AGENDA
Analyzing Input Data
Exercise/Homework

THE USE OF INPUT DATA IN SIMULATION
Observe input data
Fit to theoretical distribution
Generate data from theoretical distribution

ANALYZING INPUT DATA
Determining underlying theoretical distribution
Based on some sort of comparison between
The observed data distribution
A corresponding theoretical distribution
If the difference is small, the data could have come from the theoretical distribution 

METHODS
Graphical Approach…
Chi-square Test…
Kolmogorov-Smirnov Test
Square Error

GRAPHICAL APPROACH
Create a histogram of observed data
Create a histogram for the theoretical distribution
Visually compare the two histograms for similarity
Make a qualitative decision as to the similarity of the two data sets
Questionable
How many cells to use??? 

HOW TO DECIDE HOW MANY CELLS TO USE
Equal interval approach
Equal probable approach
Use a maximum number of cells not to exceed 100
The expected number of observations in each cell must be at least 5

CHI-SQUARE TEST
Establish null and alternative hypotheses
Determine a level of test significance
Calculate the critical value form the chi-square distribution
Calculate the chi-square test statistic from the data
Compare the test statistic with the critical vale
Accept or reject the null hypotheses
Excel examples… 

EXCEL EXAMPLES
Check arrival times for expo distribution
Check service times for normal distribution

HOW MUCH DATA NEEDS TO BE COLLECTED
We want to observe the right data.
Want to have observed the different values that are likely to occur.
Need to have enough data to perform a goodness of fit test.

WHAT HAPPENS IF I CANNOT FIT THE INPUT DATA?
Why this occurs…
What to do about it…

WHY THIS OCCURS
Not enough data was collected
Data is a combination of a number of different distributions

WHAT TO DO ABOUT IT
Collect more data
Use the observed data to generate an empirical distribution