Classes in this File | Line Coverage | Branch Coverage | Complexity | ||||||||
GammaDistributionImpl |
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| 2.1;2.1 |
1 | /* |
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2 | * Copyright 2003-2004 The Apache Software Foundation. |
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3 | * |
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4 | * Licensed under the Apache License, Version 2.0 (the "License"); |
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5 | * you may not use this file except in compliance with the License. |
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6 | * You may obtain a copy of the License at |
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7 | * |
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8 | * http://www.apache.org/licenses/LICENSE-2.0 |
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9 | * |
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10 | * Unless required by applicable law or agreed to in writing, software |
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11 | * distributed under the License is distributed on an "AS IS" BASIS, |
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12 | * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. |
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13 | * See the License for the specific language governing permissions and |
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14 | * limitations under the License. |
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15 | */ |
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16 | package org.apache.commons.math.distribution; |
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17 | ||
18 | import java.io.Serializable; |
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19 | ||
20 | import org.apache.commons.math.MathException; |
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21 | import org.apache.commons.math.special.Gamma; |
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22 | ||
23 | /** |
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24 | * The default implementation of {@link GammaDistribution} |
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25 | * |
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26 | * @version $Revision$ $Date: 2005-02-26 05:11:52 -0800 (Sat, 26 Feb 2005) $ |
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27 | */ |
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28 | public class GammaDistributionImpl extends AbstractContinuousDistribution |
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29 | implements GammaDistribution, Serializable { |
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30 | ||
31 | /** Serializable version identifier */ |
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32 | static final long serialVersionUID = -3239549463135430361L; |
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33 | ||
34 | /** The shape parameter. */ |
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35 | private double alpha; |
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36 | ||
37 | /** The scale parameter. */ |
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38 | private double beta; |
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39 | ||
40 | /** |
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41 | * Create a new gamma distribution with the given alpha and beta values. |
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42 | * @param alpha the shape parameter. |
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43 | * @param beta the scale parameter. |
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44 | */ |
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45 | public GammaDistributionImpl(double alpha, double beta) { |
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46 | 142 | super(); |
47 | 142 | setAlpha(alpha); |
48 | 134 | setBeta(beta); |
49 | 130 | } |
50 | ||
51 | /** |
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52 | * For this disbution, X, this method returns P(X < x). |
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53 | * |
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54 | * The implementation of this method is based on: |
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55 | * <ul> |
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56 | * <li> |
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57 | * <a href="http://mathworld.wolfram.com/Chi-SquaredDistribution.html"> |
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58 | * Chi-Squared Distribution</a>, equation (9).</li> |
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59 | * <li>Casella, G., & Berger, R. (1990). <i>Statistical Inference</i>. |
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60 | * Belmont, CA: Duxbury Press.</li> |
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61 | * </ul> |
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62 | * |
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63 | * @param x the value at which the CDF is evaluated. |
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64 | * @return CDF for this distribution. |
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65 | * @throws MathException if the cumulative probability can not be |
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66 | * computed due to convergence or other numerical errors. |
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67 | */ |
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68 | public double cumulativeProbability(double x) throws MathException{ |
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69 | double ret; |
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70 | ||
71 | 1580 | if (x <= 0.0) { |
72 | 2 | ret = 0.0; |
73 | } else { |
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74 | 1578 | ret = Gamma.regularizedGammaP(getAlpha(), x / getBeta()); |
75 | } |
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76 | ||
77 | 1580 | return ret; |
78 | } |
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79 | ||
80 | /** |
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81 | * For this distribution, X, this method returns the critical point x, such |
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82 | * that P(X < x) = <code>p</code>. |
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83 | * <p> |
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84 | * Returns 0 for p=0 and <code>Double.POSITIVE_INFINITY</code> for p=1. |
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85 | * |
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86 | * @param p the desired probability |
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87 | * @return x, such that P(X < x) = <code>p</code> |
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88 | * @throws MathException if the inverse cumulative probability can not be |
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89 | * computed due to convergence or other numerical errors. |
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90 | * @throws IllegalArgumentException if <code>p</code> is not a valid |
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91 | * probability. |
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92 | */ |
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93 | public double inverseCumulativeProbability(final double p) |
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94 | throws MathException { |
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95 | 36 | if (p == 0) { |
96 | 2 | return 0d; |
97 | } |
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98 | 34 | if (p == 1) { |
99 | 2 | return Double.POSITIVE_INFINITY; |
100 | } |
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101 | 32 | return super.inverseCumulativeProbability(p); |
102 | } |
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103 | ||
104 | /** |
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105 | * Modify the shape parameter, alpha. |
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106 | * @param alpha the new shape parameter. |
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107 | * @throws IllegalArgumentException if <code>alpha</code> is not positive. |
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108 | */ |
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109 | public void setAlpha(double alpha) { |
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110 | 150 | if (alpha <= 0.0) { |
111 | 12 | throw new IllegalArgumentException("alpha must be positive"); |
112 | } |
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113 | 138 | this.alpha = alpha; |
114 | 138 | } |
115 | ||
116 | /** |
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117 | * Access the shape parameter, alpha |
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118 | * @return alpha. |
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119 | */ |
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120 | public double getAlpha() { |
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121 | 1686 | return alpha; |
122 | } |
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123 | ||
124 | /** |
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125 | * Modify the scale parameter, beta. |
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126 | * @param beta the new scale parameter. |
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127 | * @throws IllegalArgumentException if <code>beta</code> is not positive. |
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128 | */ |
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129 | public void setBeta(double beta) { |
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130 | 138 | if (beta <= 0.0) { |
131 | 6 | throw new IllegalArgumentException("beta must be positive"); |
132 | } |
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133 | 132 | this.beta = beta; |
134 | 132 | } |
135 | ||
136 | /** |
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137 | * Access the scale parameter, beta |
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138 | * @return beta. |
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139 | */ |
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140 | public double getBeta() { |
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141 | 1662 | return beta; |
142 | } |
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143 | ||
144 | /** |
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145 | * Access the domain value lower bound, based on <code>p</code>, used to |
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146 | * bracket a CDF root. This method is used by |
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147 | * {@link #inverseCumulativeProbability(double)} to find critical values. |
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148 | * |
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149 | * @param p the desired probability for the critical value |
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150 | * @return domain value lower bound, i.e. |
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151 | * P(X < <i>lower bound</i>) < <code>p</code> |
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152 | */ |
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153 | protected double getDomainLowerBound(double p) { |
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154 | // TODO: try to improve on this estimate |
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155 | 28 | return Double.MIN_VALUE; |
156 | } |
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157 | ||
158 | /** |
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159 | * Access the domain value upper bound, based on <code>p</code>, used to |
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160 | * bracket a CDF root. This method is used by |
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161 | * {@link #inverseCumulativeProbability(double)} to find critical values. |
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162 | * |
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163 | * @param p the desired probability for the critical value |
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164 | * @return domain value upper bound, i.e. |
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165 | * P(X < <i>upper bound</i>) > <code>p</code> |
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166 | */ |
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167 | protected double getDomainUpperBound(double p) { |
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168 | // TODO: try to improve on this estimate |
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169 | // NOTE: gamma is skewed to the left |
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170 | // NOTE: therefore, P(X < μ) > .5 |
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171 | ||
172 | double ret; |
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173 | ||
174 | 28 | if (p < .5) { |
175 | // use mean |
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176 | 12 | ret = getAlpha() * getBeta(); |
177 | } else { |
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178 | // use max value |
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179 | 16 | ret = Double.MAX_VALUE; |
180 | } |
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181 | ||
182 | 28 | return ret; |
183 | } |
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184 | ||
185 | /** |
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186 | * Access the initial domain value, based on <code>p</code>, used to |
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187 | * bracket a CDF root. This method is used by |
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188 | * {@link #inverseCumulativeProbability(double)} to find critical values. |
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189 | * |
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190 | * @param p the desired probability for the critical value |
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191 | * @return initial domain value |
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192 | */ |
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193 | protected double getInitialDomain(double p) { |
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194 | // TODO: try to improve on this estimate |
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195 | // Gamma is skewed to the left, therefore, P(X < μ) > .5 |
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196 | ||
197 | double ret; |
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198 | ||
199 | 28 | if (p < .5) { |
200 | // use 1/2 mean |
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201 | 12 | ret = getAlpha() * getBeta() * .5; |
202 | } else { |
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203 | // use mean |
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204 | 16 | ret = getAlpha() * getBeta(); |
205 | } |
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206 | ||
207 | 28 | return ret; |
208 | } |
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209 | } |