Added hyperbolic secant distribution

docs/js/DistributionHyperbolicSecant.js

@@ -0,0 +1,136 @@
+/*
+Copyright 2024 Alexander Herzog
+
+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.
+*/
+
+export {HyperbolicSecantDistribution}
+
+import {ContinuousProbabilityDistribution} from "./Distribution.js";
+import {language} from "./Language.js";
+import {beginMathML, endMathML, isin, setR, setRHTML, setRPlusHTML, defF, variable, frac, minus, mul} from './MathMLTools.js';
+
+/**
+ * Hyperbolic secant distribution
+ */
+class HyperbolicSecantDistribution extends ContinuousProbabilityDistribution {
+
+  constructor() {
+    super(language.distributions.hyperbolicSecant.name);
+
+    this.support=setRHTML;
+    this.infoText=language.distributions.hyperbolicSecant.info;
+    this.wikipediaURL=language.distributions.hyperbolicSecant.wikipedia;
+    this.pdfText=this.#getPDFText();
+    this.cdfText=this.#getCDFText();
+
+    this._addContinuousParameter("mu","&mu;",language.distributions.hyperbolicSecant.parameterInfoMu+" (<i>a</i>"+isin+setRHTML+")",null,false,null,false,5);
+    this._addContinuousParameter("sigma","&sigma;",language.distributions.hyperbolicSecant.parameterInfoSigma+" (<i>b</i>"+isin+setRPlusHTML+")",0,false,null,false,3);
+
+    this._setCalcParameter("x",8);
+  }
+
+  #getPDFText() {
+    const f=variable("f");
+    const x=variable("x");
+    const mu=variable("&mu;");
+    const sigma=variable("&sigma;");
+
+    let pdf="";
+    pdf+=beginMathML;
+    pdf+=defF(f,x);
+    pdf+=frac("<mn>1</mn>",defF("cosh","<mn>&pi;</mn>"+frac(x+minus+mu,"<mn>2</mn>"+sigma),false)+mul+"<mn>2</mn>"+sigma);
+    pdf+=endMathML;
+    pdf+=" "+language.distributions.for+" ";
+    pdf+=beginMathML;
+    pdf+=x+"<mo>&isin;</mo>"+setR;
+    pdf+=endMathML;
+    return pdf;
+  }
+
+  #getCDFText() {
+    const F=variable("F");
+    const x=variable("x");
+    const mu=variable("&mu;");
+    const sigma=variable("&sigma;");
+
+    let cdf="";
+    cdf+=beginMathML;
+    cdf+=defF(F,x);
+    cdf+=frac("<mn>2</mn>","<mn>&pi;</mn>")+defF("atan",defF("exp","<mn>&pi;</mn>"+frac(x+minus+mu,"<mn>2</mn>"+sigma),false),false);
+    cdf+=endMathML;
+    cdf+=" "+language.distributions.for+" ";
+    cdf+=beginMathML;
+    cdf+=x+"<mo>&isin;</mo>"+setR;
+    cdf+=endMathML;
+    return cdf;
+  }
+
+  #getPDF(values, x) {
+    if (values.sigma==0) return (x==values.mu)?Infinity:0;
+
+    const z=(x-values.mu)/values.sigma;
+	return (1/(Math.cosh(Math.PI*z/2)*2*values.sigma));
+  }
+
+  #getCDF(values, x) {
+    if (values.sigma==0) return (x==values.mu)?Infinity:0;
+
+    const z=(x-values.mu)/values.sigma;
+    const arg=Math.PI*z*0.5;
+	if (arg>=750) return 1;
+	return (2*Math.atan(Math.exp(arg)))/Math.PI;
+  }
+
+  _calcDistribution(values) {
+    /* Characteristics */
+
+    const mu=variable("&mu;");
+    const sigma=variable("&sigma;");
+
+    const meanFormula=beginMathML+mu+endMathML;
+    const varianceFormula=beginMathML+sigma+endMathML;
+
+    const meanValue=values.mu;
+    const varianceValue=values.sigma**2;
+
+    this._setContinuousCharacteristics(meanFormula,meanValue,varianceFormula,varianceValue);
+
+    /* Diagram */
+
+    const that=this;
+    const minX=Math.min(0,values.mu-2*values.sigma);
+    const maxX=Math.max(10,values.mu+2*values.sigma);
+    this._setContinuousDiagram(minX,maxX,x=>that.#getPDF(values,x),x=>that.#getCDF(values,x));
+  }
+
+  calcProbability(values, x) {
+    return [this.#getPDF(values,x),this.#getCDF(values,x)];
+  }
+
+  getRandomNumber(values) {
+    const u=Math.random();
+
+    /*
+    y=2/pi*atan(exp(pi*(x-mu)/(2*sigma)))
+    log(tan(y*pi/2))=pi*(x-mu)/(2*sigma)
+    log(tan(y*pi/2))/pi*2*sigma+mu=x
+    */
+    return Math.log(Math.tan(u*Math.PI/2))/Math.PI*2*values.sigma+values.mu;
+  }
+
+  fitParameters(data) {
+    if (data.std<=0) return null;
+    return {mu: data.mean, sigma: data.std};
+  }
+}

docs/js/DistributionReciprocal.js

@@ -18,7 +18,7 @@ export {ReciprocalDistribution}
 
 import {ContinuousProbabilityDistribution} from "./Distribution.js";
 import {language} from "./Language.js";
-import {beginMathML, endMathML, isin, setRPlus, setRHTML, defF, variable, frac, plus, minus, mul} from './MathMLTools.js';
+import {beginMathML, endMathML, isin, setRPlus, setRHTML, defF, variable, frac, minus} from './MathMLTools.js';
 
 /**
  * Reciprocal distribution

docs/js/DistributionSetup.js

@@ -50,6 +50,7 @@ import {KumaraswamyDistribution} from './DistributionKumaraswamy.js';
 import {SineDistribution} from './DistributionSine.js';
 import {ArcsineDistribution} from './DistributionArcsine.js';
 import {GumbelDistribution} from './DistributionGumbel.js';
+import {HyperbolicSecantDistribution} from './DistributionHyperbolicSecant.js';
 
 
 /**
@@ -92,6 +93,7 @@ listDistributions.push(new KumaraswamyDistribution());
 listDistributions.push(new SineDistribution());
 listDistributions.push(new ArcsineDistribution());
 listDistributions.push(new GumbelDistribution());
+listDistributions.push(new HyperbolicSecantDistribution());
 
 /**
  * Returns the probability distribution object for a probability distribution name

docs/js/Language.js

@@ -446,6 +446,13 @@ lang.distributions.gumbel.wikipedia="https://de.wikipedia.org/wiki/Gumbel-Vertei
 lang.distributions.gumbel.parameterInfoMean="Erwartungswert";
 lang.distributions.gumbel.parameterInfoStd="Standardabweichung";
 
+lang.distributions.hyperbolicSecant={};
+lang.distributions.hyperbolicSecant.name="Hyperbolische Sekantenverteilung";
+lang.distributions.hyperbolicSecant.info="";
+lang.distributions.hyperbolicSecant.wikipedia="https://en.wikipedia.org/wiki/Hyperbolic_secant_distribution"; /* No German Wikipedia page */
+lang.distributions.hyperbolicSecant.parameterInfoMu="Lage (Erwartungswert)";
+lang.distributions.hyperbolicSecant.parameterInfoSigma="Skalierung (Standardabweichung)";
+
 lang.numbers={};
 lang.numbers.N="Natürliche Zahlen";
 lang.numbers.N0="Natürliche Zahlen zzgl. der Null";
@@ -889,6 +896,13 @@ lang.distributions.gumbel.wikipedia="https://en.wikipedia.org/wiki/Gumbel_distri
 lang.distributions.gumbel.parameterInfoMean="Expected value";
 lang.distributions.gumbel.parameterInfoStd="Standard deviation";
 
+lang.distributions.hyperbolicSecant={};
+lang.distributions.hyperbolicSecant.name="Hyperbolic secant distribution";
+lang.distributions.hyperbolicSecant.info="";
+lang.distributions.hyperbolicSecant.wikipedia="https://en.wikipedia.org/wiki/Hyperbolic_secant_distribution";
+lang.distributions.hyperbolicSecant.parameterInfoMu="Location (mean)";
+lang.distributions.hyperbolicSecant.parameterInfoSigma="Scale (standard deviation)";
+
 lang.numbers={};
 lang.numbers.N="Natural numbers";
 lang.numbers.N0="Natural numbers and zero";