# Hypergeometric distribution

This section contains functions for working with hypergeometric distribution. They allow to calculate density, probability, quantiles and to generate pseudo-random numbers distributed according to the hypergeometric law. The hypergeometric distribution is defined by the following formula:

where:

• x — value of the random variable (integer)
• m — total number of objects
• k — number of objects with the desired characteristic
• n — number of object draws

In addition to the calculation of the individual random variables, the library also implements the ability to work with arrays of random variables.

 Function Description MathProbabilityDensityHypergeometric Calculates the probability density function of the hypergeometric distribution MathCumulativeDistributionHypergeometric Calculates the value of the hypergeometric probability distribution function MathQuantileHypergeometric Calculates the value of the inverse hypergeometric distribution function for the specified probability MathRandomHypergeometric Generates a pseudorandom variable/array of pseudorandom variables distributed according to the hypergeometric law MathMomentsHypergeometric Calculates the theoretical numerical values of the first 4 moments of the hypergeometric distribution

Example:

 #include  #include  #include  #property script_show_inputs //--- input parameters input double m_par=60;      // the total number of objects input double k_par=30;      // the number of objects with the desired characteristic input double n_par=30;      // the number of object draws //+------------------------------------------------------------------+ //| Script program start function                                    | //+------------------------------------------------------------------+ void OnStart()   { //--- hide the price chart    ChartSetInteger(0,CHART_SHOW,false); //--- initialize the random number generator      MathSrand(GetTickCount()); //--- generate a sample of the random variable    long chart=0;    string name="GraphicNormal";    int n=1000000;       // the number of values in the sample    int ncells=15;       // the number of intervals in the histogram    double x[];          // centers of the histogram intervals    double y[];          // the number of values from the sample falling within the interval    double data[];       // sample of random values    double max,min;      // the maximum and minimum values in the sample //--- obtain a sample from the hypergeometric distribution    MathRandomHypergeometric(m_par,k_par,n_par,n,data); //--- calculate the data to plot the histogram    CalculateHistogramArray(data,x,y,max,min,ncells); //--- obtain the sequence boundaries and the step for plotting the theoretical curve    double step;    GetMaxMinStepValues(max,min,step);    PrintFormat("max=%G min=%G",max,min); //--- obtain the theoretically calculated data at the interval of [min,max]    double x2[];    double y2[];    MathSequence(0,n_par,1,x2);    MathProbabilityDensityHypergeometric(x2,m_par,k_par,n_par,false,y2); //--- set the scale    double theor_max=y2[ArrayMaximum(y2)];    double sample_max=y[ArrayMaximum(y)];    double k=sample_max/theor_max;    for(int i=0; i=cells) ind=cells-1;       frequency[ind]++;      }    return (true);   } //+------------------------------------------------------------------+ //|  Calculates values for sequence generation                       | //+------------------------------------------------------------------+ void GetMaxMinStepValues(double &maxv,double &minv,double &stepv)   { //--- calculate the absolute range of the sequence to obtain the precision of normalization    double range=MathAbs(maxv-minv);    int degree=(int)MathRound(MathLog10(range)); //--- normalize the maximum and minimum values to the specified precision    maxv=NormalizeDouble(maxv,degree);    minv=NormalizeDouble(minv,degree); //--- sequence generation step is also set based on the specified precision    stepv=NormalizeDouble(MathPow(10,-degree),degree);    if((maxv-minv)/stepv<10)       stepv/=10.;   }