Difference between revisions of "Beta distribution"
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| − | + | = Beta(X,Y,lower,upper) = | |
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| + | The Beta distribution. | ||
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| + | Creates a continuous distribution of numbers between 0 and 1 with X / (X+Y) representing the mean, if the optional parameters ''lower'' and ''upper'' are omitted. For bounds other than 0 and 1, specify the optional ''lower'' and ''upper'' bounds to offset and expand the distribution. | ||
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| + | X and Y must be positive. | ||
| + | |||
| + | = When to use = | ||
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| + | Use a beta distribution if the uncertain quantity is bounded by 0 and 1 (or 100%), is continuous, and has a single mode. This distribution is particularly useful for modeling an opinion about the fraction of a population that has some characteristic. For example, if you have observed n members of the population, of which r display the characteristic c, you can represent the uncertainty about the true fraction with c using a beta distribution with parameters X = r and Y = n - r. | ||
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| + | If the uncertain quantity has lower and upper bounds other than 0 and 1, include the ''lower'' and ''upper'' bounds parameters to obtain a transformed beta distribution. The transformed beta is a very flexible distribution for representing a wide variety of bounded quantities. | ||
| + | |||
| + | = Library = | ||
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| + | Distributions | ||
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| + | = See Also = | ||
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| + | * [[BetaFn]] -- the complete beta function | ||
| + | * [[BetaI]] -- the incomplete beta function, gives the cumulative density analytically. | ||
| + | * [[BetaIInv]] -- the inverse of [[BetaI]]. | ||
| + | * [[Pert]] - A parametric variation on the beta distribution | ||
Revision as of 23:12, 1 August 2007
Beta(X,Y,lower,upper)
The Beta distribution.
Creates a continuous distribution of numbers between 0 and 1 with X / (X+Y) representing the mean, if the optional parameters lower and upper are omitted. For bounds other than 0 and 1, specify the optional lower and upper bounds to offset and expand the distribution.
X and Y must be positive.
When to use
Use a beta distribution if the uncertain quantity is bounded by 0 and 1 (or 100%), is continuous, and has a single mode. This distribution is particularly useful for modeling an opinion about the fraction of a population that has some characteristic. For example, if you have observed n members of the population, of which r display the characteristic c, you can represent the uncertainty about the true fraction with c using a beta distribution with parameters X = r and Y = n - r.
If the uncertain quantity has lower and upper bounds other than 0 and 1, include the lower and upper bounds parameters to obtain a transformed beta distribution. The transformed beta is a very flexible distribution for representing a wide variety of bounded quantities.
Library
Distributions
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