StatBean Name: Distributions

Purpose: Computes probabilities and generates random numbers for many probability distributions.

DataSource: None.

Read/Write Properties

Name	Type	Description	Possible Values	Default Value
distributionName	String[nDists]	Name of distribution.	From list below.	"Normal"
nDists	int	Number of distributions entered.	1-25	1
parameter1	double[nDists]	First parameters for the distribution.	Valid parameter.	0.0
parameter2	double[nDists]	Second parameters for the distribution.	Valid parameter.	1.0
parameter3	double[nDists]	Third parameters for the distribution.	Valid parameter.	0.0

Other Public Methods

Name	Description	Arguments	Return Value
void calculateStatistics()	Causes the function to calculate the desired distributions.	None.	None.
double getCdf(double x,int k)	Computes cumulative distribution function.	Value of random variable x, distribution number.	cdf at x.
double getInverseCdf(double p,int k)	Computes inverse cumulative distribution function.	Value of cdf p, distribution number.	Smallest value of x for which cdf is less than or equal to p.
double getMean(int k)	Returns the mean of the distribution.	Distribution number.	Mean.
double getPdf(double x,int k)	Computes probability density or mass function.	Value of random variable x, distribution number.	pdf or pmf at x.
boolean getRandomNumbers(double x[],int n,int k)	Generates n random numbers from the distribution, distribution number.	Output array,number of random numbers to be generated.	true if success
double getVariance(int k)	Returns the variance of the distribution.	Distribution number.	Variance.

Available Discrete Distributions

Name	Range of X	Parameters	Restrictions	Mean
Bernoulli	0,1	probability p	0<=p<=1	p
Binomial	0,1,...,n	probability p, sample size n	n>=1, 0<=p<=1	np
Discrete Uniform	a,a+1,...,b	lower limit a, upper limit b	a<=b	(a+b)/2
Geometric	0,1,2,...	probability p	1>=p>0	(1-p)/p
Hypergeometric	0,1,...,min(m,n)	number of successes m, sample size n, population size N	N>=m>=0, N>=n>=1	mn/N
Negative Binomial	k,k+1,...	probability p, number of successes k	1>=p>0, k>0	k/p
Poisson	0,1,2,...	mean lambda	lambda>0	lambda

Available Continuous Distributions

Name	Range of X	Parameters	Restrictions	Mean
Beta	0<=X<=1	shape alpha1, shape alpha2	alpha1>0, alpha2>0	alpha1/(alpha1+alpha2)
Cauchy	all real X	median theta, shape beta	beta>0	not defined
Chi-Square	X>=0	degrees of freedom v	v>0	v
Erlang	X>=0	shape alpha, scale lambda	integer alpha>=1, lambda>0	alpha/lambda
Exponential	X>=0	scale lambda	lambda>0	1/lambda
Extreme Value	all real X	shape alpha, scale beta	beta>0	alpha-0.57721*beta
F	X>=0	num. d.f. v, den. d.f. w	integer v>=1, integer w>=1	w/(w-2)
Gamma	X>=0	shape alpha, scale lambda	alpha>0, lambda>0	alpha/lambda
Laplace	all real X	mean mu, scale lambda	lambda>0	mu (note: sigma=sqrt(2)/lambda)
Logistic	all real X	mean mu, std. dev. sigma	sigma>0	mu
Lognormal	X>0	mean mu, std. dev. sigma	sigma>0	exp(mu+sigma*sigma/2)
Normal	all real X	mean mu, std. dev. sigma	sigma>0	mu
Pareto	X>=1	scale c	c>0	c/(c-1)
Student's t	all real X	degrees of freedom v	v>=1	0
Triangular	a<=X<=b	minimum a, mode c, maximum b	a<=c<=b	(a+b+c)/3
Uniform	a<=X<=b	minimum a, maximum b	a<=b	(a+b)/2
Weibull	X>=0	shape alpha, scale beta	alpha>0, beta>0	(beta*gamma(1/alpha))/alpha

Code Sample

//create a calculation bean
Distributions distributions1 = new STATBEANS.Distributions();

//set the number of distributions to be evaluated
distributions1.setNDists(2);

//define each distribution
distributions1.setDistributionName("Normal",0);
distributions1.setParameter1(50.0,0);
distributions1.setParameter2(10.0,0);
distributions1.setDistributionName("Lognormal",1);
distributions1.setParameter1(50.0,1);
distributions1.setParameter2(20.0,1);

//set up a table to display probabilities
DistributionsTable distributionsTable1 = new STATBEANS.DistributionsTable();

//define values for which probabilities are desired
double x[]=new double[6];
x[0]=10.0;
x[1]=20.0;
x[2]=30.0;
x[3]=40.0;
x[4]=50.0;
x[5]=60.0;
distributionsTable1.setValues(x);

//add the table to the display
add(distributionsTable1);

//create a plot bean
DistributionsPlot distributionsPlot1 = new STATBEANS.DistributionsPlot();

//add the plot to the display
add(distributionsPlot1);

//make the table and plot beans listeners for changes in the calculation bean
distributions1.addDataChangeListener(distributionsTable1.listenerForDataChange);
distributions1.addDataChangeListener(distributionsPlot1.listenerForDataChange);

//instruct the calculation bean to compute the probabilities
distributions1.calculateStatistics();