ocn_g08.h

图像处理的压缩算法

	}
	nag_mann_whitney(n1, x, n2, y, Nag_LowerTail, Nag_CompProbApprox, &u, &z, &p);
	printf("\n\n");
	printf("Test statistics              =%8.4f\n", u);
	printf("Normal statistics 		 =%8.4f\n", z);
	printf("Approximate tail probability =%8.4f\n", p);
	nag_mann_whitney(n1, x, n2, y, Nag_LowerTail, Nag_CompProbExact, &u, &z, &p);
	printf("Exact tail probability       =%8.4f\n",p);	
}

The output is following:
	
Sample size of group 1 =    16
Sample size of group 2 =    23
Mann-Whitney U test
Data values
	Group 1	 13.0  6.0 12.0  7.0 12.0  7.0 10.0  7.0
 10.0  7.0 16.0  7.0 10.0  8.0  9.0  8.0

	Group 2	 17.0  6.0 10.0  8.0 15.0  8.0 15.0 10.0
 15.0 10.0 14.0 10.0 14.0 11.0 14.0 11.0
 13.0 12.0 13.0 12.0 13.0 12.0 12.0

Test statistics              = 86.0000
Normal statistics 		 = -2.8039
Approximate tail probability =  0.0025
Exact tail probability       =  0.0020


Parameters:

Return:
	This function returns NAG error code, 0 if no error.
	
*/
int	nag_mann_whitney(
	int n1, // The number of non-tied pairs, n1>=1. 
	const double x[], // The first vector of observations.
	int n2, // The size of the second sample, n2>=1. 
	const double y[], // The second vector of observations.
	Nag_TailProbability tail, // Indicates choice of tail probability and hence the alternative hypothesis.
	Nag_CompProb exact, // Indicates if exact probability is to be computed
	double *u, // The returned Mann-Whitney rank sum statistic, U. 
	double *z, // The returned approximate Normal test statistic, z.
	double *p // The returned exact tail probability, p, as specified by the parameter tail.
); // Performs the Mann-Whitney U test on two independent samples.

/**	g08cbc
		Performs the one-sample Kolmogorov-Smirnov test for standard distributions.
	
	
Example:


void test_nag_1_sample_ks_test()
{
	double d, p, z;
	int i, n, np, ntype;
	Nag_TestStatistics ntype_enum;
	n = 30;
	
	double x[] ={0.01, 0.30, 0.20, 0.90, 1.20, 0.09, 1.30, 0.18, 0.90, 0.48,
				 1.98, 0.03, 0.50, 0.70, 0.07, 0.60, 0.95, 1.00, 0.31, 1.45,
				 1.04, 1.25, 0.15, 0.75, 0.85, 0.22, 1.56, 0.81, 0.57, 0.55};
				 
	np =2;
	double par[] ={0.0, 2.0};
	ntype = 1;
	ntype_enum = Nag_TestStatisticsDAbs;
	
	nag_1_sample_ks_test(n, x, Nag_Uniform, par, Nag_ParaSupplied, ntype_enum, &d, &z, &p);
	printf("Test against uniform distribution on(0, 2)\n");
	printf("Test statistics  D    	= %8.4f\n", d);
	printf("Z statistic    			= %8.4f\n", z);
	printf("Tail probability		= %8.4f\n", p);
	
	
	np = 2;
	par[0] = 0.0;
	par[1] = 1.0;
	ntype = 1;
	ntype_enum = Nag_TestStatisticsDAbs;
	nag_1_sample_ks_test(n, x, Nag_Normal, par, Nag_ParaEstimated, ntype_enum, &d, &z, &p);
	printf("Test  against Normal distribution with parameters estimated from the data\n");
	printf("\n");
	printf("Mean = %6.4f	and varaince = %6.4f\n",par[0],par[1]);
	printf("Test statistics  D    	= %8.4f\n", d);
	printf("Z statistic    			= %8.4f\n", z);
	printf("Tail probability		= %8.4f\n", p); 	
	
}

The output is following:
	
Test against uniform distribution on(0, 2)
Test statistics  D    	=   0.2800
Z statistic    			=   1.5336
Tail probability		=   0.0143
Test  against Normal distribution with parameters estimated from the data

Mean = 0.6967	and varaince = 0.2564
Test statistics  D    	=   0.1108
Z statistic    			=   0.6068
Tail probability		=   0.8925


Parameters:

Return:
	This function returns NAG error code, 0 if no error.
	
*/
int nag_1_sample_ks_test(
	int n, // The number of observations in the sample, n >= 3.
	const double x[], // The sample observations x1, x2,...,xN.
	Nag_Distributions dist, // The NAG distribution.
	double par[], // Contains the known values of the parameter(s) of the null distribution.
	Nag_ParaEstimates estima, // Specifies whether the values of the parameter(s) are known or estimated from data.
	Nag_TestStatistics dtype, // The test statistic to be calculated...i.e. the choice of alternative hypothesis.
	double *d, // The Kolmogorov-Smirnov test statistic.
	double *z, // A standardized value, Z, of the test statistic, D, without correction for continuity.
	double *p // The probability, P, associated with the observerd value of D. 
); // Performs the one-sample Kolmogorov-Smirnov test for standard distributions.



/**	g08cdc
		Performs the two-sample Kolmogorov-Smirnov distribution test.
Example:


void test_nag_2_sample_ks_test()
{
	double d, enda, endb, p, z;
	int init, i, m, n, ntype;
	Nag_TestStatistics ntype_enum;
	double x[100], y[50];
	n = 100;
	m = 50;
	init = 0;
	enda = 0.0;
	endb = 2.0;
	for(i = 0; i < n; i++)
		x[i] = enda +(endb -enda) * ran(init);
	enda = 0.25;
	endb = 2.25;
	for(i = 0; i < m; i++)
		y[i] = enda + (endb - enda) * ran(init);
		
	ntype = 1;
	ntype_enum = Nag_TestStatisticsDAbs;
	nag_2_sample_ks_test(n, x, m, y, ntype_enum, &d, &z, &p);
	printf("Test statistics  D    	= %8.4f\n", d);
	printf("Z statistic    			= %8.4f\n", z);
	printf("Tail probability		= %8.4f\n", p); 
}

Parameters:

Return:
	This function returns NAG error code, 0 if no error.
	
*/
int	nag_2_sample_ks_test(
	int n1, // The number of observations in the first sample, n1>=1. 
	const double x[], // The observations from the first sample. 
	int n2, // The number of observations in the second sample, n2>=1.  
	const double y[], // The observations from the second sample.
	Nag_TestStatistics ntype, // The statistic to be computed or the choice of alternative hypothesis. 
	double *d, // The  returned Kolmogorov-Smirnov test statistic according to the value of ntype.
	double *z, // The returned standardized value, Z, of the test statistic, D, without correction for continuity.
	double *p // The returned tail probability, P, associated with the observerd value of D.
); // Performs the two-sample Kolmogorov-Smirnov distribution test.


/**	g08cgc
		Performs the chi^2 goodness of fit test, for standard continuous distributions and for data
		with a chosen number of class intervals.
Example:

void test_nag_chi_sq_goodness_of_fit_test()
{
	double chisq, p, xmax, xmin;
	int i, iclass, init, n, nclass, ndf, npest;
	double x[100], cint[4], par[2] = {0.0, 1.0};
	int ifreq[5];
	double chisqi[5], eval[5], prob[5];
	Nag_Distributions cdist_enum;
	Nag_ClassBoundary class_enum;
	 
	n = 100;
	nclass = 5;
	cdist_enum = Nag_Uniform;
	
	npest = 0;
	init = 0;
	for( i =0; i < n; i++)
		x[i] = 	ran(init);		//generate random variable from 0 to 1.
	iclass = 1;
	cint[0] = par[0] + (par[1] -par[0])/nclass;
	for(i = 1; i < nclass -1; i++)
		cint[i] = cint[i - 1] +(par[1] - par[0])/nclass;
		
	class_enum = Nag_ClassBoundaryUser;
	nag_frequency_table(n, x, nclass, class_enum, cint, ifreq, &xmin, &xmax);
	nag_chi_sq_goodness_of_fit_test(nclass, ifreq, cint, cdist_enum, par, npest, prob, &chisq, &p, &ndf, eval, chisqi);
	printf("\n");
	printf("Chi-squared test statistic			=%10.4f\n",chisq);
	printf("Degrees of freedom.					=%5ld\n", ndf);
	printf("Significance level					=%10.4f\n", p);
	printf("\n");
	printf("The contributions to the test statistic are :");
	for(i = 0; i < nclass; i++)
		printf("%10.4f\n", chisqi[i]);

}

Parameters:

Return:
	This function returns NAG error code, 0 if no error.
	
*/
int	nag_chi_sq_goodness_of_fit_test(
	int k2, // The number of clsses, k2, into which the data is divided.
	const int ifreq[], // ifreq[i-1] specifies the frequency of the ith class.
	const double cint[], // cint[i-1] specifies the upper boundary value for the ith class, cint[i]<cint[i+1].  For exponential, gamma, and chi^2 cint[0]>=0..
	Nag_Distributions dist, // The NAG distribution.
	const double par[], // par[] specifies the parameters of the distribution being tested. 
	int iparam, // The number of estimated parameters of the distribution.
	const double prob[], // If the user is supplying the probability distribution then prob[i-1] contains the probability that X lies in the ith class.
	double *chisq, // The returned test statistic, chi^2, for the chi^2 goodness of fit test.
	double *p, // The returned upper tail probability from the chi^2 distribution.
	int *ndf, // Returns the degrees of freedom associated with test.
	double eval[], // eval[i-1] contains the returned expected frequency for the ith class.  
	double chisqi[] // chisqi[i-1] contains the returned contribution from the ith class to the test statistic.
); // Performs the chi^2 goodness of fit test, for standard continuous distributions.


/**	g08eac
		Performs the runs up or runs down test on a sequence of observations.

Example:

void test_nag_runs_test()
{
	double chi, df, p;
	int i, init, max_run, n, nruns;
	n = 10000;
	double x[10000];
	init =0;
	
	for(i = 0; i < n; i++)
		x[i] = 	ran(init);		//generate random variable from 0 to 1.
	max_run = 6;
	nag_runs_test(n, x, max_run, &nruns, &chi, &df, &p);
	printf("\n");
	printf("Total number of runs found =%10ld\n" , nruns);
	printf("chisq = %10.4f\n",chi);
	printf("df    = %10,4f\n",df);
	printf("Prob  = %10.4f\n", p); 	
}

Parameters:

Return:
	This function returns NAG error code, 0 if no error.
	
*/
int	nag_runs_test(
	int n, // The length of the current sequence of observations, n>=3. 
	const double x[], // The sequence of observations. 
	int maxr, // The length of the longest run for which tabulation is desired, r. That is, all runs with length greater than or equal to r are counted together.
	int *nruns, // The returned number of runs actually found.  
	double *chi, // The returned approximate chi^2 test statistic.
	double *df, // The returned number of degrees of freedom of the chi^2 statistic.
	double *prob // The returned upper tail probability corresponding to the chi^2 test statistic (i.e. significance level).
); // Performs the runs up or runs down test for randomness. 



/**	g08ebc
		Performs the pairs (serial) test for randomness on a sequence of observations in the interval [0,1].


Example:

void test_nag_pairs_test()
{
	double chi, df, p;
	int i, max_count, n, init, lag;
	init = 0;
	n = 10000;
	double x[10000];
	for(i = 0; i < n; i++)
		x[i] = 	ran(init);		//generate random variable from 0 to 1.
	max_count = 10;
	lag =1;
	nag_pairs_test(n, x, max_count, lag, &chi, &df, &p);
	printf("\n\n");	
	printf("CHISQ	= %10.4f\n",chi);
	printf("DF		= %8.2f\n", df);
	printf("Probabitlity =%10.4f",p);	
}


Parameters:

Return:
	This function returns NAG error code, 0 if no error.
	
*/

int	nag_pairs_test(
	int n, // The number of observations, n>=2.
	const double x[], // The sequence of observations in the interval [0,1].
	int msize, // The size of the matrix of counts, m>=2.
	int lag, // The lag, l, to be used in choosing pairs.
	double *chi, // The returned chi^2 test statistic for testing the null hypothesis of randomness.
	double *df, // The returned degrees of freedom for the chi^2 test statistic. 
	double *p // The returned upper tail probability associated with the chi^2 test statistic (i.e. significance level).
); // Performs the pairs (serial) test for randomness.



/**	g08ecc
		Performs the triplets test for randomness on a sequence of observations from the interval [0,1]..

Example:

void test_nag_triplets_test()
{
	double chi, df, p;
	int i, init, max_count, n;
	n = 10000;
	double x[10000];
	for(i = 0; i < n; i++)
		x[i] = 	ran(init);		//generate random variable from 0 to 1.
	max_count = 5;
	nag_triplets_test(n, x, max_count, &chi, &df, &p);
	printf("\n");
	printf("CHISQ	= %10.4f\n",chi);
	printf("DF		= %8.2f\n", df);
	printf("Prob	=%10.4f",p);
}


Parameters:

Return:
	This function returns NAG error code, 0 if no error.
	
*/
int	nag_triplets_test(
	int n, // The number of observations, n>=3.
	const double x[], // The sequence of observations in the interval [0,1].
	int msize, // The size of the matrix of counts, m>=2.
	double *chi, // The returned chi^2 test statistic for testing the null hypothesis of randomness.
	double *df, // The returned degrees of freedom for the chi^2 test statistic. 
	double *p // The returned upper tail probability associated with the chi^2 test statistic (i.e. significance level).
); // Performs the triplets test for randomness.


/**	g08edc
		Performs the gaps test for randomness


Example:

void test_nag_gaps_test()
{
	int i, init, max_gap, n, num_gaps;
	double chi, df, lower, length, p, upper;
	init = 0;
	n = 5000;
	double x[5000];
	for(i = 0; i < n; i++)
		x[i] = 	ran(init);		//generate random variable from 0 to 1.
	num_gaps = 0;
	max_gap = 10;
	length = 1.0;
	lower = 0.4;
	upper = 0.6;
	nag_gaps_test(n, x, num_gaps, max_gap, lower, upper, length, &chi, &df, &p);
	printf("\n");
	printf("CHISQ	= %10.4f\n",chi);
	printf("DF		= %8.2f\n", df);
	printf("Prob	=%10.4f",p);
}


Parameters:

Return:
	This function returns NAG error code, 0 if no error.
	
*/
int	nag_gaps_test(
	int n, // The length of the current sequence of observations, n>=1.
	const double x[], // The sequence of observations.
	int m, // The maximum number of gaps to be sought. If m<=0 then there is no limit placed on the number of gaps that are found.
	int k, // The length of the longest gap for which tabulation is desired. 
	double rl, // The lower limit of the interval to be used to define the gaps (rl<ru and ru-rl<til).  
	double ru, // The upper limit of the interval to be used to define the gaps (ru>rl and ru-rl<til).
	double til, // The total lengeth of the interval which contains all possible numbers that may arise in the sequence (til>0 and ru-rl<til).
	double *chi, // The returned chi^2 test statistic for testing the null hypothesis of randomness.
	double *df, // The returned degrees of freedom for the chi^2 test statistic. 
	double *prob // The returned upper tail probability associated with the chi^2 test statistic (i.e. significance level). 
); // Performs the gaps test for randomness.

/* end proto */
#endif //!_O_NAG_G08_H