NormalDistribution.java
/*
* Java Genetic Algorithm Library (@__identifier__@).
* Copyright (c) @__year__@ Franz Wilhelmstötter
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*
* Author:
* Franz Wilhelmstötter (franz.wilhelmstoetter@gmx.at)
*/
package org.jenetics.stat;
import static java.lang.String.format;
import static java.util.Objects.requireNonNull;
import static org.jenetics.internal.math.statistics.Φ;
import static org.jenetics.internal.math.statistics.φ;
import static org.jenetics.internal.util.object.eq;
import static org.jenetics.internal.util.object.nonNegative;
import java.io.Serializable;
import java.util.Locale;
import org.jscience.mathematics.number.Float64;
import org.jenetics.internal.util.HashBuilder;
import org.jenetics.util.Function;
import org.jenetics.util.Range;
/**
* Normal (Gaussian) distribution. With
*
* <p>
* <img
* src="doc-files/normal-pdf.gif"
* alt="f(x)=\frac{1}{\sqrt{2\pi \sigma^{2}}}\cdot
* e^{-\frac{(x-\mu)^2}{2\sigma^{2}}})"
* />
* </p>
* as <i>pdf</i> and
* <p>
* <img
* src="doc-files/normal-cdf.gif"
* alt="f(x)=\frac{1}{2}\cdot \left [ 1 + \textup{erf} \left(
* \frac{x - \mu }{\sqrt{2\sigma^{2}}} \right) \right ]"
* />
* </p>
* as <i>cdf</i>.
*
* @see <a href="http://en.wikipedia.org/wiki/Normal_distribution">Normal distribution</a>
*
* @author <a href="mailto:franz.wilhelmstoetter@gmx.at">Franz Wilhelmstötter</a>
* @since 1.0
* @version 1.0 — <em>$Date: 2014-03-01 $</em>
*/
public class NormalDistribution<
N extends Number & Comparable<? super N>
>
implements Distribution<N>
{
/**
* <p>
* <img
* src="doc-files/normal-pdf.gif"
* alt="f(x)=\frac{1}{\sqrt{2\pi \sigma^{2}}}\cdot
* e^{-\frac{(x-\mu)^2}{2\sigma^{2}}})"
* />
* </p>
*
* @author <a href="mailto:franz.wilhelmstoetter@gmx.at">Franz Wilhelmstötter</a>
* @since 1.0
* @version 1.0 — <em>$Date: 2014-03-01 $</em>
*/
static final class PDF<N extends Number & Comparable<? super N>>
implements
Function<N, Float64>,
Serializable
{
private static final long serialVersionUID = 1L;
private final Range<N> _domain;
private final double _mean;
private final double _var;
private final double _stddev;
public PDF(final Range<N> domain, final double mean, final double var) {
_domain = domain;
_mean = mean;
_var = var;
_stddev = Math.sqrt(var);
}
@Override
public Float64 apply(final N value) {
final double x = value.doubleValue();
Float64 result = Float64.ZERO;
if (_domain.contains(value)) {
result = Float64.valueOf(φ(x, _mean, _stddev));
}
return result;
}
@Override
public String toString() {
return format(
Locale.ENGLISH,
"p(x) = N[µ=%f, σ²=%f](x)", _mean, _var
);
}
}
/**
* <p>
* <img
* src="doc-files/normal-cdf.gif"
* alt="f(x)=\frac{1}{2}\cdot \left [ 1 + \textup{erf} \left(
* \frac{x - \mu }{\sqrt{2\sigma^{2}}} \right) \right ]"
* />
* </p>
*
* @author <a href="mailto:franz.wilhelmstoetter@gmx.at">Franz Wilhelmstötter</a>
* @since 1.0
* @version 1.0 — <em>$Date: 2014-03-01 $</em>
*/
static final class CDF<N extends Number & Comparable<? super N>>
implements
Function<N, Float64>,
Serializable
{
private static final long serialVersionUID = 1L;
private final double _min;
private final double _max;
private final double _mean;
private final double _var;
private final double _stddev;
public CDF(final Range<N> domain, final double mean, final double var) {
_min = domain.getMin().doubleValue();
_max = domain.getMax().doubleValue();
_mean = mean;
_var = var;
_stddev = Math.sqrt(var);
}
@Override
public Float64 apply(final N value) {
final double x = value.doubleValue();
Float64 result = null;
if (x < _min) {
result = Float64.ZERO;
} else if (x > _max) {
result = Float64.ONE;
} else {
result = Float64.valueOf(Φ(x, _mean, _stddev));
}
return result;
}
@Override
public String toString() {
return format(
Locale.ENGLISH,
"P(x) = 1/2(1 + erf((x - %f)/(sqrt(2·%f))))",
_mean, _var
);
}
}
private final Range<N> _domain;
private final Function<N, Float64> _cdf;
private final Function<N, Float64> _pdf;
private final double _mean;
private final double _var;
/**
* Create a new normal distribution object.
*
* @param domain the domain of the distribution.
* @param mean the mean value of the normal distribution.
* @param var the variance of the normal distribution.
* @throws NullPointerException if the {@code domain} is {@code null}.
* @throws IllegalArgumentException if the variance is negative.
*/
public NormalDistribution(
final Range<N> domain,
final double mean,
final double var
) {
_domain = requireNonNull(domain, "Domain");
_mean = mean;
_var = nonNegative(var, "Variance");
_pdf = new PDF<>(_domain, _mean, _var);
_cdf = new CDF<>(_domain, _mean, _var);
}
@Override
public Range<N> getDomain() {
return _domain;
}
/**
* Return a new CDF object.
*
* <p>
* <img
* src="doc-files/normal-cdf.gif"
* alt="f(x)=\frac{1}{2}\cdot \left [ 1 + \textup{erf} \left(
* \frac{x - \mu }{\sqrt{2\sigma^{2}}} \right) \right ]"
* />
* </p>
*/
@Override
public Function<N, Float64> getCDF() {
return _cdf;
}
/**
* Return a new PDF object.
*
* <p>
* <img
* src="doc-files/normal-pdf.gif"
* alt="f(x)=\frac{1}{\sqrt{2\pi \sigma^{2}}}\cdot e^{-\frac{(x-\mu)^2}{2\sigma^{2}}})"
* />
* </p>
*/
@Override
public Function<N, Float64> getPDF() {
return _pdf;
}
@Override
public int hashCode() {
return HashBuilder.of(getClass()).and(_domain).and(_mean).and(_var).value();
}
@Override
public boolean equals(final Object obj) {
if (obj == this) {
return true;
}
if (obj == null || obj.getClass() != getClass()) {
return false;
}
final NormalDistribution<?> dist = (NormalDistribution<?>)obj;
return eq(_domain, dist._domain) &&
eq(_mean, dist._mean) &&
eq(_var, dist._var);
}
@Override
public String toString() {
return format("N[µ=%f, σ²=%f]", _mean, _var);
}
}