Cumulative distribution function - Probability

19 août 2020

Cumulative distribution function (tScore and zScore)

This script provides the calculation of the cumulative distribution function (i.e., probability). The measure allows you to calculate the chances of a value of interest being above or below a hypothesized value over the measurement period—nothing fancy here, just good old statistics and mathematics. The closer you are to 0 or 1, the more significant your measurement. We’ve included a significance level highlighting feature. The ability to turn price and/or volume off.

We have included both the Z and T statistics. Where the ‘Z’ is looking at the difference of the current value, minus the mean, and divided by the standard deviation. This is usually pretty noisy on a single value, so a smoother is included. Nice shoutout to the Pinecoders Github Page with this function also. The t-statistic is measuring the difference between a short measurement, an extended measurement, and divided by the standard error (sigma/sqrt(n)). Both of these are neatly wrapped into a function, so please feel free to use them in your code. Add a bit of science to your guessing game. For the purists out there, we have chosen to use sigma in the t-statistic because we know the population's behavior (as opposed to the s-measure). We’ve also included two levels of the t-statistic cumulative distribution function if you are using a short sample period below 6.

Finally, because everyone loves choices, we’ve included the ability to measure the probability of:

• the current value (Price and volume)
  
• change
  
• percent change
  
• momentum (change over a period of time)
  
• Acceleration (change of the change)
  
• contribution (amount of the current bar over the sum)
  
• volatility (natural log ratio of today and the previous bar)
  

Here is a chart example explaining some of the data for the function.


Here are the various options you have the print the different measurements



A comparison of the t-statistic and z-statistic (t-score and z-score)


And the coloring options