manipulate data to better fit a Gaussian Distribution

Question

I have got a question concerning normal distribution (with mu = 0 and sigma = 1).

Let say that I firstly call randn or normrnd this way

x = normrnd(0,1,[4096,1]); % x = randn(4096,1)

Now, to assess how good x values fit the normal distribution, I call

[a,b] = normfit(x);

and to have a graphical support

histfit(x)

Now come to the core of the question: if I am not satisfied enough on how x fits the given normal distribution, how can I optimize x in order to better fit the expected normal distribution with 0 mean and 1 standard deviation?? Sometimes because of the few representation values (i.e. 4096 in this case), x fits really poorly the expected Gaussian, so that I wanna manipulate x (linearly or not, it does not really matter at this stage) in order to get a better fitness.

I'd like remarking that I have access to the statistical toolbox.

EDIT

1. I made the example with normrnd and randn cause my data are supposed and expected to have normal distribution. But, within the question, those functions are only helpful to better understand my concern.

2. Would it be possible to appy a least-squares fitting?

3. Generally the distribution I get is similar to the following:

My

Answer 1

Maybe, you can try to normalize your input data to have mean=0 and sigma=1. Like this:

y=(x-mean(x))/std(x);