Goodness-of-Fit Tests for RAND29

Chi-Square Test

	Beta (4-Parameter)	Exponential	Gamma (3-Parameter)	Loglogistic (3-Parameter)	Lognormal (3-Parameter)
Chi-Square	27,52	18,56	18,24	33,6	21,12
D.f.
P-Value	0,436028	0,948745	0,919942	0,214354	0,82031

Kolmogorov-Smirnov Test

	Beta (4-Parameter)	Exponential	Gamma (3-Parameter)	Loglogistic (3-Parameter)	Lognormal (3-Parameter)
DPLUS	0,0504193	0,0213833	0,0136884	0,0431031	0,0366641
DMINUS	0,0281886	0,0212866	0,0380872	0,0561711	0,0589022
DN	0,0504193	0,0213833	0,0380872	0,0561711	0,0589022
P-Value	0,689439	0,999989	0,93377	0,553314	0,503134

Modified Kolmogorov-Smirnov D

	Beta (4-Parameter)	Exponential	Gamma (3-Parameter)	Loglogistic (3-Parameter)	Lognormal (3-Param)
D	0,0504193	0,0213833	0,0380872	0,0561711	0,0589022
Modified Form	0,719479	0,294284	0,543501	0,801557	0,840529
P-Value	>=0.10	>=0.10	>=0.10	>=0.10	>=0.10

Cramer-Von Mises W^2

	Beta (4-Parameter)	Exponential	Gamma (3-Parameter)	Loglogistic (3-Parameter)	Lognormal (3-Paramet)
W^2	0,110988	0,0170931	0,000422917	0,136962	0,118823
Modified Form	0,109548	0,0171068		0,135652	0,117423
P-Value	>=0.10	0,994109		>=0.10	>=0.10

Anderson-Darling A^2

	Beta (4-Parameter)	Exponential	Gamma (3-Parameter)	Loglogistic (3-Parameter)	Lognormal (3-Param)
A^2	0,830918	0,125744		1,09845	0,705441
Modified Form	0,830918	0,126121		1,09845	0,705441
P-Value	>=0.10	0,995776		>=0.10	>=0.10

 

*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 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)

Goodness-of-Fit Tests for RAND35

Chi-Square Test

	Beta	Gamma (3-Parameter)	Laplace	Normal	Uniform
Chi-Square	24,0	205,76	239,36	149,12	106,24
D.f.
P-Value	0,728932	0,0	0,0	0,0	9,58613E-11

 

Kolmogorov-Smirnov Test

	Beta	Gamma (3-Parameter)	Laplace	Normal	Uniform
DPLUS	0,0313339	0,124906	0,103512	0,0955848	0,135887
DMINUS	0,0517606	0,165313	0,106939	0,0951846	0,064354
DN	0,0517606	0,165313	0,106939	0,0955848	0,135887
P-Value	0,657504	0,0000357763	0,020626	0,0517452	0,00123962

 

Modified Kolmogorov-Smirnov D

	Beta	Gamma (3-Parameter)	Laplace	Normal	Uniform
D	0,0517606	0,165313	0,106939	0,0955848	0,135887
Modified Form	0,73862	2,359	1,52601	1,35656	1,93909
P-Value	>=0.10	<0.01	<0.05	<0.01	<0.01

 

Cramer-Von Mises W^2

	Beta	Gamma (3-Parameter)	Laplace	Normal	Uniform
W^2	0,114775	1,89509	0,865302	0,641629	0,000422917
Modified Form	0,113354		0,867634	0,643233	-0,00156989
P-Value	>=0.10		<0.01	1,66985E-7	>=0.10

 

Anderson-Darling A^2

	Beta	Gamma (3-Parameter)	Laplace	Normal	Uniform
A^2	0,652858	10,5829	6,09075	4,73725
Modified Form	0,652858		6,09075	4,75528
P-Value	>=0.10*	*	<0.01*	9,00171E-12*	*

*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 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]