Examples - pi.science.distribution.PIParetoDistribution
1. How to compute Pareto distribution propability for X (CDF, sigma=1) ?
PIParetoDistribution distribution = new PIParetoDistribution();
distribution.SetAlpha( 3 );
distribution.SetXM( 1 );
Console.WriteLine( "Probability for x=0.0 : " + distribution.GetCDF( 0.0 ) );
Console.WriteLine( "Probability for x=1.0 : " + distribution.GetCDF( 1.0 ) );
Console.WriteLine( "Probability for x=2.0 : " + distribution.GetCDF( 2.0 ) );
Console.WriteLine( "Probability for x=2.5 : " + distribution.GetCDF( 2.5 ) );
Output:
Probability for x=0.0 : 0
Probability for x=1.0 : 0
Probability for x=2.0 : 0,875
Probability for x=2.5 : 0,936
2. How to compute X for Pareto distribution propability (InverseCDF, sigma=1) ?
PIParetoDistribution distribution = new PIParetoDistribution();
distribution.SetAlpha( 3 );
distribution.SetXM( 1 );
Console.WriteLine( "X value for probability for prob=0.0 : " + distribution.GetInverseCDF( 0.0 ) );
Console.WriteLine( "X value for probability for prob=0.8752 : " + distribution.GetInverseCDF( 0.8752 ) );
Console.WriteLine( "X value for probability for prob=0.9363 : " + distribution.GetInverseCDF( 0.9363 ) );
X value for probability for prob=0.0 : 0
X value for probability for prob=0.8752 : 2,00106750056148
X value for probability for prob=0.9363 : 2,50391886010766
3. How to compute Pareto probability density for X (=curve points, PDF) ?
PIParetoDistribution distribution = new PIParetoDistribution();
distribution.SetAlpha( 3 );
distribution.SetXM( 1 );
Console.WriteLine( "x=0.1 : " + distribution.GetPDF( 0.1 ) );
Console.WriteLine( "x=0.5 : " + distribution.GetPDF( 0.5 ) );
Console.WriteLine( "x=1.0 : " + distribution.GetPDF( 1.0 ) );
Console.WriteLine( "x=2.0 : " + distribution.GetPDF( 2.0 ) );
Console.WriteLine( "x=5.0 : " + distribution.GetPDF( 5.0 ) );
Output:
x=0.1 : 0
x=0.5 : 0
x=1.0 : 3
x=2.0 : 0,1875
x=5.0 : 0,0048
