An efficient method of generation of a random sample using random numbers significantly less than the sample size
- 1Department of Computer Science and Engineering, BIT Mesra, Ranchi-835215, India
- 2Department of Mathematics, BIT Mesra, Ranchi-835215, India
Res. J. Mathematical & Statistical Sci., Volume 7, Issue (2), Pages 27-29, May,12 (2019)
Given that the pseudo-random numbers generated by the computer have a cycle; it is wise not to lose random numbers in simulation studies. For drawing a random sample of size n from a population of size N (n<=N), the existing sampling algorithms require n pseudo-random numbers. If N is large, accordingly n should also be large for better representation of the population. Since most simulation studies require at least 500 samples, we would need 500xn pseudo random numbers which can lead to cycle break. We are therefore motivated to develop an efficient sampling algorithm which generates the desired sample using random numbers significantly less than the sample size. Our algorithm has the facility that a single pseudo-random number can generate the sample of size 60 for a population of size 100000 using a python code. We would of course need more than one pseudo-random number if the sample size exceeds 60 for this population.
- Lehmer D.H. (1951)., Mathematical methods in large-scale computing units., Annu. Comput. Lab. Harvard Univ., 26, 141-146.
- Tausworthe R.C. (1965)., Random Numbers Generated by Linear Recurrence Modulo Two., Math.Comp., 19, 201-209.
- Allard J.L., Dobell A.R. and Hull T.E. (1963)., Mixed congruential random number generators for decimal machines., Journal of the ACM (JACM), 10(2), 131-141.
- Kennedy Jr. W.J. and Gentle J.E. (1980)., Statistical Computing., Marcel Dekker Inc, 33.
- Kundu D. and Basu A. (2004)., Statistical Computing: Existing Methods and Recent Development., Alpha Science International Ltd.
- Gentle J.E. (2009)., Computational Statistics., Springer.
- Kneusel R. (2018)., Random numbers and computers., Springer Publishing Company, Incorporated.
- Givens G.H. (2005)., Computational Statistics., Wiley Interscience.
- Rizzo M.L. (2007)., Statistical Computing with R., Chapman and Hall.
- Martinez W.L. and Martinez A.R. (2015)., Computational Statistics Handbook with MATLAB., Chapman and Hall.
- Sawitzki G. (2009)., Computational Statistics: an introduction to R., Chapman and Hall.
- Dirschedl P. and Ostermann R. (1994)., Computational Statistics, Papers Collected on the Occasion of the 25th Conference on Statistical Computing at Schloß Reisensburg., Springer.