指数分布测试Java版

 

指数分布(Exponential Distrubution):

 

f(x;rate) = rate*exp(-rate*x) when x>=0

            0                 when x<0

 

F(x,rate) = 1 - exp(-rate*x) when x>=0

            0                when x<0

 

E(x) = 1/rate

V(x) = 1/rate**2

 

反变换法(Inverse transform method):

 

How does non transform a sample of the uniform[0,1] random variable into a sample of a given distribution?

 

Problem: Generate sample of random variable X with a given density f(x)?

 

Answer: Example exp(rate)?

 

1.Generate random umber U

2.Set X = -(1/rate)ln(1-U)

   or  X = -(1/rate)ln(U)

 

测试代码和结果：

 test_exppdf.java

 

 

 

 

 

 

import java.util.Enumeration;
import java.util.Random;
import java.util.Vector;



public class test_exppdf {

    public static void main(String args[]){
        int i;
        float dly;
        float rate;
        float rnd;
        Random rndGen;
        
        rate = (float)1;
        rndGen = new Random();
        
        
        for(i=0;i<1000;i++){
                rnd = rndGen.nextFloat();
                dly = (float)( (1/rate)*Math.log(1/rnd));
                System.out.println(i+" "+dly+" "+rnd);
        }
        
    }
}

 

 

javac test_exppdf.java

java  test_exppdf >result.txt

start Dataplot GUI

READ result.txt X Y Z

4-PLOT Y

 

结果证明该方法能够产生相应的随机数.

 

为了扩展Dataplot的容量，需要使用以下命令：

 

 DIMENSION 200 VARIABLES

 DIMENSION 200 OBSERVATIONS

 DIMENSION 200 200

 DIMENSION 200 COLUMNS

 DIMENSION 200 ROWS

取X的数学期望:

 LET EX = MEAN X