Re: Randomness Test

• To: mathgroup at smc.vnet.net
• Subject: [mg58036] Re: Randomness Test
• From: Torsten Coym <torsten.coym at eas.iis.fraunhofer.de>
• Date: Thu, 16 Jun 2005 06:43:54 -0400 (EDT)
• References: <d8oul6\$a\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Dave miller wrote:
> Okay, I have a sequence of numbers as below. When i do a scatter plot, there seems to be a bias toward positive numbers. Although when I run some tests like "runs test", it shows me that the numbers are random. If that is the case, then when i plot the numbers on a scatter plot, should'nt they be equally divided up and below the x axis? My goal is to prove that that there is a significant bias towards positive numbers.
>
>
> -0.164971751
> 1.137014315
> 0.622389791
> 0.048958333
> 1.232944503
> 0.3241877
> 0.1015
> 0.075538717
> 0.265537849
> -0.175252257
> 0.279807692
> -0.409979424
> 0.628232355
> -0.137667494
> 0.210711568
> -0.984059857
> -0.016778523
> 0.384063745
> 0.079707844
> -0.183936235
> -0.567394095
> 0
> 0.277777778
> 0.785185185
> 0.267555556
> 0.078717201
> 0.344352617
> 0
> 0.442245021
> 0.310665658
> 0.788764045
> 0.015850552
> -0.054098361
> 0
> 0
> 0.929482371
> 0.278787879
> 0.123773346
> 0.125175809
> 0
> 0
>

Dave,

try the following:

x={you list goes here}

ListPlot[Abs[Fourier[x]]]

Sequences of gaussian distributed numbers (mu=0) have a flat frequency
spectrum. Your data shows a significant peak at the first Fourier
coefficient, which (spoken in terms of electrical engineering) refers to
the DC level. Your data seems to be biased, around Mean[x]=0.182068.

Torsten

```

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