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java.lang.Objectorg.apache.mahout.math.jet.stat.Probability
public final class Probability
Partially deprecated until unit tests are in place. Until this time, this class/interface is unsupported.
| Method Summary | |
|---|---|
static double |
beta(double a,
double b,
double x)
Returns the area from zero to x under the beta density function. |
static double |
gamma(double alpha,
double beta,
double x)
Returns the integral from zero to x of the gamma probability density function. |
static double |
negativeBinomial(int k,
int n,
double p)
Returns the sum of the terms 0 through k of the Negative Binomial Distribution. |
static double |
normal(double a)
Returns the area under the Normal (Gaussian) probability density function, integrated from minus infinity to x (assumes mean is zero, variance is one). |
static double |
normal(double mean,
double variance,
double x)
Returns the area under the Normal (Gaussian) probability density function, integrated from minus infinity to x. |
static double |
poisson(int k,
double mean)
Returns the sum of the first k terms of the Poisson distribution. |
| Methods inherited from class java.lang.Object |
|---|
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait |
| Method Detail |
|---|
public static double beta(double a,
double b,
double x)
x
- -
| (a+b) | | a-1 b-1
P(x) = ---------- | t (1-t) dt
- - | |
| (a) | (b) -
0
This function is identical to the incomplete beta integral function Gamma.incompleteBeta(a, b, x).
The complemented function is
1 - P(1-x) = Gamma.incompleteBeta( b, a, x );
public static double gamma(double alpha,
double beta,
double x)
alpha - x
beta | alpha-1 -beta t
y = --------- | t e dt
- |
| (alpha) - 0
The incomplete gamma integral is used, according to the relation
y = Gamma.incompleteGamma( alpha, beta*x ).
See http://en.wikipedia.org/wiki/Gamma_distribution#Probability_density_function
alpha - the shape parameter of the gamma distribution.beta - the rate parameter of the gamma distribution.x - integration end point.
public static double negativeBinomial(int k,
int n,
double p)
k -- ( n+j-1 ) n j > ( ) p (1-p) -- ( j ) j=0In a sequence of Bernoulli trials, this is the probability that k or fewer failures precede the n-th success.
The terms are not computed individually; instead the incomplete beta integral is employed, according to the formula
y = negativeBinomial( k, n, p ) = Gamma.incompleteBeta( n, k+1, p ). All arguments must be positive,
k - end term.n - the number of trials.p - the probability of success (must be in (0.0,1.0)).public static double normal(double a)
x
-
1 | | 2
normal(x) = --------- | exp( - t /2 ) dt
sqrt(2pi) | |
-
-inf.
= ( 1 + erf(z) ) / 2
= erfc(z) / 2
where z = x/sqrt(2). Computation is via the functions errorFunction and
errorFunctionComplement.
Computed using method 26.2.17 from Abramovitz and Stegun (see http://www.math.sfu.ca/~cbm/aands/page_932.htm and http://en.wikipedia.org/wiki/Normal_distribution#Numerical_approximations_of_the_normal_cdf
public static double normal(double mean,
double variance,
double x)
x
-
1 | | 2
normal(x) = --------- | exp( - (t-mean) / 2v ) dt
sqrt(2pi*v)| |
-
-inf.
where v = variance. Computation is via the functions errorFunction.
mean - the mean of the normal distribution.variance - the variance of the normal distribution.x - the integration limit.
public static double poisson(int k,
double mean)
k j -- -m m > e -- -- j! j=0The terms are not summed directly; instead the incomplete gamma integral is employed, according to the relation
y = poisson( k, m ) = Gamma.incompleteGammaComplement( k+1, m ). The arguments must both be positive.
k - number of terms.mean - the mean of the poisson distribution.
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