Add better explanation comments for the QV fitter module

[HuangJunye]

While attempting to solve issue #473, I try to read and understand the code in QV fitter module. I find the code difficult to understand. It assumes very good level of understanding of statistics.

For example, when calculating the confidence level, the equation cfd = 0.5 * (1 + math.erf((hmean - 2/3)/ (1e-10 + self._ydata[1][depth_ind])/2**0.5)) come out from nowhere. It should be great to add some comments to explain why the confidence level can be calculated using the equation. (see this comment #473 (comment))

Another example is in the calc_statistics method. In lines 243-250:

self._ydata[0][depthidx] = np.sum(exp_vals)/np.sum(exp_shots)
self._ydata[1][depthidx] = (self._ydata[0][depthidx] *
                                        (1.0-self._ydata[0][depthidx])
                                        / self._ntrials)**0.5
self._ydata[2][depthidx] = np.mean(ideal_vals)
self._ydata[3][depthidx] = (self._ydata[2][depthidx] *
                                        (1.0-self._ydata[2][depthidx])
                                        / self._ntrials)**0.5

It's not clear what each line does. If I understand it correctly, the first line self._ydata[0][depthidx] calculates hmean, the second line self._ydata[1][depthidx] calculates the standard deviation sigma, the third line self._ydata[2][depthidx] calculates the ideal hmean and the fourth line self._ydata[3][depthidx] calculate the ideal standard deviation sigma.

I don't understand how we can calculate sigma using only mean and ntrials:

self._ydata[1][depthidx] = (self._ydata[0][depthidx] *
                                        (1.0-self._ydata[0][depthidx])
                                        / self._ntrials)**0.5

($$\sigma = \sqrt{(\mu * (1-\mu))/n}$$). Is there any reference I can read to understand that?

[HuangJunye]

The equation for calculating standard deviation is based on the assumption of binomial distribution. Variance is npq or np(1-p). Success probability p in QV measurement is self._ydata[0][depthidx]/self._ntrials. Square root of np(1-p) gives the equation in the code.

[HuangJunye]

Closed by #482