# Binomial distribution

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

where:

• x – value of the random variable
• n – number of tests
• p – probability of success for each test

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 MathProbabilityDensityBinomial Calculates the probability density function of the binomial distribution MathCumulativeDistributionBinomial Calculates the value of the binomial probability distribution function MathQuantileBinomial Calculates the value of the inverse binomial distribution function for the specified probability MathRandomBinomial Generates a pseudorandom variable/array of pseudorandom variables distributed according to the binomial law MathMomentsBinomial Calculates the theoretical numerical values of the first 4 moments of the binomial distribution

Example:

 #include  #include  #include  #property script_show_inputs //--- input parameters input double n_par=40;        // the number of tests input double p_par=0.75;      // probability of success for each test //+------------------------------------------------------------------+ //| 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=20;       // 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 binomial distribution    MathRandomBinomial(n_par,p_par,n,data); //--- calculate the data to plot the histogram    CalculateHistogramArray(data,x,y,max,min,ncells);   //--- obtain the theoretically calculated data at the interval of [min,max]    double x2[];    double y2[];    MathSequence(0,n_par,1,x2);    MathProbabilityDensityBinomial(x2,n_par,p_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);   }