Binary entropy function
In information theory, the binary entropy function, denoted or , is defined as the entropy of a Bernoulli process with probability of one of two values. It is a special case of , the entropy function. Mathematically, the Bernoulli trial is modelled as a random variable that can take on only two values: 0 and 1, which are mutually exclusive and exhaustive. If , then and the entropy of (in shannons) is given by , where is taken to be 0. The logarithms in this formula are usually taken (as shown in the graph) to the base 2. See binary logarithm.
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- enIn information theory, the binary entropy function, denoted or , is defined as the entropy of a Bernoulli process with probability of one of two values. It is a special case of , the entropy function. Mathematically, the Bernoulli trial is modelled as a random variable that can take on only two values: 0 and 1, which are mutually exclusive and exhaustive. If , then and the entropy of (in shannons) is given by , where is taken to be 0. The logarithms in this formula are usually taken (as shown in the graph) to the base 2. See binary logarithm.
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- Has abstract
- enIn information theory, the binary entropy function, denoted or , is defined as the entropy of a Bernoulli process with probability of one of two values. It is a special case of , the entropy function. Mathematically, the Bernoulli trial is modelled as a random variable that can take on only two values: 0 and 1, which are mutually exclusive and exhaustive. If , then and the entropy of (in shannons) is given by , where is taken to be 0. The logarithms in this formula are usually taken (as shown in the graph) to the base 2. See binary logarithm. When , the binary entropy function attains its maximum value. This is the case of an unbiased coin flip. is distinguished from the entropy function in that the former takes a single real number as a parameter whereas the latter takes a distribution or random variable as a parameter.Sometimes the binary entropy function is also written as .However, it is different from and should not be confused with the Rényi entropy, which is denoted as .
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- Binary entropy function
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- enBinary entropy function
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- web.archive.org/web/20160217105359/http:/www.inference.phy.cam.ac.uk/mackay/itila/book.html
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- Bernoulli process
- Binary logarithm
- Category:Entropy and information
- David J. C. MacKay
- Derivative
- Entropy (information theory)
- Fair coin
- File:Binary entropy plot.svg
- Information entropy
- Information theory
- Logit
- Metric entropy
- Parameter
- Probability
- Quantities of information
- Random variable
- Rényi entropy
- Shannon (unit)
- Taylor series
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- 4Yf9v
- Entropia binarna
- m.0dc1gm
- Q4913893
- 二値エントロピー関数
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- Category:Entropy and information
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