Statistical Distributions

Statistical Distributions

June 1983 | Robert E. Wheeler
The paper discusses two main topics: the use of semicolons in function parameter passing and the implementation of probability integrals and inverses for common continuous statistical distributions. In the first part, the author explores the use of semicolons in function definitions to pass multiple parameters. The semicolon notation allows for the assignment of nested-array arguments to local variables, simplifying the process of passing multiple parameters to a function. This approach is more efficient than the current method of passing an array and then splitting it inside the function. In the second part, the paper presents probability integrals and inverses for various continuous statistical distributions, including the Gaussian, gamma, beta, chi-squared, F, t, half-normal, exponential, Weibull, and Johnson distributions. These functions are implemented using series or continued fractions for probability integrals and Newtonian iteration for inverses. The functions are designed to handle arrays with up to two parameters, and the parameters are specified in the left arguments. The paper also provides detailed function specifications and definitions for each distribution, including the use of auxiliary functions like GAMMAL for the natural logarithm of the gamma function. The paper concludes with a note on the importance of the ideas presented and a call for further comments from readers. It also includes a quote from W.C. Fields to emphasize the importance of innovation. The paper is written by Robert E. Wheeler from the Engineering Department of E.I. du Pont de Nemours & Co. and is referenced in the context of statistical distributions and their implementations.The paper discusses two main topics: the use of semicolons in function parameter passing and the implementation of probability integrals and inverses for common continuous statistical distributions. In the first part, the author explores the use of semicolons in function definitions to pass multiple parameters. The semicolon notation allows for the assignment of nested-array arguments to local variables, simplifying the process of passing multiple parameters to a function. This approach is more efficient than the current method of passing an array and then splitting it inside the function. In the second part, the paper presents probability integrals and inverses for various continuous statistical distributions, including the Gaussian, gamma, beta, chi-squared, F, t, half-normal, exponential, Weibull, and Johnson distributions. These functions are implemented using series or continued fractions for probability integrals and Newtonian iteration for inverses. The functions are designed to handle arrays with up to two parameters, and the parameters are specified in the left arguments. The paper also provides detailed function specifications and definitions for each distribution, including the use of auxiliary functions like GAMMAL for the natural logarithm of the gamma function. The paper concludes with a note on the importance of the ideas presented and a call for further comments from readers. It also includes a quote from W.C. Fields to emphasize the importance of innovation. The paper is written by Robert E. Wheeler from the Engineering Department of E.I. du Pont de Nemours & Co. and is referenced in the context of statistical distributions and their implementations.
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