Recurrence relations for the minimum variance unbiased estimator of the probability function of the R distribution

Abstract

We obtain a new technique to calculate the value of the minimum variance unbiased estimator (MVUE) of the probability function (p.f.) of the R distribution. This technique is based on an investigation of the ratios of r numbers. A recurrence relation for the MVUE of the p.f. of the R distribution is derived. It is interesting that the derived relation does not depend on the r numbers but depends on the ratios of the r numbers. The new method is efficient, convenient and accurate.

Keywords:

• r numbers
• r_I numbers
• Ratios of r numbers
• Ratios of r_I numbers

^∗Research supported in part by NSERC, Canada.

^∗Research supported in part by NSERC, Canada.

Notes

^∗Research supported in part by NSERC, Canada.