Published: Modified: V1.3
statistics

Probability density

Today I am continuing to look into statistics to see if this is something that I want to learn more about by writing a post on Probability density. This seems like a topic that I could stand to to a little more research on, so for now this post is just some brief notes on the topic, and should not be used as any kind of practical guide on the topic.

1 - Sometimes it is better to test for a range, then an precise value.

Probability density has to do with the issue of testing for a certain value that may not ever really happen, so it is better to test for a range. That is the probability of it happening is very close to zero, or is pretty much zero, but not if we are talking about a small range rather than a very precise value.

2 - A javaScript example of probability density

For an example of probability density I made a quick module that creates a bunch of objects that have a number that represents the amount of time that passed when a bug died. 

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var bugs = (function() {
 
  var api = {};
 
  // initilize
  api.init = function(options) {
 
    options = options || {};
 
    this.count = options.count || 100;
    this.tBase = options.tBase || 1000;
    this.tRange = options.tRange || 2000;
    this.bugs = [];
    this.st = new Date();
 
    var i = 0;
 
    while (i < this.count) {
 
      this.bugs.push({
 
        dieAt: Math.random() * this.tRange + this.tBase
 
      });
 
      i += 1;
 
    }
 
  };
  
  // get a count of how many died at a given time stamp, and range
  api.diedAtCount = function(time,range){
  
      // dfault time at the base + 1/2 range
      time = time || Math.floor(this.tBase + this.tRange / 2);
  
      // default range to 10ms
      range = range === undefined ? 10 : range;
  
      return this.bugs.reduce(function(acc,bug){    
          
          if(bug.dieAt >= time-range && bug.dieAt <= time + range){
          
              return acc += 1;
          
          }
          
          return acc;
      
      },0);
  
  };
  
  api.diedAtPer = function(time,range){
  
        // dfault time at the base + 1/2 range
      time = time || Math.floor(this.tBase + this.tRange / 2);
  
      // default range to 10ms
      range = range === undefined ? 10 : range;
      
      var died = this.diedAtCount(time,range);
      
      return died / this.count;
  
  };
 
  api.init();
 
  return api;
 
}());

3 - Conclusion

I will be holding off on expanding my collection of posts on statistics until I work out more demos, and refine my understating of things like this. There is much about statistics that seems simple enough, but it can get a little involves. Another road block that I have run into is not finding a half way decent resource on statistics on line that explains things with javaScript examples, or at least Python examples now that I have learned a little bit when it comes to that programing environment.