Prescribing the Moments of a Probability Distribution

How To Use The Applet

  1. Click "Reset Pop" first, to initialize distribution, before generating data!

  2. Click the "Properties" button to bring up a dialog box where you can

    1. Set the minimum and maximum values that define boundaries (i.e., range) for scores in the distribution.
    2. Set the number of points (i.e., scores), precision (i.e., decimal places), and number of classes (i.e., bars) used to define the distribution.  Click the "Reset Pop" button to effect the specified changes.

    3. To shape the distribution, hold the left mouse button down and drag the cursor across the bars.  Click here to view a video of this process.  To make minor modifications to your distribution, click any bar, hold the left mouse button down, and raise or lower the bar.  The resulting distribution (red bars) represents the population.  Click the "Properties" button to view the mean, standard deviation, skewness, and kurtosis of the population (parameters).  Click the "Write Data" button to randomly generate a sample of the size specified from the population.  The sample is depicted as blue bars.  Finally, click the "Properties" button to display corresponding sample statistics and population parameters.

  3. Click the "Options" button to bring up a dialog box where you can
    1. Show the first, second and third quartiles of the sample (shown in green)
    2. Show the mean (vertical black line) and blue lines one or two standard deviations away from the mean (for the sample).
  4. The default population distribution is uniform (constant).
  5. Click "Write Data" to write data into textarea in right.
  6. Click "Read Data" to read data from textarea in right.
  7. Click "Reset Sample" to generate new data, without changing the distribution.
  8. Click "Sort" to sort sample.  (Clicking it again reverses order.)
Note:  Frequency Distribution is shown in red, and the actual probability distribution curve of the data generated overlaid in blue on top of the histogram.

Note:  The statistics of the input histogram are inherited by the output histogram, but the actual statistics of the generated data will differ slightly from the input distribution.

This applet can be used to generate data on [0,1] with presecribed mean, standard deviation, skewness and kurtosis.  You can cut and past the data in the scrolling window to another application such as Excel or SPSS. [In unix click 3 or 4 times in a row in the scrolling data window, in Windows highlight the data and use ctrl-c to copy]