An approximate method for generating symmetric random variables

ABSTRACT

A method for generating values of continuous symmetric random variables that is relatively fast, requires essentially no computer memory, and is easy to use is developed. The method, which uses a uniform zero-one random number source, is based on the inverse function of the lambda distribution of Tukey. Since it approximates many of the continuous theoretical distributions and empirical distributions frequently used in simulations, the method should be useful to simulation practitioners.

REFERENCES

• 1: Filliben, J.J. Simple and robust linear estimation of the location parameter of a symmetric distribution. Princeton U., Princeton, N.J., 1969.
• 2: Hogg, R.V., and Craig, A.T. Introduction to Mathematical Statistics. Macmillan, New York, 1970.
• 3: Johnson, N.L., and Leone, F.C. Statistics and Experimental Design. Wiley, New York, 1964.
• 4: Naylor, T.H., Balintfy, J.L., Burdick, D.S., and Chu, K. Computer Simulation Techniques. Wiley, New York, 1966.
• 5: Tukey, J.W. Technical Report 36, Stat. Techniques Res. Group, Princeton U., Princeton, N.J., 1960.

INDEX TERMS

Keywords:
Monte Carlo, approximations, distribution, moments, probability, random numbers, random variables, simulation, statistics