Bapat–Beg theorem (original) (raw)
In probability theory, the Bapat–Beg theorem gives the joint probability distribution of order statistics of independent but not necessarily identically distributed random variables in terms of the cumulative distribution functions of the random variables. Ravindra Bapat and Beg published the theorem in 1989, though they did not offer a proof. A simple proof was offered by Hande in 1994.
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| dbo:abstract | In probability theory, the Bapat–Beg theorem gives the joint probability distribution of order statistics of independent but not necessarily identically distributed random variables in terms of the cumulative distribution functions of the random variables. Ravindra Bapat and Beg published the theorem in 1989, though they did not offer a proof. A simple proof was offered by Hande in 1994. Often, all elements of the sample are obtained from the same population and thus have the same probability distribution. The Bapat–Beg theorem describes the order statistics when each element of the sample is obtained from a different statistical population and therefore has its own probability distribution. (en) En teoría de la probabilidad, el teorema Bapat-Beg da la distribución de probabilidad conjunta de estadísticos de orden independientes, pero no necesariamente de variables aleatorias idénticamente distribuidas en términos de las funciones de distribución acumulada de las variables aleatorias. Bapat y Beg publicaron el teorema en 1989, aunque no dieron demostración de ese resultado. En 1994, Hande dio una demostrción sencilla del teorema. A menudo, todos los elementos de la muestra se obtienen de la misma población y por lo tanto tienen la misma distribución de probabilidad. El teorema Bapat-Beg describe las estadísticas de orden cuando se obtiene cada elemento de la muestra a partir de una diferente población estadística y por lo tanto tiene su propia distribución de probabilidad. (es) |
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| rdfs:comment | In probability theory, the Bapat–Beg theorem gives the joint probability distribution of order statistics of independent but not necessarily identically distributed random variables in terms of the cumulative distribution functions of the random variables. Ravindra Bapat and Beg published the theorem in 1989, though they did not offer a proof. A simple proof was offered by Hande in 1994. (en) En teoría de la probabilidad, el teorema Bapat-Beg da la distribución de probabilidad conjunta de estadísticos de orden independientes, pero no necesariamente de variables aleatorias idénticamente distribuidas en términos de las funciones de distribución acumulada de las variables aleatorias. Bapat y Beg publicaron el teorema en 1989, aunque no dieron demostración de ese resultado. En 1994, Hande dio una demostrción sencilla del teorema. (es) |
| rdfs:label | Bapat–Beg theorem (en) Teorema Bapat-Beg (es) |
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