Distribution is Guassian ??

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nitu

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How can I say that some distribution is guassian or not (any checks)?? In case it is not guassian then how would anybody calculates the probability of the sample points in that distribution ?? In case anyone has some relevent matrial please upload it ...

Thanks
Nitu
 

i think i can answer the first one. by distribution u mean the set of points..

then, from the data, find the mean and variance of them... and then substitute to find the value of hte f(x) function of the Gaussian Distribution.. which is

1/sigma * sqrt(2*Pi) * exp(-(x-mean)/sigma)^2

and then compare with ur distribution f(x) values.

think its possible.. just give a try! incase any problems.. just post here.. we ll try to sort it out.. and. reg. te other questions.. i ll try to give a positive reply ASAP

/cedance
 

Thanks for the response
I have used the microsoft excel for plotting both a gaussian and distribution I had. First problem I faced is..
1. How many points should I have to plot the graph..
2. In case visually I found that the graph does not fit the gaussian but is there any numerical check for doing the same ... May be some script..
I heard something about the kurtosis etc .. It tell the distribution is gaussian or not by finding higher order ( > 2) moments of any distribution. I have used this and found always found that my distribution is not exactly gaussian. So, now if the distribution is not gaussian how to find the probability.... I am waiting for your response ..
 

Hi,
For a symmetric distribution like gaussian higher order moments oiher than mean and correlation will be zero.
For gaussian, if you have the data you can plot the pdf oand incase data set is mall it is difficult to find the gaussian nature.
brmadhukar
 

I think you must consider the Limit Central theorem. It states that under certain general conditions, the distribution of the sum of n independent random variables approaches a gaussian distribution with the same mean and variance as n increases.

For small n you can check it if it is gaussian or not with a Chi-square test.

Please try:

Probability, Random Variables and Stochasitc Process. Athanasios Papoulis & S. Unnikrishna Pillai
 

its better if u plot the graph in some professional math softwares as they would definitely give more information than in excel... matlab is more than enough. it also has inbuilt functions that could be used to calculate the various statistics properties.. i remember those kurtosis and skewness vaguely.

but if i am right, skewness gives the measure of skew from the original (normal) distribution or must it be gaussian? kurtosis and skewness doesnt have much mathematical computations difference i believe.

i think the method suggested by madhukar is better exploiting the fundemental property, moments.

/cedance
 

Hi,
Thanks for your response.. Ok now I found that my distribution is not guassian...
But now how would I can calculate the probability of one the sample in my distribution.. In case this was guassian probability calculation might have been easy...
But now I am stuck...
 

generally most of the random distribution r of gaussian.from central limit theorem u can conclude that the sum of distributions in the limiting case approches to gaussian.there is a standard formula for this distribution.if u know the µ(mean)and σ(standard deviation ) of a sample then u can easily calculate the density and distribution function.gaussian nature is a natural phenomena.
 

The Chi-Squared test can be used to determine whether the hypothesis that a distribution is of a given type can be rejected or not (for a specified probability). Excel has a "CHIDIST" function that can aid in this calculation.
 

cedance, your gaussian pdf function listed as:

1/sigma * sqrt(2*Pi) * exp(-(x-mean)/sigma)^2

is missing a 1/2 in the exponential term!

When mean =0 and variance =1 its a normal distribution.
 

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