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written 5.5 years ago by |

There are following steps in the development of a useful model of input data:

Collect data from the real system of interest. This often requires a substantial time and resource commitment.

Unfortunately, in some situations it is not possible to collect data (for example, when time is extremely limited, when the input process does not yet exist, or when laws or rules prohibit the collection of data).

When data are not available, expert opinion and knowledge of the process must be used to make educated guesses.

Identify a probability distribution to represent the input process.

When data are available, this step typically begins with the development of a frequency distribution, or histogram, of the data.

Given the frequency distribution and a structural knowledge of the process, a family of distributions is chosen.

Choose parameters that determine a specific instance of the distribution family. When data are available, these parameters may be estimated from the data.

Evaluate the chosen distribution and the associated parameters for goodness of fit.

Goodness of fit may be evaluated informally, via graphical methods, or formally, via statistical tests.

The chi-square and the Kolmogorov-Smimov tests are standard goodness-of-fit tests. If not satisfied that the chosen distribution is a good approximation of the data, then the analyst returns to the second step, chooses a different family of distributions, and repeats the procedure.

If several iterations of this procedure fail to yield a fit between an assumed distributional form and the collected data, the empirical form of the distribution may be used.