Class BetaDistribution
- java.lang.Object
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- dev.nm.stat.distribution.univariate.BetaDistribution
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- All Implemented Interfaces:
ProbabilityDistribution
public class BetaDistribution extends Object implements ProbabilityDistribution
The beta distribution is the posterior distribution of the parameter p of a binomial distribution after observing α - 1 independent events with probability p and β - 1 with probability 1 - p, if the prior distribution of p is uniform. The R equivalent functions aredbeta, pbeta, qbeta, rbeta.- See Also:
- Wikipedia: BetaDistribution distribution
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Constructor Summary
Constructors Constructor Description BetaDistribution(double alpha, double beta)Construct a Beta distribution.
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Method Summary
All Methods Instance Methods Concrete Methods Deprecated Methods Modifier and Type Method Description doubleccdf(double x)doublecdf(double x)Gets the cumulative probability F(x) = Pr(X ≤ x).doubledensity(double x)The density function, which, if exists, is the derivative of F.doubleentropy()Gets the entropy of this distribution.doublekurtosis()Gets the excess kurtosis of this distribution.doublemean()Gets the mean of this distribution.doublemedian()Gets the median of this distribution.doublemoment(double x)Deprecated.Not supported yet.doublequantile(double u)Gets the quantile, the inverse of the cumulative distribution function.doubleskew()Gets the skewness of this distribution.doublevariance()Gets the variance of this distribution.
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Method Detail
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mean
public double mean()
Description copied from interface:ProbabilityDistributionGets the mean of this distribution.- Specified by:
meanin interfaceProbabilityDistribution- Returns:
- the mean
- See Also:
- Wikipedia: Expected value
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median
public double median()
Description copied from interface:ProbabilityDistributionGets the median of this distribution.- Specified by:
medianin interfaceProbabilityDistribution- Returns:
- the median
- See Also:
- Wikipedia: Median
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variance
public double variance()
Description copied from interface:ProbabilityDistributionGets the variance of this distribution.- Specified by:
variancein interfaceProbabilityDistribution- Returns:
- the variance
- See Also:
- Wikipedia: Variance
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skew
public double skew()
Description copied from interface:ProbabilityDistributionGets the skewness of this distribution.- Specified by:
skewin interfaceProbabilityDistribution- Returns:
- the skewness
- See Also:
- Wikipedia: Skewness
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kurtosis
public double kurtosis()
Description copied from interface:ProbabilityDistributionGets the excess kurtosis of this distribution.- Specified by:
kurtosisin interfaceProbabilityDistribution- Returns:
- the excess kurtosis
- See Also:
- Wikipedia: Kurtosis
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entropy
public double entropy()
Description copied from interface:ProbabilityDistributionGets the entropy of this distribution.- Specified by:
entropyin interfaceProbabilityDistribution- Returns:
- the entropy
- See Also:
- Wikipedia: Entropy (information theory)
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cdf
public double cdf(double x)
Description copied from interface:ProbabilityDistributionGets the cumulative probability F(x) = Pr(X ≤ x).- Specified by:
cdfin interfaceProbabilityDistribution- Parameters:
x- x- Returns:
- F(x) = Pr(X ≤ x)
- See Also:
- Wikipedia: Cumulative distribution function
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ccdf
public double ccdf(double x)
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density
public double density(double x)
Description copied from interface:ProbabilityDistributionThe density function, which, if exists, is the derivative of F. It describes the density of probability at each point in the sample space.f(x) = dF(X) / dx
This may not always exist. For the discrete cases, this is the probability mass function. It gives the probability that a discrete random variable is exactly equal to some value.- Specified by:
densityin interfaceProbabilityDistribution- Parameters:
x- x- Returns:
- f(x)
- See Also:
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quantile
public double quantile(double u)
Description copied from interface:ProbabilityDistributionGets the quantile, the inverse of the cumulative distribution function. It is the value below which random draws from the distribution would fall u×100 percent of the time.
This may not always exist.F-1(u) = x, such that Pr(X ≤ x) = u
- Specified by:
quantilein interfaceProbabilityDistribution- Parameters:
u-u, a quantile- Returns:
- F-1(u)
- See Also:
- Wikipedia: Quantile function
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moment
@Deprecated public double moment(double x)
Deprecated.Not supported yet.Description copied from interface:ProbabilityDistributionThe moment generating function is the expected value of etX. That is,E(etX)
This may not always exist.- Specified by:
momentin interfaceProbabilityDistribution- Parameters:
x- t- Returns:
- E(exp(tX))
- See Also:
- Wikipedia: Moment-generating function
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