# Bapat–Beg theorem

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.wikipedia

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### Order statistic

**order statisticsorderedth-smallest of items**

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.

Then they are independent, but not necessarily identically distributed, and their joint probability distribution is given by the Bapat–Beg theorem.

### Ravindra Bapat

**Bapat, Ravindra**

Ravindra Bapat and Beg published the theorem in 1989, though they did not offer a proof.

He is known for the Bapat–Beg theorem.

### Permanent (mathematics)

**permanentmatrix permanentspermanent of a matrix**

is the permanent of the given block matrix.

Bapat–Beg theorem, an application of permanents in order statistics

### Probability theory

**theory of probabilityprobabilityprobability theorist**

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.

### Joint probability distribution

**joint distributionjoint probabilitymultivariate distribution**

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.

### Independence (probability theory)

**independentstatistically independentindependence**

### Random variable

**random variablesrandom variationrandom**

### Sample (statistics)

**samplesamplesstatistical sample**

Often, all elements of the sample are obtained from the same population and thus have the same probability distribution.

### Probability distribution

**distributioncontinuous probability distributiondiscrete probability distribution**

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.

### Statistical population

**populationsubpopulationsubpopulations**

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.

### Block matrix

**block diagonal matrixblock diagonalblock matrices**

is the permanent of the given block matrix.

### Independent and identically distributed random variables

**independent and identically distributedi.i.d.iid**

### Cumulative distribution function

**distribution functionCDFcumulative probability distribution function**

### List of statistics articles

**list of statistical topicslist of statistics topics**

Bapat–Beg theorem