Data-fit lab
Choose one of the lab's datasets and a distribution to fit to it. The histogram shows the data with the fitted curve over it; the Q-Q plot puts the data's quantiles against the fit's, so a good fit lies along the line and a bad one bends away from it. For a normal fit, the tail table counts the values far from the mean and compares them with what the normal expects.
Goes with chapter 7. The normal distribution
Histogram and fit
Q-Q plot
Summary statistics
| Values (n) | 251 |
|---|---|
| Mean | 0.0012 |
| Standard deviation | 0.0279 |
| Smallest | -0.1595 |
| Lower quartile | -0.0122 |
| Median | 0.0018 |
| Upper quartile | 0.013 |
| Largest | 0.1243 |
| Skewness | -0.3923 |
| Excess kurtosis | 6.7476 |
The tails against the normal
| Beyond | Observed | A normal expects |
|---|---|---|
| |z| > 2 | 15 | 11.4 |
| |z| > 3 | 4 | 0.678 |
| |z| > 4 | 2 | 0.016 |
The worst day, day 67: a log return of -0.1595, a fall of 14.7 %, at z = -5.76. The fitted normal gives a day at least this bad a probability of 4.23E-9.
How to read the plots
The Q-Q plot sorts the data and sets each value against the quantile the fitted distribution puts at the same position. If the fit is right, the points follow the dashed line. Points that bend below the line on the left and above it on the right mean the data have more extreme values than the fit, fat tails; an S the other way means thinner tails; a curve means skew.
The simulated share's returns lie along the line in the middle and leave it at both ends: the crash and the rebound are far more extreme than a normal with the same mean and standard deviation allows. The excess kurtosis, 0 for a normal, says the same in one number. The dose times, a sample that is close to normal, stay near the line throughout.
Try the bug-fix times with an exponential fit: the histogram is flat and the fit is not, and the Q-Q plot curves. A good-looking mean and standard deviation do not make a good fit; the shape has to match too.