# On Finding Geodesic Equation of Two Parameters Binomial Distribution

• William W.S. Chen Department of Statistics The George Washington University Washington D.C. 20013
Keywords: Bernoulli Trial, binomial distribution, Darboux Theory, differential geometry, geodesic equation, digamma function, Rotation axis, second order partial differential equation, trigamma function.

### Abstract

The purpose of this paper is to find a general form of the geodesic equation of the binomial distribution. Using Darboux’s theory we will set up a second order partial differential equation. Then we will apply the chain rule to transform the variable and rotate the axis to remove the interaction term, which will lead us to find the geodesic equation of binomial distribution. To illustrate how we can find such a geodesic equation in practice, we demonstrate by an example.

### References

(1) Apostol T.M.(1974) Mathematical Analysis. Addison-Wesley Publishing Company. Second Edition.

(2) Balakrishnan N. and Nevzorov V.B.(2003) A Primer on Statistical Distributions. John Wiley & Sons, Inc.

(3) Chen W.W.S (1982) Evaluation of the first 12 derivatives of
the digamma psi functions with applications . Proceeding of Statistical Computing Section, 1982, pp293-298.

(4) Chen W.W.S. (2017) On Finding Geodesic Equation of Student T Distribution. Journal of Mathematics Research. Vol. 9.No. 2, April 2017, pp32-37.

(5) Crawley M.J.(2007) The R Book. John Wiley & Sons Ltd. The Atrium, Southern Gate, Chichester, West Sussex PO19 8SQ, England.

(6) Darboux, G.(2nd ed, 1914) Lecons sur la theorie generale des surfaces. 4 vols, Gauthier-Villars, Paris. I, 1887, 513pp. ;II,1889,522pp.; III,1894,512pp.; IV,1896, 548pp.

(7) Grey A.(1993) Modern differential geometry of curves and surfaces. CRC Press, Inc. Boca Raton.

(8) Kass, R.E, and Vos, P.W.(1997) Geometrical foundations of asymptotic inference. John Wiley & Sons, Inc. New York.

(9) https://doi.org/10.1002/9781118165980 Struik, D.J.(1961) Lectures on classical differential geometry. Second Edition. Dover Publications, Inc.
Published
2019-07-01
Section
Articles