Goodness-of-Fit Tests for RAND3

Goodness-of-Fit Tests for RAND3

Chi-Square Test

	Binomial	Discrete Uniform	Geometric	Poisson	Triangular
Chi-Square	6,7069	110,97	144,507	6,31039	15,3702
D.f.
P-Value	0,568561	0,0	0,0	0,612508	0,0175646

 

Kolmogorov-Smirnov Test

	Binomial	Discrete Uniform	Geometric	Poisson	Triangular
DPLUS					0,116421
DMINUS					0,121423
DN					0,121423
P-Value					0,00549293

 

Modified Kolmogorov-Smirnov D

	Binomial	Discrete Uniform	Geometric	Poisson	Triangular
D					0,121423
Modified Form					1,7327
P-Value					<0.01

 

Cramer-Von Mises W^2

	Binomial	Discrete Uniform	Geometric	Poisson	Triangular
W^2					0,577903
Modified Form					0,578797
P-Value					<0.05

 

Anderson-Darling A^2

	Binomial	Discrete Uniform	Geometric	Poisson	Triangular
A^2					3,4001
Modified Form					3,4001
P-Value					<0.05

*Indicates that the P-Value has been compared to tables of critical values specially constructed for fitting the selected distribution. Other P-values are based on general tables and may be very conservative (except for the Chi-Square Test).

 

The StatAdvisor

This pane shows the results of tests run to determine whether RAND3 can be adequately modeled by various distributions. The chi-square test divides the range of RAND3 into nonoverlapping intervals and compares the number of observations in each class to the number expected based on the fitted distribution. The Kolmogorov-Smirnov test computes the maximum distance between the cumulative distribution of RAND3 and the CDF of the fitted distribution. The other statistics compare the empirical distribution function to the fitted CDF in different ways.

 

P-values less than 0,05 would indicate that RAND3 does not come from the selected distribution with 95% confidence.

 

RAND4 - Равномерное распределение (lower limit = 0,0140383, upper limit = 2,99975)

Goodness-of-Fit Tests for RAND4

Chi-Square Test

	Chi-Square	Gamma	Normal	Uniform	Weibull
Chi-Square	126,72	107,52	80,96	30,72	76,8
D.f.
P-Value	7,4829E-14	5,91914E-11	8,37522E-7	0,378742	0,00000337147

 

Kolmogorov-Smirnov Test

	Chi-Square	Gamma	Normal	Uniform	Weibull
DPLUS	0,228625	0,097676	0,0788659	0,0317271	0,0727645
DMINUS	0,0697265	0,10737	0,0899839	0,0433768	0,089851
DN	0,228625	0,10737	0,0899839	0,0433768	0,089851
P-Value	0,0	0,019878	0,0784207	0,846001	0,0791743

 

Modified Kolmogorov-Smirnov D

	Chi-Square	Gamma	Normal	Uniform	Weibull
D	0,228625	0,10737	0,0899839	0,0433768	0,089851
Modified Form	3,26245	1,53215	1,27707	0,618984	1,27069
P-Value	<0.01*	<0.05*	<0.01*	>=0.10*	<0.01*

 

Cramer-Von Mises W^2

	Chi-Square	Gamma	Normal	Uniform	Weibull
W^2	1,46688	0,65957	0,31951	0,000422917	0,430021
Modified Form	1,47222		0,320309	-0,00156989	0,436103
P-Value	<0.01*	*	0,000195397*	>=0.10*	<0.01*

 

Anderson-Darling A^2

	Chi-Square	Gamma	Normal	Uniform	Weibull
A^2	9,87324	4,07313	2,51094		3,12265
Modified Form	9,87324		2,52049		3,16681
P-Value	<0.01*	*	0,00000231145*	*	<0.01*

*Indicates that the P-Value has been compared to tables of critical values specially constructed for fitting the selected distribution. Other P-values are based on general tables and may be very conservative (except for the Chi-Square Test).

 

The StatAdvisor

This pane shows the results of tests run to determine whether RAND4 can be adequately modeled by various distributions. The chi-square test divides the range of RAND4 into nonoverlapping intervals and compares the number of observations in each class to the number expected based on the fitted distribution. The Kolmogorov-Smirnov test computes the maximum distance between the cumulative distribution of RAND4 and the CDF of the fitted distribution. The other statistics compare the empirical distribution function to the fitted CDF in different ways.

 

P-values less than 0,05 would indicate that RAND4 does not come from the selected distribution with 95% confidence.

RAND9 - Гамма (3 параметра) - shape = 219,992 scale = 5,70041, lower threshold = -39,3596

The StatAdvisor

This pane shows the results of tests run to determine whether RAND9 can be adequately modeled by various distributions. The chi-square test divides the range of RAND9 into nonoverlapping intervals and compares the number of observations in each class to the number expected based on the fitted distribution. The Kolmogorov-Smirnov test computes the maximum distance between the cumulative distribution of RAND9 and the CDF of the fitted distribution. The other statistics compare the empirical distribution function to the fitted CDF in different ways.

 

P-values less than 0,05 would indicate that RAND9 does not come from the selected distribution with 95% confidence.

RAND15 - Хи-Квадрат c количеством степеней свободы - degrees of freedom = 6,22819

The StatAdvisor

This pane shows the results of tests run to determine whether RAND15 can be adequately modeled by various distributions. The chi-square test divides the range of RAND15 into nonoverlapping intervals and compares the number of observations in each class to the number expected based on the fitted distribution. The Kolmogorov-Smirnov test computes the maximum distance between the cumulative distribution of RAND15 and the CDF of the fitted distribution. The other statistics compare the empirical distribution function to the fitted CDF in different ways.

 

P-values less than 0,05 would indicate that RAND15 does not come from the selected distribution with 95% confidence.

 

RAND18 - Лог-логистическое (median = 50,2727 shape = 0,0239156 lower threshold = -51,4883)

The StatAdvisor

This pane shows the results of tests run to determine whether RAND18 can be adequately modeled by various distributions. The chi-square test divides the range of RAND18 into nonoverlapping intervals and compares the number of observations in each class to the number expected based on the fitted distribution. The Kolmogorov-Smirnov test computes the maximum distance between the cumulative distribution of RAND18 and the CDF of the fitted distribution. The other statistics compare the empirical distribution function to the fitted CDF in different ways.

 

P-values less than 0,05 would indicate that RAND18 does not come from the selected distribution with 95% confidence.

RAND27 - Равномерное распределение

Goodness-of-Fit Tests for RAND27

Chi-Square Test

	Beta (4-Parameter)	Gamma (3-Parameter)	Normal	Triangular	Uniform
Chi-Square	42,56	78,08	66,56	60,8	29,76
D.f.
P-Value	0,0289612	0,00000128499	0,0000882718	0,000321565	0,426056

 

Kolmogorov-Smirnov Test

	Beta (4-Parameter)	Gamma (3-Parameter)	Normal	Triangular	Uniform
DPLUS	0,0251278	0,0576424	0,0603382	0,0744455	0,0414552
DMINUS	0,103336	0,0803238	0,0765786	0,0872536	0,0417551
DN	0,103336	0,0803238	0,0765786	0,0872536	0,0417551
P-Value	0,0279253	0,151465	0,191642	0,0951717	0,876598

 

Modified Kolmogorov-Smirnov D

	Beta (4-Parameter)	Gamma (3-Parameter)	Normal	Triangular	Uniform
D	0,103336	0,0803238	0,0765786	0,0872536	0,0417551
Modified Form	1,4746	1,14621	1,08682	1,2451	0,595842
P-Value	<0.05	>=0.10	<0.01	<0.10	>=0.10

 

Cramer-Von Mises W^2

	Beta (4-Parameter)	Gamma (3-Parameter)	Normal	Triangular	Uniform
W^2	0,860478	0,318546	0,310825	0,501063	0,000422917
Modified Form	0,862786		0,311602	0,501573	-0,00156989
P-Value	<0.01		0,00024532	<0.05	>=0.10

 

Anderson-Darling A^2

	Beta (4-Parameter)	Gamma (3-Parameter)	Normal	Triangular	Uniform
A^2	5,35834	2,45149	2,39539	3,66899
Modified Form	5,35834		2,40451	3,66899
P-Value	<0.01		0,00000443457	<0.05

*Indicates that the P-Value has been compared to tables of critical values specially constructed for fitting the selected distribution. Other P-values are based on general tables and may be very conservative (except for the Chi-Square Test).

 

The StatAdvisor

This pane shows the results of tests run to determine whether RAND27 can be adequately modeled by various distributions. The chi-square test divides the range of RAND27 into nonoverlapping intervals and compares the number of observations in each class to the number expected based on the fitted distribution. The Kolmogorov-Smirnov test computes the maximum distance between the cumulative distribution of RAND27 and the CDF of the fitted distribution. The other statistics compare the empirical distribution function to the fitted CDF in different ways.

 

P-values less than 0,05 would indicate that RAND27 does not come from the selected distribution with 95% confidence.

RAND29 - Экспоненциальное (mean = 0,974828)

The StatAdvisor

This pane shows the results of tests run to determine whether RAND29 can be adequately modeled by various distributions. The chi-square test divides the range of RAND29 into nonoverlapping intervals and compares the number of observations in each class to the number expected based on the fitted distribution. The Kolmogorov-Smirnov test computes the maximum distance between the cumulative distribution of RAND29 and the CDF of the fitted distribution. The other statistics compare the empirical distribution function to the fitted CDF in different ways.

 

P-values less than 0,05 would indicate that RAND29 does not come from the selected distribution with 95% confidence.

RAND35 Бета (shape 1 = 0,487408 shape 2 = 0,602051)

The StatAdvisor

This pane shows the results of tests run to determine whether RAND35 can be adequately modeled by various distributions. The chi-square test divides the range of RAND35 into nonoverlapping intervals and compares the number of observations in each class to the number expected based on the fitted distribution. The Kolmogorov-Smirnov test computes the maximum distance between the cumulative distribution of RAND35 and the CDF of the fitted distribution. The other statistics compare the empirical distribution function to the fitted CDF in different ways.

 

P-values less than 0,05 would indicate that RAND35 does not come from the selected distribution with 95% confidence.

 

 

В результате было получено два распределения с равномерным распределением: RAND4 и RAND27
Сравним..

 

Paired Samples - RAND4 & RAND27

Data variable: RAND4-RAND27

200 values ranging from -0,752163 to 4,70767
Confidence Intervals for RAND4 - RAND27

95,0% confidence interval for mean: 2,00378 +/- 0,169834 [1,83395; 2,17361]

95,0% confidence interval for standard deviation: [1,10916; 1,35067]

The StatAdvisor

This pane displays the results of tests concerning the population from which the sample of RAND4-RAND27 comes. The t-test tests the null hypothesis that the mean RAND4-RAND27 equals 0,0 versus the alternative hypothesis that the mean RAND4-RAND27 is not equal to 0,0. Since the P-value for this test is less than 0,05, we can reject the null hypothesis at the 95,0% confidence level. The sign test tests the null hypothesis that the median RAND4-RAND27 equals 0,0 versus the alternative hypothesis that the median RAND4-RAND27 is not equal to 0,0. It is based on counting the number of values above and below the hypothesized median. Since the P-value for this test is less than 0,05, we can reject the null hypothesis at the 95,0% confidence level. The signed rank test tests the null hypothesis that the median RAND4-RAND27 equals 0,0 versus the alternative hypothesis that the median RAND4-RAND27 is not equal to 0,0. It is based on comparing the average ranks of values above and below the hypothesized median. Since the P-value for this test is less than 0,05, we can reject the null hypothesis at the 95,0% confidence level. The sign and signed rank tests are less sensitive to the presence of outliers but are somewhat less powerful than the t-test if the data all come from a single normal distribution.

 

The chi-square test tests the null hypothesis that the standard deviation of RAND4-RAND27 equals 1,0 versus the alternative hypothesis that the standard deviation of RAND4-RAND27 is not equal to 1,0. Since the P-value for this test is less than 0,05, we can reject the null hypothesis at the 95,0% confidence level.

 

Goodness-of-Fit Tests for RAND3

Chi-Square Test

	Binomial	Discrete Uniform	Geometric	Poisson	Triangular
Chi-Square	6,7069	110,97	144,507	6,31039	15,3702
D.f.
P-Value	0,568561	0,0	0,0	0,612508	0,0175646

 

Kolmogorov-Smirnov Test

	Binomial	Discrete Uniform	Geometric	Poisson	Triangular
DPLUS					0,116421
DMINUS					0,121423
DN					0,121423
P-Value					0,00549293

 

Modified Kolmogorov-Smirnov D

	Binomial	Discrete Uniform	Geometric	Poisson	Triangular
D					0,121423
Modified Form					1,7327
P-Value					<0.01

 

Cramer-Von Mises W^2

	Binomial	Discrete Uniform	Geometric	Poisson	Triangular
W^2					0,577903
Modified Form					0,578797
P-Value					<0.05

 

Anderson-Darling A^2

	Binomial	Discrete Uniform	Geometric	Poisson	Triangular
A^2					3,4001
Modified Form					3,4001
P-Value					<0.05

*Indicates that the P-Value has been compared to tables of critical values specially constructed for fitting the selected distribution. Other P-values are based on general tables and may be very conservative (except for the Chi-Square Test).

 

The StatAdvisor

This pane shows the results of tests run to determine whether RAND3 can be adequately modeled by various distributions. The chi-square test divides the range of RAND3 into nonoverlapping intervals and compares the number of observations in each class to the number expected based on the fitted distribution. The Kolmogorov-Smirnov test computes the maximum distance between the cumulative distribution of RAND3 and the CDF of the fitted distribution. The other statistics compare the empirical distribution function to the fitted CDF in different ways.

 

P-values less than 0,05 would indicate that RAND3 does not come from the selected distribution with 95% confidence.

 

RAND4 - Равномерное распределение (lower limit = 0,0140383, upper limit = 2,99975)