Cumulative distribution function - Probability

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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