Java Code Examples for org.apache.commons.math3.special.Gamma#LANCZOS_G
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org.apache.commons.math3.special.Gamma#LANCZOS_G .
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Example 1
| Source File: GammaDistribution.java From astor with GNU General Public License v2.0 | 6 votes |
|
/** {@inheritDoc} **/
@Override
public double logDensity(double x) {
/*
* see the comment in {@link #density(double)} for computation details
*/
if (x < 0) {
return Double.NEGATIVE_INFINITY;
}
final double y = x / scale;
if ((y <= minY) || (FastMath.log(y) >= maxLogY)) {
/*
* Overflow.
*/
final double aux1 = (y - shiftedShape) / shiftedShape;
final double aux2 = shape * (FastMath.log1p(aux1) - aux1);
final double aux3 = -y * (Gamma.LANCZOS_G + 0.5) / shiftedShape +
Gamma.LANCZOS_G + aux2;
return logDensityPrefactor2 - FastMath.log(x) + aux3;
}
/*
* Natural calculation.
*/
return logDensityPrefactor1 - y + FastMath.log(y) * (shape - 1);
}
Example 2
| Source File: GammaDistributionTest.java From astor with GNU General Public License v2.0 | 6 votes |
|
public static double logGamma(double x) {
/*
* This is a copy of
* double Gamma.logGamma(double)
* prior to MATH-849
*/
double ret;
if (Double.isNaN(x) || (x <= 0.0)) {
ret = Double.NaN;
} else {
double sum = Gamma.lanczos(x);
double tmp = x + Gamma.LANCZOS_G + .5;
ret = ((x + .5) * FastMath.log(tmp)) - tmp +
HALF_LOG_2_PI + FastMath.log(sum / x);
}
return ret;
}
Example 3
| Source File: GammaDistributionTest.java From astor with GNU General Public License v2.0 | 6 votes |
|
public static double logGamma(double x) {
/*
* This is a copy of
* double Gamma.logGamma(double)
* prior to MATH-849
*/
double ret;
if (Double.isNaN(x) || (x <= 0.0)) {
ret = Double.NaN;
} else {
double sum = Gamma.lanczos(x);
double tmp = x + Gamma.LANCZOS_G + .5;
ret = ((x + .5) * FastMath.log(tmp)) - tmp +
HALF_LOG_2_PI + FastMath.log(sum / x);
}
return ret;
}
Example 4
| Source File: GammaDistributionTest.java From astor with GNU General Public License v2.0 | 6 votes |
|
public static double logGamma(double x) {
/*
* This is a copy of
* double Gamma.logGamma(double)
* prior to MATH-849
*/
double ret;
if (Double.isNaN(x) || (x <= 0.0)) {
ret = Double.NaN;
} else {
double sum = Gamma.lanczos(x);
double tmp = x + Gamma.LANCZOS_G + .5;
ret = ((x + .5) * FastMath.log(tmp)) - tmp +
HALF_LOG_2_PI + FastMath.log(sum / x);
}
return ret;
}
Example 5
| Source File: GammaDistributionTest.java From astor with GNU General Public License v2.0 | 6 votes |
|
public static double logGamma(double x) {
/*
* This is a copy of
* double Gamma.logGamma(double)
* prior to MATH-849
*/
double ret;
if (Double.isNaN(x) || (x <= 0.0)) {
ret = Double.NaN;
} else {
double sum = Gamma.lanczos(x);
double tmp = x + Gamma.LANCZOS_G + .5;
ret = ((x + .5) * FastMath.log(tmp)) - tmp +
HALF_LOG_2_PI + FastMath.log(sum / x);
}
return ret;
}
Example 6
| Source File: GammaDistribution.java From astor with GNU General Public License v2.0 | 6 votes |
|
/** {@inheritDoc} **/
@Override
public double logDensity(double x) {
/*
* see the comment in {@link #density(double)} for computation details
*/
if (x < 0) {
return Double.NEGATIVE_INFINITY;
}
final double y = x / scale;
if ((y <= minY) || (FastMath.log(y) >= maxLogY)) {
/*
* Overflow.
*/
final double aux1 = (y - shiftedShape) / shiftedShape;
final double aux2 = shape * (FastMath.log1p(aux1) - aux1);
final double aux3 = -y * (Gamma.LANCZOS_G + 0.5) / shiftedShape +
Gamma.LANCZOS_G + aux2;
return logDensityPrefactor2 - FastMath.log(x) + aux3;
}
/*
* Natural calculation.
*/
return logDensityPrefactor1 - y + FastMath.log(y) * (shape - 1);
}
Example 7
| Source File: GammaDistributionTest.java From astor with GNU General Public License v2.0 | 6 votes |
|
public static double logGamma(double x) {
/*
* This is a copy of
* double Gamma.logGamma(double)
* prior to MATH-849
*/
double ret;
if (Double.isNaN(x) || (x <= 0.0)) {
ret = Double.NaN;
} else {
double sum = Gamma.lanczos(x);
double tmp = x + Gamma.LANCZOS_G + .5;
ret = ((x + .5) * FastMath.log(tmp)) - tmp +
HALF_LOG_2_PI + FastMath.log(sum / x);
}
return ret;
}
Example 8
| Source File: GammaDistribution.java From astor with GNU General Public License v2.0 | 5 votes |
|
/**
* Creates a Gamma distribution.
*
* @param rng Random number generator.
* @param shape the shape parameter
* @param scale the scale parameter
* @param inverseCumAccuracy the maximum absolute error in inverse
* cumulative probability estimates (defaults to
* {@link #DEFAULT_INVERSE_ABSOLUTE_ACCURACY}).
* @throws NotStrictlyPositiveException if {@code shape <= 0} or
* {@code scale <= 0}.
* @since 3.1
*/
public GammaDistribution(RandomGenerator rng,
double shape,
double scale,
double inverseCumAccuracy)
throws NotStrictlyPositiveException {
super(rng);
if (shape <= 0) {
throw new NotStrictlyPositiveException(LocalizedFormats.SHAPE, shape);
}
if (scale <= 0) {
throw new NotStrictlyPositiveException(LocalizedFormats.SCALE, scale);
}
this.shape = shape;
this.scale = scale;
this.solverAbsoluteAccuracy = inverseCumAccuracy;
this.shiftedShape = shape + Gamma.LANCZOS_G + 0.5;
final double aux = FastMath.E / (2.0 * FastMath.PI * shiftedShape);
this.densityPrefactor2 = shape * FastMath.sqrt(aux) / Gamma.lanczos(shape);
this.densityPrefactor1 = this.densityPrefactor2 / scale *
FastMath.pow(shiftedShape, -shape) *
FastMath.exp(shape + Gamma.LANCZOS_G);
this.minY = shape + Gamma.LANCZOS_G - FastMath.log(Double.MAX_VALUE);
this.maxLogY = FastMath.log(Double.MAX_VALUE) / (shape - 1.0);
}
Example 9
| Source File: GammaDistribution.java From astor with GNU General Public License v2.0 | 5 votes |
|
/**
* Creates a Gamma distribution.
*
* @param rng Random number generator.
* @param shape the shape parameter
* @param scale the scale parameter
* @param inverseCumAccuracy the maximum absolute error in inverse
* cumulative probability estimates (defaults to
* {@link #DEFAULT_INVERSE_ABSOLUTE_ACCURACY}).
* @throws NotStrictlyPositiveException if {@code shape <= 0} or
* {@code scale <= 0}.
* @since 3.1
*/
public GammaDistribution(RandomGenerator rng,
double shape,
double scale,
double inverseCumAccuracy)
throws NotStrictlyPositiveException {
super(rng);
if (shape <= 0) {
throw new NotStrictlyPositiveException(LocalizedFormats.SHAPE, shape);
}
if (scale <= 0) {
throw new NotStrictlyPositiveException(LocalizedFormats.SCALE, scale);
}
this.shape = shape;
this.scale = scale;
this.solverAbsoluteAccuracy = inverseCumAccuracy;
this.shiftedShape = shape + Gamma.LANCZOS_G + 0.5;
final double aux = FastMath.E / (2.0 * FastMath.PI * shiftedShape);
this.densityPrefactor2 = shape * FastMath.sqrt(aux) / Gamma.lanczos(shape);
this.logDensityPrefactor2 = FastMath.log(shape) + 0.5 * FastMath.log(aux) -
FastMath.log(Gamma.lanczos(shape));
this.densityPrefactor1 = this.densityPrefactor2 / scale *
FastMath.pow(shiftedShape, -shape) *
FastMath.exp(shape + Gamma.LANCZOS_G);
this.logDensityPrefactor1 = this.logDensityPrefactor2 - FastMath.log(scale) -
FastMath.log(shiftedShape) * shape +
shape + Gamma.LANCZOS_G;
this.minY = shape + Gamma.LANCZOS_G - FastMath.log(Double.MAX_VALUE);
this.maxLogY = FastMath.log(Double.MAX_VALUE) / (shape - 1.0);
}
Example 10
| Source File: GammaDistribution.java From astor with GNU General Public License v2.0 | 5 votes |
|
/**
* Creates a Gamma distribution.
*
* @param rng Random number generator.
* @param shape the shape parameter
* @param scale the scale parameter
* @param inverseCumAccuracy the maximum absolute error in inverse
* cumulative probability estimates (defaults to
* {@link #DEFAULT_INVERSE_ABSOLUTE_ACCURACY}).
* @throws NotStrictlyPositiveException if {@code shape <= 0} or
* {@code scale <= 0}.
* @since 3.1
*/
public GammaDistribution(RandomGenerator rng,
double shape,
double scale,
double inverseCumAccuracy)
throws NotStrictlyPositiveException {
super(rng);
if (shape <= 0) {
throw new NotStrictlyPositiveException(LocalizedFormats.SHAPE, shape);
}
if (scale <= 0) {
throw new NotStrictlyPositiveException(LocalizedFormats.SCALE, scale);
}
this.shape = shape;
this.scale = scale;
this.solverAbsoluteAccuracy = inverseCumAccuracy;
this.shiftedShape = shape + Gamma.LANCZOS_G + 0.5;
final double aux = FastMath.E / (2.0 * FastMath.PI * shiftedShape);
this.densityPrefactor2 = shape * FastMath.sqrt(aux) / Gamma.lanczos(shape);
this.densityPrefactor1 = this.densityPrefactor2 / scale *
FastMath.pow(shiftedShape, -shape) *
FastMath.exp(shape + Gamma.LANCZOS_G);
this.minY = shape + Gamma.LANCZOS_G - FastMath.log(Double.MAX_VALUE);
this.maxLogY = FastMath.log(Double.MAX_VALUE) / (shape - 1.0);
}
Example 11
| Source File: GammaDistribution.java From astor with GNU General Public License v2.0 | 5 votes |
|
/**
* Creates a Gamma distribution.
*
* @param rng Random number generator.
* @param shape the shape parameter
* @param scale the scale parameter
* @param inverseCumAccuracy the maximum absolute error in inverse
* cumulative probability estimates (defaults to
* {@link #DEFAULT_INVERSE_ABSOLUTE_ACCURACY}).
* @throws NotStrictlyPositiveException if {@code shape <= 0} or
* {@code scale <= 0}.
* @since 3.1
*/
public GammaDistribution(RandomGenerator rng,
double shape,
double scale,
double inverseCumAccuracy)
throws NotStrictlyPositiveException {
super(rng);
if (shape <= 0) {
throw new NotStrictlyPositiveException(LocalizedFormats.SHAPE, shape);
}
if (scale <= 0) {
throw new NotStrictlyPositiveException(LocalizedFormats.SCALE, scale);
}
this.shape = shape;
this.scale = scale;
this.solverAbsoluteAccuracy = inverseCumAccuracy;
this.shiftedShape = shape + Gamma.LANCZOS_G + 0.5;
final double aux = FastMath.E / (2.0 * FastMath.PI * shiftedShape);
this.densityPrefactor2 = shape * FastMath.sqrt(aux) / Gamma.lanczos(shape);
this.logDensityPrefactor2 = FastMath.log(shape) + 0.5 * FastMath.log(aux) -
FastMath.log(Gamma.lanczos(shape));
this.densityPrefactor1 = this.densityPrefactor2 / scale *
FastMath.pow(shiftedShape, -shape) *
FastMath.exp(shape + Gamma.LANCZOS_G);
this.logDensityPrefactor1 = this.logDensityPrefactor2 - FastMath.log(scale) -
FastMath.log(shiftedShape) * shape +
shape + Gamma.LANCZOS_G;
this.minY = shape + Gamma.LANCZOS_G - FastMath.log(Double.MAX_VALUE);
this.maxLogY = FastMath.log(Double.MAX_VALUE) / (shape - 1.0);
}
Example 12
| Source File: GammaDistribution.java From astor with GNU General Public License v2.0 | 5 votes |
|
/**
* Creates a Gamma distribution.
*
* @param rng Random number generator.
* @param shape the shape parameter
* @param scale the scale parameter
* @param inverseCumAccuracy the maximum absolute error in inverse
* cumulative probability estimates (defaults to
* {@link #DEFAULT_INVERSE_ABSOLUTE_ACCURACY}).
* @throws NotStrictlyPositiveException if {@code shape <= 0} or
* {@code scale <= 0}.
* @since 3.1
*/
public GammaDistribution(RandomGenerator rng,
double shape,
double scale,
double inverseCumAccuracy)
throws NotStrictlyPositiveException {
super(rng);
if (shape <= 0) {
throw new NotStrictlyPositiveException(LocalizedFormats.SHAPE, shape);
}
if (scale <= 0) {
throw new NotStrictlyPositiveException(LocalizedFormats.SCALE, scale);
}
this.shape = shape;
this.scale = scale;
this.solverAbsoluteAccuracy = inverseCumAccuracy;
this.shiftedShape = shape + Gamma.LANCZOS_G + 0.5;
final double aux = FastMath.E / (2.0 * FastMath.PI * shiftedShape);
this.densityPrefactor2 = shape * FastMath.sqrt(aux) / Gamma.lanczos(shape);
this.densityPrefactor1 = this.densityPrefactor2 / scale *
FastMath.pow(shiftedShape, -shape) *
FastMath.exp(shape + Gamma.LANCZOS_G);
this.minY = shape + Gamma.LANCZOS_G - FastMath.log(Double.MAX_VALUE);
this.maxLogY = FastMath.log(Double.MAX_VALUE) / (shape - 1.0);
}
Example 13
| Source File: GammaDistribution.java From astor with GNU General Public License v2.0 | 5 votes |
|
/**
* Creates a Gamma distribution.
*
* @param rng Random number generator.
* @param shape the shape parameter
* @param scale the scale parameter
* @param inverseCumAccuracy the maximum absolute error in inverse
* cumulative probability estimates (defaults to
* {@link #DEFAULT_INVERSE_ABSOLUTE_ACCURACY}).
* @throws NotStrictlyPositiveException if {@code shape <= 0} or
* {@code scale <= 0}.
* @since 3.1
*/
public GammaDistribution(RandomGenerator rng,
double shape,
double scale,
double inverseCumAccuracy)
throws NotStrictlyPositiveException {
super(rng);
if (shape <= 0) {
throw new NotStrictlyPositiveException(LocalizedFormats.SHAPE, shape);
}
if (scale <= 0) {
throw new NotStrictlyPositiveException(LocalizedFormats.SCALE, scale);
}
this.shape = shape;
this.scale = scale;
this.solverAbsoluteAccuracy = inverseCumAccuracy;
this.shiftedShape = shape + Gamma.LANCZOS_G + 0.5;
final double aux = FastMath.E / (2.0 * FastMath.PI * shiftedShape);
this.densityPrefactor2 = shape * FastMath.sqrt(aux) / Gamma.lanczos(shape);
this.densityPrefactor1 = this.densityPrefactor2 / scale *
FastMath.pow(shiftedShape, -shape) *
FastMath.exp(shape + Gamma.LANCZOS_G);
this.minY = shape + Gamma.LANCZOS_G - FastMath.log(Double.MAX_VALUE);
this.maxLogY = FastMath.log(Double.MAX_VALUE) / (shape - 1.0);
}
Example 14
| Source File: GammaDistribution.java From astor with GNU General Public License v2.0 | 4 votes |
|
/** {@inheritDoc} */
public double density(double x) {
/* The present method must return the value of
*
* 1 x a - x
* ---------- (-) exp(---)
* x Gamma(a) b b
*
* where a is the shape parameter, and b the scale parameter.
* Substituting the Lanczos approximation of Gamma(a) leads to the
* following expression of the density
*
* a e 1 y a
* - sqrt(------------------) ---- (-----------) exp(a - y + g),
* x 2 pi (a + g + 0.5) L(a) a + g + 0.5
*
* where y = x / b. The above formula is the "natural" computation, which
* is implemented when no overflow is likely to occur. If overflow occurs
* with the natural computation, the following identity is used. It is
* based on the BOOST library
* http://www.boost.org/doc/libs/1_35_0/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/igamma.html
* Formula (15) needs adaptations, which are detailed below.
*
* y a
* (-----------) exp(a - y + g)
* a + g + 0.5
* y - a - g - 0.5 y (g + 0.5)
* = exp(a log1pm(---------------) - ----------- + g),
* a + g + 0.5 a + g + 0.5
*
* where log1pm(z) = log(1 + z) - z. Therefore, the value to be
* returned is
*
* a e 1
* - sqrt(------------------) ----
* x 2 pi (a + g + 0.5) L(a)
* y - a - g - 0.5 y (g + 0.5)
* * exp(a log1pm(---------------) - ----------- + g).
* a + g + 0.5 a + g + 0.5
*/
if (x < 0) {
return 0;
}
final double y = x / scale;
if ((y <= minY) || (FastMath.log(y) >= maxLogY)) {
/*
* Overflow.
*/
final double aux1 = (y - shiftedShape) / shiftedShape;
final double aux2 = shape * (FastMath.log1p(aux1) - aux1);
final double aux3 = -y * (Gamma.LANCZOS_G + 0.5) / shiftedShape +
Gamma.LANCZOS_G + aux2;
return densityPrefactor2 / x * FastMath.exp(aux3);
}
/*
* Natural calculation.
*/
return densityPrefactor1 * FastMath.exp(-y) *
FastMath.pow(y, shape - 1);
}
Example 15
| Source File: GammaDistribution.java From astor with GNU General Public License v2.0 | 4 votes |
|
/** {@inheritDoc} */
public double density(double x) {
/* The present method must return the value of
*
* 1 x a - x
* ---------- (-) exp(---)
* x Gamma(a) b b
*
* where a is the shape parameter, and b the scale parameter.
* Substituting the Lanczos approximation of Gamma(a) leads to the
* following expression of the density
*
* a e 1 y a
* - sqrt(------------------) ---- (-----------) exp(a - y + g),
* x 2 pi (a + g + 0.5) L(a) a + g + 0.5
*
* where y = x / b. The above formula is the "natural" computation, which
* is implemented when no overflow is likely to occur. If overflow occurs
* with the natural computation, the following identity is used. It is
* based on the BOOST library
* http://www.boost.org/doc/libs/1_35_0/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/igamma.html
* Formula (15) needs adaptations, which are detailed below.
*
* y a
* (-----------) exp(a - y + g)
* a + g + 0.5
* y - a - g - 0.5 y (g + 0.5)
* = exp(a log1pm(---------------) - ----------- + g),
* a + g + 0.5 a + g + 0.5
*
* where log1pm(z) = log(1 + z) - z. Therefore, the value to be
* returned is
*
* a e 1
* - sqrt(------------------) ----
* x 2 pi (a + g + 0.5) L(a)
* y - a - g - 0.5 y (g + 0.5)
* * exp(a log1pm(---------------) - ----------- + g).
* a + g + 0.5 a + g + 0.5
*/
if (x < 0) {
return 0;
}
final double y = x / scale;
if ((y <= minY) || (FastMath.log(y) >= maxLogY)) {
/*
* Overflow.
*/
final double aux1 = (y - shiftedShape) / shiftedShape;
final double aux2 = shape * (FastMath.log1p(aux1) - aux1);
final double aux3 = -y * (Gamma.LANCZOS_G + 0.5) / shiftedShape +
Gamma.LANCZOS_G + aux2;
return densityPrefactor2 / x * FastMath.exp(aux3);
}
/*
* Natural calculation.
*/
return densityPrefactor1 * FastMath.exp(-y) * FastMath.pow(y, shape - 1);
}
Example 16
| Source File: GammaDistribution.java From astor with GNU General Public License v2.0 | 4 votes |
|
/** {@inheritDoc} */
public double density(double x) {
/* The present method must return the value of
*
* 1 x a - x
* ---------- (-) exp(---)
* x Gamma(a) b b
*
* where a is the shape parameter, and b the scale parameter.
* Substituting the Lanczos approximation of Gamma(a) leads to the
* following expression of the density
*
* a e 1 y a
* - sqrt(------------------) ---- (-----------) exp(a - y + g),
* x 2 pi (a + g + 0.5) L(a) a + g + 0.5
*
* where y = x / b. The above formula is the "natural" computation, which
* is implemented when no overflow is likely to occur. If overflow occurs
* with the natural computation, the following identity is used. It is
* based on the BOOST library
* http://www.boost.org/doc/libs/1_35_0/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/igamma.html
* Formula (15) needs adaptations, which are detailed below.
*
* y a
* (-----------) exp(a - y + g)
* a + g + 0.5
* y - a - g - 0.5 y (g + 0.5)
* = exp(a log1pm(---------------) - ----------- + g),
* a + g + 0.5 a + g + 0.5
*
* where log1pm(z) = log(1 + z) - z. Therefore, the value to be
* returned is
*
* a e 1
* - sqrt(------------------) ----
* x 2 pi (a + g + 0.5) L(a)
* y - a - g - 0.5 y (g + 0.5)
* * exp(a log1pm(---------------) - ----------- + g).
* a + g + 0.5 a + g + 0.5
*/
if (x < 0) {
return 0;
}
final double y = x / scale;
if ((y <= minY) || (FastMath.log(y) >= maxLogY)) {
/*
* Overflow.
*/
final double aux1 = (y - shiftedShape) / shiftedShape;
final double aux2 = shape * (FastMath.log1p(aux1) - aux1);
final double aux3 = -y * (Gamma.LANCZOS_G + 0.5) / shiftedShape +
Gamma.LANCZOS_G + aux2;
return densityPrefactor2 / x * FastMath.exp(aux3);
}
/*
* Natural calculation.
*/
return densityPrefactor1 * FastMath.exp(-y) *
FastMath.pow(y, shape - 1);
}
Example 17
| Source File: GammaDistribution.java From astor with GNU General Public License v2.0 | 4 votes |
|
/** {@inheritDoc} */
public double density(double x) {
/* The present method must return the value of
*
* 1 x a - x
* ---------- (-) exp(---)
* x Gamma(a) b b
*
* where a is the shape parameter, and b the scale parameter.
* Substituting the Lanczos approximation of Gamma(a) leads to the
* following expression of the density
*
* a e 1 y a
* - sqrt(------------------) ---- (-----------) exp(a - y + g),
* x 2 pi (a + g + 0.5) L(a) a + g + 0.5
*
* where y = x / b. The above formula is the "natural" computation, which
* is implemented when no overflow is likely to occur. If overflow occurs
* with the natural computation, the following identity is used. It is
* based on the BOOST library
* http://www.boost.org/doc/libs/1_35_0/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/igamma.html
* Formula (15) needs adaptations, which are detailed below.
*
* y a
* (-----------) exp(a - y + g)
* a + g + 0.5
* y - a - g - 0.5 y (g + 0.5)
* = exp(a log1pm(---------------) - ----------- + g),
* a + g + 0.5 a + g + 0.5
*
* where log1pm(z) = log(1 + z) - z. Therefore, the value to be
* returned is
*
* a e 1
* - sqrt(------------------) ----
* x 2 pi (a + g + 0.5) L(a)
* y - a - g - 0.5 y (g + 0.5)
* * exp(a log1pm(---------------) - ----------- + g).
* a + g + 0.5 a + g + 0.5
*/
if (x < 0) {
return 0;
}
final double y = x / scale;
if ((y <= minY) || (FastMath.log(y) >= maxLogY)) {
/*
* Overflow.
*/
final double aux1 = (y - shiftedShape) / shiftedShape;
final double aux2 = shape * (FastMath.log1p(aux1) - aux1);
final double aux3 = -y * (Gamma.LANCZOS_G + 0.5) / shiftedShape +
Gamma.LANCZOS_G + aux2;
return densityPrefactor2 / x * FastMath.exp(aux3);
}
/*
* Natural calculation.
*/
return densityPrefactor1 * FastMath.exp(-y) *
FastMath.pow(y, shape - 1);
}
Example 18
| Source File: GammaDistribution.java From astor with GNU General Public License v2.0 | 4 votes |
|
/** {@inheritDoc} */
public double density(double x) {
/* The present method must return the value of
*
* 1 x a - x
* ---------- (-) exp(---)
* x Gamma(a) b b
*
* where a is the shape parameter, and b the scale parameter.
* Substituting the Lanczos approximation of Gamma(a) leads to the
* following expression of the density
*
* a e 1 y a
* - sqrt(------------------) ---- (-----------) exp(a - y + g),
* x 2 pi (a + g + 0.5) L(a) a + g + 0.5
*
* where y = x / b. The above formula is the "natural" computation, which
* is implemented when no overflow is likely to occur. If overflow occurs
* with the natural computation, the following identity is used. It is
* based on the BOOST library
* http://www.boost.org/doc/libs/1_35_0/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/igamma.html
* Formula (15) needs adaptations, which are detailed below.
*
* y a
* (-----------) exp(a - y + g)
* a + g + 0.5
* y - a - g - 0.5 y (g + 0.5)
* = exp(a log1pm(---------------) - ----------- + g),
* a + g + 0.5 a + g + 0.5
*
* where log1pm(z) = log(1 + z) - z. Therefore, the value to be
* returned is
*
* a e 1
* - sqrt(------------------) ----
* x 2 pi (a + g + 0.5) L(a)
* y - a - g - 0.5 y (g + 0.5)
* * exp(a log1pm(---------------) - ----------- + g).
* a + g + 0.5 a + g + 0.5
*/
if (x < 0) {
return 0;
}
final double y = x / scale;
if ((y <= minY) || (FastMath.log(y) >= maxLogY)) {
/*
* Overflow.
*/
final double aux1 = (y - shiftedShape) / shiftedShape;
final double aux2 = shape * (FastMath.log1p(aux1) - aux1);
final double aux3 = -y * (Gamma.LANCZOS_G + 0.5) / shiftedShape +
Gamma.LANCZOS_G + aux2;
return densityPrefactor2 / x * FastMath.exp(aux3);
}
/*
* Natural calculation.
*/
return densityPrefactor1 * FastMath.exp(-y) *
FastMath.pow(y, shape - 1);
}
Example 19
| Source File: GammaDistribution.java From astor with GNU General Public License v2.0 | 4 votes |
|
/** {@inheritDoc} */
public double density(double x) {
/* The present method must return the value of
*
* 1 x a - x
* ---------- (-) exp(---)
* x Gamma(a) b b
*
* where a is the shape parameter, and b the scale parameter.
* Substituting the Lanczos approximation of Gamma(a) leads to the
* following expression of the density
*
* a e 1 y a
* - sqrt(------------------) ---- (-----------) exp(a - y + g),
* x 2 pi (a + g + 0.5) L(a) a + g + 0.5
*
* where y = x / b. The above formula is the "natural" computation, which
* is implemented when no overflow is likely to occur. If overflow occurs
* with the natural computation, the following identity is used. It is
* based on the BOOST library
* http://www.boost.org/doc/libs/1_35_0/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/igamma.html
* Formula (15) needs adaptations, which are detailed below.
*
* y a
* (-----------) exp(a - y + g)
* a + g + 0.5
* y - a - g - 0.5 y (g + 0.5)
* = exp(a log1pm(---------------) - ----------- + g),
* a + g + 0.5 a + g + 0.5
*
* where log1pm(z) = log(1 + z) - z. Therefore, the value to be
* returned is
*
* a e 1
* - sqrt(------------------) ----
* x 2 pi (a + g + 0.5) L(a)
* y - a - g - 0.5 y (g + 0.5)
* * exp(a log1pm(---------------) - ----------- + g).
* a + g + 0.5 a + g + 0.5
*/
if (x < 0) {
return 0;
}
final double y = x / scale;
if ((y <= minY) || (FastMath.log(y) >= maxLogY)) {
/*
* Overflow.
*/
final double aux1 = (y - shiftedShape) / shiftedShape;
final double aux2 = shape * (FastMath.log1p(aux1) - aux1);
final double aux3 = -y * (Gamma.LANCZOS_G + 0.5) / shiftedShape +
Gamma.LANCZOS_G + aux2;
return densityPrefactor2 / x * FastMath.exp(aux3);
}
/*
* Natural calculation.
*/
return densityPrefactor1 * FastMath.exp(-y) *
FastMath.pow(y, shape - 1);
}
Example 20
| Source File: GammaDistribution.java From astor with GNU General Public License v2.0 | 4 votes |
|
/** {@inheritDoc} */
public double density(double x) {
/* The present method must return the value of
*
* 1 x a - x
* ---------- (-) exp(---)
* x Gamma(a) b b
*
* where a is the shape parameter, and b the scale parameter.
* Substituting the Lanczos approximation of Gamma(a) leads to the
* following expression of the density
*
* a e 1 y a
* - sqrt(------------------) ---- (-----------) exp(a - y + g),
* x 2 pi (a + g + 0.5) L(a) a + g + 0.5
*
* where y = x / b. The above formula is the "natural" computation, which
* is implemented when no overflow is likely to occur. If overflow occurs
* with the natural computation, the following identity is used. It is
* based on the BOOST library
* http://www.boost.org/doc/libs/1_35_0/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/igamma.html
* Formula (15) needs adaptations, which are detailed below.
*
* y a
* (-----------) exp(a - y + g)
* a + g + 0.5
* y - a - g - 0.5 y (g + 0.5)
* = exp(a log1pm(---------------) - ----------- + g),
* a + g + 0.5 a + g + 0.5
*
* where log1pm(z) = log(1 + z) - z. Therefore, the value to be
* returned is
*
* a e 1
* - sqrt(------------------) ----
* x 2 pi (a + g + 0.5) L(a)
* y - a - g - 0.5 y (g + 0.5)
* * exp(a log1pm(---------------) - ----------- + g).
* a + g + 0.5 a + g + 0.5
*/
if (x < 0) {
return 0;
}
final double y = x / scale;
if ((y <= minY) || (FastMath.log(y) >= maxLogY)) {
/*
* Overflow.
*/
final double aux1 = (y - shiftedShape) / shiftedShape;
final double aux2 = shape * (FastMath.log1p(aux1) - aux1);
final double aux3 = -y * (Gamma.LANCZOS_G + 0.5) / shiftedShape +
Gamma.LANCZOS_G + aux2;
return densityPrefactor2 / x * FastMath.exp(aux3);
}
/*
* Natural calculation.
*/
return densityPrefactor1 * FastMath.exp(-y) * FastMath.pow(y, shape - 1);
}
