FPL Statistics Group

Probability Distributions Java Package

Currently (as 2/12/03) this package contains Java methods that permit a user to calculate 2 parameter Weibull, 3 parameter Weibull, Normal, and Noncentral T cumulative distribution functions and their inverses. It also contains methods to calculate the error function and the complementary error function. Most of the methods are translations of FORTRAN routines written by others.

At some point I intend to add Chi-Squared and F distribution (both central and noncentral) material. If you are aware of high quality probability distribution routines written in Java, I would appreciate hearing about them. Please e-mail me (Steve Verrill) at sverrill@fs.fed.us.

Warning!!!

This work was performed by a user of numerical analysis routines rather than a developer. When probability distribution routines written in Java by professional numerical analysts become available, they should be used.
I have tried to be careful with the coding and have done some simple testing (see the CDF_Normal_Amos_Test, CDF_Normal_Test, CDF_Weibull2_Test, CDF_Weibull3_Test, DerfTest, NctTest, and Nct_invTest applications). However, it is quite possible that I have introduced errors into the routines in the course of the translations. If you detect bugs in these routines, PLEASE contact me (Steve Verrill at sverrill@fs.fed.us or 608-231-9375).

DISCLAIMER OF WARRANTIES

THIS SOFTWARE IS PROVIDED "AS IS" WITHOUT WARRANTY OF ANY KIND. THE AUTHOR/TRANSLATOR DOES NOT WARRANT, GUARANTEE OR MAKE ANY REPRESENTATIONS REGARDING THE SOFTWARE OR DOCUMENTATION IN TERMS OF THEIR CORRECTNESS, RELIABILITY, CURRENTNESS, OR OTHERWISE. THE ENTIRE RISK AS TO THE RESULTS AND PERFORMANCE OF THE SOFTWARE IS ASSUMED BY YOU. IN NO CASE WILL ANY PARTY INVOLVED WITH THE CREATION OR DISTRIBUTION OF THE SOFTWARE BE LIABLE FOR ANY DAMAGE THAT MAY RESULT FROM THE USE OF THIS SOFTWARE.

Sorry about that.

Documentation

Here is the documentation generated by javadoc. Also see the source code of the routines.

CDF_Normal.java

CDF_Normal.java contains two methods. The normp method calculates the normal cumulative distribution function (cdf). It is claimed to be accurate to within 1.0e-15. It is a translation of a routine written in FORTRAN in 1986 by Alan Miller. It is based on algorithm 5666 from Computer Approximations by J.F. Hart and others (Wiley, 1968). The xnormi method calculates the inverse of the normal cdf. It is claimed to be accurate to within 4.5e-4. It was written in June of 1996 by Steve Verrill. It is based on formula 26.2.23 on page 933 of Abramowitz and Stegun's Handbook of Mathematical Functions (Dover, 9th printing).

CDF_Normal_Amos.java

CDF_Normal_Amos.java contains one method. The fnorm method calculates the normal cumulative distribution function. It is claimed to be accurate to within 1.0e-13. It is a translation of a routine written in FORTRAN in 1974 by Don Amos and S.L. Daniel.

CDF_Weibull2.java

CDF_Weibull2.java contains two methods. The w2cdf method calculates the 2 parameter Weibull cdf. The w2inv method calculates the inverse of the 2 parameter Weibull cdf. Both methods were written by Steve Verrill in 2001.

CDF_Weibull3.java

CDF_Weibull3.java contains two methods. The w3cdf method calculates the 3 parameter Weibull cdf. The w3inv method calculates the inverse of the 3 parameter Weibull cdf. Both methods were written by Steve Verrill in 2001.

CDF_nct_Amos.java

CDF_nct_Amos.java contains three main methods.

The fnct method calculates the noncentral T cdf. It is a translation of a routine written in FORTRAN in 1972 (modified in 1991) by D.E. Amos and S.L. Daniel. It references "A Survey of Properties and Applications of the Non-central T Distribution" by D.B. Owen, Technometrics, 10, no. 3, pages 464-465.

The fnct_inv method calculates the inverse of the noncentral T cdf. It should be accurate to 1.0e-5. It was written by Steve Verrill in 2002. The tha method computes the t(h,a) integral of Owen. It is a translation of a routine written in FORTRAN in 1975 by D.E. Amos and S.L. Daniel.

Derf.java

Derf.java contains two main methods. Both are translations of FORTRAN routines written in 1977 (last updated in 1992) by W. Fullerton of Los Alamos National Laboratory. The method derf calculates the error function. The method derfc calculates the complementary error function.

Installation

The code is available in compressed tar, Windows 95 zip, and Windows 98 and later zip, form. Alternatively, the code comes in nineteen files:

Given the manner in which the routines are currently written, you will need to import them (see, for example, the beginning of CDF_nct_Amos.java). All of the classes will have to be placed in subdirectories of a directory in your CLASSPATH. The Fzero and Fzero_methods classes will have to be placed in a subdirectory called optimization. The Gaus8 and Gaus8_fcn classes will have to be placed in a subdirectory called quadrature. The Blas_f77 class will have to be placed in a subdirectory called linear_algebra. Console.class will have to be placed in a subdirectory called corejava. The remaining classes will have to be placed in a subdirectory called distributions.

Note that if you install the software in this manner, then to run, for example, NctTest you will have to issue the command:

java distributions.NctTest

Alternatively, you could remove the package and import statements (other than import java.lang.*) in the source code, and compile all of the necessary files in the same directory.

Console.java

Console.java is software described in Cornell and Horstmann's Core Java (SunSoft Press/Prentice-Hall). (I like this book.) It may be used for non-commerical purposes. I only make use of it in the testing routines.

Support

If you have questions about this software, or suggestions for improvement, please contact me at sverrill@fs.fed.us or 608-231-9375.

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Last modified on 2/12/03.

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