CUPID
A Program for Computations with Univariate Probability Distributions

CUPID was designed to accomplish a variety of tasks involving univariate probability distributions. These include:

• Computation: Compute numerical values of many quantities associated with probability distributions, including probability densities, cumulative probabilities, inverse cumulative probabilities, mean, variance, skewness, etc.
• Generate Random Numbers
• Estimation: Find the best estimates of the parameters of a distribution to fit a given data set, with ``best'' defined in terms of one of several alternative criteria (e.g., maximum-likelihood).
• Graphing: Make crude (character-screen) plots of the PDF, CDF, MGF, and Hazard functions.

CUPID knows about a variety of standard and derived probability distributions, including:

• Standard distributions:

  Beta	Binomial	Cauchy	Chi-square
  Ex-gaussian	Exponential	Extreme Value	F (Fisher's)
  Gamma	Laplace	Lilliefors	Log-normal
  Logistic	Normal	Poisson	Pearson's r
  Rayleigh	Studentized Range	t (Student's)	Triangular
  Uniform	Weibull

• Transformations: A very simple derived distribution is a linear transformation of a primitive one (e.g., an exponential plus a constant). More complicated transformations include the exponential transform (e.g., Y = e^X), the natural log (Y = ln(X)) and inverse (1/X) transformations, and power function transformations. In addition, more complicated transformations can be constructed by combining several of these.
• Truncated distributions: New distributions may be defined by restricting other distributions to part of their usual range (e.g., a standard normal restricted to the range from -2 to +2).
• Mixture distributions: A new distribution may be formed by randomly selecting a number from one of several independent distributions (e.g., a number that is equally likely to be from a normal with mean 10 or mean 20).
• Convolutions: A distribution may be formed by summing values from independent distributions.
• Order distributions: A distribution may be formed by choosing the i'th order statistic from a sample of n independent random variables (e.g., the minimum of 10 standard normals).

User Interface

CUPID is command-driven, and all commands are entered at the program's prompt ( > ). One class of commands tells the program which distribution to use. For example, typing Uniform(0,100) in response to the program prompt tells the program that it should start performing operations with a Uniform distribution ranging from 0 to 100.

Other commands tell the program what quantities to compute. For example, typing SD tells the program to print out the standard deviation of the distribution currently in use. There are also a number of commands that control the program (e.g., opening an output file for results) rather than doing any statistical computation.

While perhaps not as nice for the novice user as a friendly menu system, the command-driven approach has the advantage that the program can also take commands from ASCII files using standard DOS I/O redirection (or even from the command line).

Here is a brief example CUPID session:
 > t(12)
 > mean
   mean = 0
 > sd
   sd = 1.095
 > skewness kurtosis
   skewness = 0
   kurtosis = 3.75
 > cdf(3.112)
   cdf(3.112) = 0.9955
 > inversecdf(.95)
   inversecdf(.95) = 1.782
 > stop

The DOS-executable program comes with extensive documentation in a variety of formats, including postscript and Adobe PDF. The program and its documentation may be duplicated and used without charge for any educational or noncommercial purposes.