Empirical Continuous Distributions

• If the modeler has been unable to find a theoretical distribution that provides a good model for the input data, it may be necessary to use the empirical distribution of the data.

• A typical way of resolving this difficult is through ``curve fitting''.

• Steps involved: (see Exmaple 9.2 on page 328)
  • Collect empirical data and group them accordingly.
  • Tabulate the frequency and cumulative frequency.
  • Now assume the value of cumulative frequency as a function of the empirical data, i.e. F(x) = r
  • Establish a relation between x and r using linear interpolation
    
    $$X_1 = x_a + \frac{R_1 - y_a}{y_b - y_a} (x_b - x_a)$$
    
    
    for each of the intervals.

• Example 9.3 on page 332: note that in this example, five response time are used which are all distinct. If there are values are the same, or if the number of samples are large, we can certainly group them in the different ways.