The parameters of a distribution are variables that are included in an example's density function so that the distribution can be adapted to a variety of situations. There are many different parameters of a distribution, but of greatest importance are the parameters we outline 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 log-normal 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

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What are some practical examples where each of the four parameters might be used?

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