RandomNumberGeneratorWrongPareto - Revision history

Craigdo at 07:57, 30 May 2009

2009-05-30T07:57:20Z

← Older revision		Revision as of 07:57, 30 May 2009
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	[[User:Craigdo\|Craigdo]] 23:51, ~~17 April~~ 2009 (UTC)		[[User:Craigdo\|Craigdo]] 07:57, 30 May 2009 (UTC)

Craigdo: /* Outcome */

2009-04-19T21:13:56Z

Outcome

← Older revision		Revision as of 21:13, 19 April 2009
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	<font color="Red" size=5> Fail </font>		<font color="Red" size=5> Fail </font>

	Since 4695.05 is massively greater than the rejection value of 67.5048 we can state that the chi square statistic we measured is inconistent with statistical fluctuations and that the ns-3 Pareto random number generator, when given a shape parameter of 1.1, does '''not''' generate random numbers distributed according to the Pareto distribution with shape parameter 1.0.		Since 4695.05 is (massively) greater than the rejection value of 67.5048 we can state that the chi square statistic we measured is inconistent with statistical fluctuations and that the ns-3 Pareto random number generator, when given a shape parameter of 1.1, does '''not''' generate random numbers distributed according to the Pareto distribution with shape parameter 1.0.

	=== Data ===		=== Data ===

Craigdo: /* Outcome */

2009-04-19T21:13:34Z

Outcome

← Older revision		Revision as of 21:13, 19 April 2009
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	<font color="Red" size=5> Fail </font>		<font color="Red" size=5> Fail </font>

	Since ~~this~~ massively greater than the rejection value of 67.5048 we can state that the chi square statistic we measured is inconistent with statistical fluctuations and that the ns-3 Pareto random number generator, when given a shape parameter of 1.1, does '''not''' generate random numbers distributed according to the Pareto distribution with shape parameter 1.0.		Since 4695.05 is massively greater than the rejection value of 67.5048 we can state that the chi square statistic we measured is inconistent with statistical fluctuations and that the ns-3 Pareto random number generator, when given a shape parameter of 1.1, does '''not''' generate random numbers distributed according to the Pareto distribution with shape parameter 1.0.

	=== Data ===		=== Data ===

Craigdo: /* Confused Random Number Generator */

2009-04-18T00:08:05Z

Confused Random Number Generator

← Older revision		Revision as of 00:08, 18 April 2009
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	This test is an illustration of what might happen if a random number generator produced an incorrect distribution. The Pareto distribution takes a shape parameter. In this test, we intentionally generate a Pareto distribution with a slightly different shape parameter (alpha = 1.1) and compare it to a Pareto distribution with alpha = 1.0.		This test is an illustration of what might happen if a random number generator produced an incorrect distribution. The Pareto distribution takes a shape parameter. In this test, we intentionally generate a Pareto distribution with a slightly different shape parameter (alpha = 1.1) and compare it to a Pareto distribution with alpha = 1.0.

	Our goal is to show that a random number generator that generates an "incorrectly" shaped Pareto distribution fails the chi square test.		Our goal is to show that a random number generator that generates an "incorrectly" shaped Pareto distribution fails the chi square test for one with a "correctly" shaped Pareto distribution.

	=== Methodology ===		=== Methodology ===

Craigdo at 00:07, 18 April 2009

2009-04-18T00:07:05Z

← Older revision		Revision as of 00:07, 18 April 2009
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	=== Outcome ===		=== Outcome ===

			<font color="Red" size=5> Fail </font>

	Since this massively greater than the rejection value of 67.5048 we can state that the chi square statistic we measured is inconistent with statistical fluctuations and that the ns-3 Pareto random number generator, when given a shape parameter of 1.1, does '''not''' generate random numbers distributed according to the Pareto distribution with shape parameter 1.0.		Since this massively greater than the rejection value of 67.5048 we can state that the chi square statistic we measured is inconistent with statistical fluctuations and that the ns-3 Pareto random number generator, when given a shape parameter of 1.1, does '''not''' generate random numbers distributed according to the Pareto distribution with shape parameter 1.0.

Craigdo at 23:59, 17 April 2009

2009-04-17T23:59:43Z

← Older revision		Revision as of 23:59, 17 April 2009
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	Since the expected value is provided for us (we do not calculate it from the data) the degrees of freedom in the chi square test is 50. Using this value, we calculate a maximum chi squared statistic corresponding to the 0.05 significance level (using the GNU Scientific Library gsl_cdf_chisq_Qinv function) as 67.5048. We calculate the expected values using a shape parameter of alpha = 1.0. Ten runs of the test for goodness of fit results in an average chi square statistic of 4695.05.		Since the expected value is provided for us (we do not calculate it from the data) the degrees of freedom in the chi square test is 50. Using this value, we calculate a maximum chi squared statistic corresponding to the 0.05 significance level (using the GNU Scientific Library gsl_cdf_chisq_Qinv function) as 67.5048. We calculate the expected values using a shape parameter of alpha = 1.0. Ten runs of the test for goodness of fit results in an average chi square statistic of 4695.05.

			=== Outcome ===

	Since this massively greater than the rejection value of 67.5048 we can state that the chi square statistic we measured is inconistent with statistical fluctuations and that the ns-3 Pareto random number generator, when given a shape parameter of 1.1, does '''not''' generate random numbers distributed according to the Pareto distribution with shape parameter 1.0.		Since this massively greater than the rejection value of 67.5048 we can state that the chi square statistic we measured is inconistent with statistical fluctuations and that the ns-3 Pareto random number generator, when given a shape parameter of 1.1, does '''not''' generate random numbers distributed according to the Pareto distribution with shape parameter 1.0.

Craigdo: /* Confused Random Number Generator */

2009-04-17T23:56:23Z

Confused Random Number Generator

← Older revision		Revision as of 23:56, 17 April 2009
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	This test is an illustration of what might happen if a random number generator produced an incorrect distribution. The Pareto distribution takes a shape parameter. In this test, we intentionally generate a Pareto distribution with a slightly different shape parameter (alpha = 1.1) and compare it to a Pareto distribution with alpha = 1.0.		This test is an illustration of what might happen if a random number generator produced an incorrect distribution. The Pareto distribution takes a shape parameter. In this test, we intentionally generate a Pareto distribution with a slightly different shape parameter (alpha = 1.1) and compare it to a Pareto distribution with alpha = 1.0.

	Our goal is to show that a random number generator that generates an incorrectly shaped Pareto distribution fails the chi square test.		Our goal is to show that a random number generator that generates an "incorrectly" shaped Pareto distribution fails the chi square test.

	=== Methodology ===		=== Methodology ===

Craigdo: /* Data */

2009-04-17T23:55:41Z

Data

← Older revision		Revision as of 23:55, 17 April 2009
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	The following is a histogram of the random numbers generated in one run of the test. Expected values are calulated based on the area of the cumulative distribution function corresponding to the histogram bin. This expected value is calculated using the GNU Scientific Library gsl_cdf_pareto_P function.		The following is a histogram of the random numbers generated in one run of the test. Expected values are calulated based on the area of the cumulative distribution function corresponding to the histogram bin. This expected value is calculated using the GNU Scientific Library gsl_cdf_pareto_P function.

	Note that the actual values correspond to a Pareto distribution and the expected values correspond to ~~an exponential~~ distribution.		Note that the actual values correspond to a Pareto distribution of shape 1.1 and the expected values correspond to a Pareto distribution of shape 1.0.

	[[Image:Rng-wrongpareto.png]]		[[Image:Rng-wrongpareto.png]]

Craigdo: /* Data */

2009-04-17T23:55:05Z

Data

← Older revision		Revision as of 23:55, 17 April 2009
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	=== Data ===		=== Data ===

	The following is a histogram of the random numbers generated in one run of the test. Expected values are calulated based on the area of the cumulative distribution function corresponding to the histogram bin. This expected value is calculated using the GNU Scientific Library ~~gsl_cdf_exponential_P~~ function.		The following is a histogram of the random numbers generated in one run of the test. Expected values are calulated based on the area of the cumulative distribution function corresponding to the histogram bin. This expected value is calculated using the GNU Scientific Library gsl_cdf_pareto_P function.

	Note that the actual values correspond to a Pareto distribution and the expected values correspond to an exponential distribution.		Note that the actual values correspond to a Pareto distribution and the expected values correspond to an exponential distribution.

Craigdo: /* Methodology */

2009-04-17T23:52:21Z

Methodology

← Older revision		Revision as of 23:52, 17 April 2009
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	Since the expected value is provided for us (we do not calculate it from the data) the degrees of freedom in the chi square test is 50. Using this value, we calculate a maximum chi squared statistic corresponding to the 0.05 significance level (using the GNU Scientific Library gsl_cdf_chisq_Qinv function) as 67.5048. We calculate the expected values using a shape parameter of alpha = 1.0. Ten runs of the test for goodness of fit results in an average chi square statistic of 4695.05.		Since the expected value is provided for us (we do not calculate it from the data) the degrees of freedom in the chi square test is 50. Using this value, we calculate a maximum chi squared statistic corresponding to the 0.05 significance level (using the GNU Scientific Library gsl_cdf_chisq_Qinv function) as 67.5048. We calculate the expected values using a shape parameter of alpha = 1.0. Ten runs of the test for goodness of fit results in an average chi square statistic of 4695.05.

	Since this massively greater than the rejection value of 67.5048 we can state that the chi square statistic we measured is inconistent with statistical fluctuations and that the ns-3 Pareto random number, when given a shape parameter of 1.1 ~~generator~~ does~~, in fact,~~ '''not''' generate random numbers distributed according to the Pareto distribution with shape parameter 1.0.		Since this massively greater than the rejection value of 67.5048 we can state that the chi square statistic we measured is inconistent with statistical fluctuations and that the ns-3 Pareto random number generator, when given a shape parameter of 1.1, does '''not''' generate random numbers distributed according to the Pareto distribution with shape parameter 1.0.

	=== Data ===		=== Data ===