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I have an observation and I want to transform it to a normal distribution. I have checked the normality assumption but it didn't attain the normal distribution. I have tried different function to transform it to normal distribution but it didn't work out. here under the Q-Q plot and density plot of the data. Could you suggest me which function can transform my data to a normal distribution? The data is regression coefficients and I want to do genetic parameter estimation on it.

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  • $\begingroup$ Try box cox transform $\endgroup$ – SmallChess Feb 10 '17 at 10:08
  • $\begingroup$ What type of data are you analysing? Could you post the density distribution please? It may be that there are no suitable transformation g such that Y = g(X) ~ N(0,1) $\endgroup$ – user64106 Feb 10 '17 at 10:08
  • $\begingroup$ @StatMan- See the edit. $\endgroup$ – Alula Feb 10 '17 at 10:24
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    $\begingroup$ What exactly do you want to transform? The regressors, the response, or the coefficients themselves? And why, specifically? ("Do genetic parameter estimation" tells us very little.) $\endgroup$ – whuber Feb 10 '17 at 14:00
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    $\begingroup$ @whuber- I want to transform the coefficients which are considered as a response variable. I want to determine the genetic difference among subjects. To do so the response variable should follow a normal distribution. $\endgroup$ – Alula Feb 10 '17 at 14:16
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Your plots show a mixture distribution of (a) a point mass at zero (b) a symmetric distribution with light tails at the extremes. If the point mass at zero is genuinely a point mass (all values equal) then you are not going to be able to find a simple way to transform it into a normal distribution.

Two questions arise though. (1) Why do you want it to be normal? What analysis are you proposing which relies on normality. (2) Would it not be scientifically more appropriate to try to find out why the point mass is arising?

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    $\begingroup$ +1. It's vital to recognise that a spike in the raw data must transform to a spike in the transformed data, as the same values must have the same transformed values. $\endgroup$ – Nick Cox Feb 10 '17 at 16:22
  • $\begingroup$ @mdewey- I use linear mixed model for analysis. $\endgroup$ – Alula Feb 10 '17 at 16:27

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