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Re: Normal Probability plot

  • To: mathgroup at smc.vnet.net
  • Subject: [mg91641] Re: Normal Probability plot
  • From: Bill Rowe <readnews at sbcglobal.net>
  • Date: Sat, 30 Aug 2008 01:52:38 -0400 (EDT)

On 8/29/08 at 4:11 AM, y.eaidgah at gmail.com (Youness Eaidgah) wrote:

>I have a set of data and I want to plot them on a normal probability
>plot, to verify their normality. How can I make a normal probability
>plot by Mathematica? In addiction, is it possible to find the best
>straight line which fit the data?

All of this is possible. How much effort it would require
depends on precisely what you want. I could interpret "normal
probability plot" as plotting the empirical distribution
function versus quantiles of the normal distribution. A plot
that might work for you that is relatively simple would be:

data = Sort@RandomReal[NormalDistribution[5, 1], {20}];

ListPlot[Transpose@{Quantile[
     NormalDistribution[0, 1], (Range@20 - .5)/20], data},
  Frame -> True, Axes -> None]

And FindFit can be used to find the parameters of the best fit
line by doing:

In[12]:= FindFit[
  Transpose@{Quantile[NormalDistribution[0, 1], (Range@20 - .5)/20],
    data}, a x + b, {a, b}, x]

Out[12]= {a->0.877822,b->4.90027}

However, if your data is from a normal distribution it is more
efficient to do:

In[13]:= {Mean[data], StandardDeviation[data]}

Out[13]= {4.90027,0.885315}


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