Contents
- Index
Parameters of a Distribution
The parameters of a distribution are variables included in the density function so that the distribution can be adapted to a variety of situations. Of greatest importance is the number of parameters as shown below:
2 Parameters: The two parameters determine the average and standard deviation of the distribution. Such distributions are represented as a point on a skewness-kurtosis plot as they have fixed values of the skewness and kurtosis. Examples are the exponential, normal and uniform distributions.
3 Parameters: The three parameters determine the average, standard deviation and skewness of the distribution. Such distributions are represented as a curve on a skewness-kurtosis plot as the kurtosis depends of the skewness. Examples are the gamma and lognormal distributions.
4 Parameters: The four parameters determine the average, standard deviation, skewness and kurtosis of the distribution. Such distributions are represented as a region on a skewness-kurtosis plot as they can take on a variety of skewness and kurtosis values. Examples are the beta, Johnson and Pearson distributions.
Different books and articles will sometimes parametrize the same distribution differently. One set of parameters can always be calculated from the other. Further, sometimes different numbers of parameters are used so there are 2 and 3 parameter versions of the lognormal distribution. This greatly complicates comparing and using distributions. For this reason, Distribution Analyzer re-parametrizes all the distributions in terms of the average, standard deviation, skewness and kurtosis as needed for use in the Select Distribution to Fit Data and Select/View Distribution dialog boxes. Further, the distributions are expanded to always include the average and standard deviation as parameters. There are tabs in both dialog boxes that display the traditional parameters as well.