‏ أو دالة التجزيئ في علم الإحصاء ونظرية الاحتمالات هي دالة تحدد ما هو احتمال أن تكون قيمة متغير عشوائي ما (س) أقل من أو تساوي قيمة معينة (د). أو بمعنى آخر، فإنها دالة تعطي توزيع الاحتمالات لمتغير عشوائي على أن تكون قيمته عددا حقيقيا. وينبغي عدم الخلط بين دالة التوزيع التراكمي ودالة الكثافة الاحتمالية أو الخاصة بالمتغيرات العشوائية المنفصلة.
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