1 package nl.tudelft.simulation.jstats.distributions; 2 3 import org.djutils.exceptions.Throw; 4 5 import nl.tudelft.simulation.jstats.math.ProbMath; 6 import nl.tudelft.simulation.jstats.streams.StreamInterface; 7 8 /** 9 * The Erlang distribution. For more information on this distribution see 10 * <a href="https://mathworld.wolfram.com/ErlangDistribution.html"> http://mathworld.wolfram.com/ErlangDistribution.html 11 * </a><br> 12 * The Erlang distribution is the distribution of a sum of k independent exponential variables with the scale parameter as the 13 * mean. The scale parameter is equal to 1/rate or 1/λ, giving the entire Erlang distribution a mean of k*scale. 14 * <p> 15 * Copyright (c) 2002-2024 Delft University of Technology, Jaffalaan 5, 2628 BX Delft, the Netherlands. All rights reserved. See 16 * for project information <a href="https://simulation.tudelft.nl/" target="_blank"> https://simulation.tudelft.nl</a>. The DSOL 17 * project is distributed under a three-clause BSD-style license, which can be found at 18 * <a href="https://https://simulation.tudelft.nl/dsol/docs/latest/license.html" target="_blank"> 19 * https://https://simulation.tudelft.nl/dsol/docs/latest/license.html</a>. 20 * </p> 21 * @author <a href="https://www.linkedin.com/in/peterhmjacobs">Peter Jacobs </a> 22 * @author <a href="https://www.tudelft.nl/averbraeck">Alexander Verbraeck</a> 23 */ 24 public class DistErlang extends DistContinuous 25 { 26 /** */ 27 private static final long serialVersionUID = 1L; 28 29 /** 30 * k is the shape parameter of the Erlang distribution. The shape k is the number of times a drawing is done from the 31 * exponential distribution, where the Erlang distribution is the sum of these k independent exponential variables. 32 */ 33 private final int k; 34 35 /** scale is the mean of a single exponential distribution (1/rate), of which k are summed. */ 36 private final double scale; 37 38 /** the rate value of the Erlang distribution (1 / scale). */ 39 private final double lambda; 40 41 /** distGamma is the underlying gamma distribution. */ 42 private final DistGamma distGamma; 43 44 /** GAMMATHRESHOLD is the threshold above which we use a gamma function and below repeated drawing. */ 45 private static final short GAMMATHRESHOLD = 10; 46 47 /** 48 * Construct a new Erlang distribution with k and a mean (so not k and a rate) as parameters. It is the distribution of a 49 * sum of k independent exponential variables with the scale parameter as the mean. The scale parameter is equal to 1/rate 50 * or 1/λ, giving the entire Erlang distribution a mean of k*scale. 51 * @param stream StreamInterface; the random number stream 52 * @param scale double; the mean of a single sample from the exponential distribution, of which k are summed. Equal to 53 * 1/rate or 1/λ. 54 * @param k int; the shape parameter of the Erlang distribution. The shape k is the number of times a drawing is done from 55 * the exponential distribution, where the Erlang distribution is the sum of these k independent exponential 56 * variables. 57 * @throws IllegalArgumentException when k <= 0 or scale <= 0 58 */ 59 public DistErlang(final StreamInterface stream, final double scale, final int k) 60 { 61 super(stream); 62 Throw.when(k <= 0 || scale <= 0.0, IllegalArgumentException.class, "Error Erlang - k <= 0 or scale <= 0"); 63 this.k = k; 64 this.scale = scale; 65 this.lambda = 1.0 / scale; 66 this.distGamma = this.k <= DistErlang.GAMMATHRESHOLD ? null : new DistGamma(stream, this.k, this.scale); 67 } 68 69 /** {@inheritDoc} */ 70 @Override 71 public double draw() 72 { 73 if (this.k <= DistErlang.GAMMATHRESHOLD) 74 { 75 // according to Law and Kelton, Simulation Modeling and Analysis 76 // repeated drawing and composition is usually faster for k<=10 77 double product = 1.0; 78 for (int i = 1; i <= this.k; i++) 79 { 80 product = product * this.stream.nextDouble(); 81 } 82 return -this.scale * Math.log(product); 83 } 84 // and using the gamma distribution is faster for k>10 85 return this.distGamma.draw(); 86 } 87 88 /** {@inheritDoc} */ 89 @Override 90 public double getProbabilityDensity(final double x) 91 { 92 if (x < 0) 93 { 94 return 0; 95 } 96 return this.lambda * Math.exp(-this.lambda * x) * Math.pow(this.lambda * x, this.k - 1) 97 / ProbMath.factorial(this.k - 1); 98 } 99 100 /** 101 * @return k 102 */ 103 public int getK() 104 { 105 return this.k; 106 } 107 108 /** 109 * @return scale parameter 110 */ 111 public double getScale() 112 { 113 return this.scale; 114 } 115 116 /** {@inheritDoc} */ 117 @Override 118 public void setStream(final StreamInterface stream) 119 { 120 super.setStream(stream); 121 if (this.distGamma != null) 122 { 123 this.distGamma.setStream(stream); 124 } 125 } 126 127 /** {@inheritDoc} */ 128 @Override 129 public String toString() 130 { 131 return "Erlang(" + this.scale + "," + this.k + ")"; 132 } 133 }