On Finding Geodesic Equation of Two Parameters Logistic Distribution
Abstract: In this paper, we used two different algorithms to solve some partial differential equations, where these equations originated from the well-known two parameters of logistic distributions. The first method was the classical one that involved solving a triply of partial differential equations. The second approach was the well-known Darboux Theory. We found that the geodesic equations are a pair of isotropic curves or minimal curves. As expected, the two methods reached the same result.
Cite this paper: Chen, W. (2015) On Finding Geodesic Equation of Two Parameters Logistic Distribution. Applied Mathematics, 6, 2169-2174. doi: 10.4236/am.2015.612189.
References

[1]   Mitchell, A.F.S. (1992) Estimative and Predictive Distances. Test, 1, 105-121.
http://dx.doi.org/10.1007/BF02562666

[2]   Mitchell, A.F.S. and Krzanowski, W.J. (1985) The Mahalanobis Distance and Elliptic Distributions. Biometrika, 72, 464-467.
http://dx.doi.org/10.1093/biomet/72.2.464

[3]   Kass, R.E. and Vos, P.W. (1997) Geometrical Foundations of Asymptotic Inference. John Wiley & Sons, Inc.
http://dx.doi.org/10.1002/9781118165980

[4]   Amari, S.-I. (1990) Differential-Geometrical Methods in Statistics. Springer, New York.

[5]   Jensen, U. (1995) Review of “The Derivation and Calculation of Rao Distances with an Application to Portfolio Theory”. In: Maddala, P., Phillips, G.S. and Srinivasan, T., Eds., Advances in Econometrics and Quantitative Economics: Essays in Honor of C.R. Rao, Blackwell, Cambridge, 413-462.

[6]   Struik, D.J. (1961) Lectures on Classical Differential Geometry. 2nd Edition, Dover Publications, Inc.

[7]   Grey, A. (1993) Modern Differential Geometry of Curves and Surfaces. CRC Press, Inc., Boca Raton.

[8]   Chen, W.W.S. (2014) A Note on Finding Geodesic Equation of Two Parameters Gamma Distribution. Applied Mathematics, 5, 3511-3517. www.scirp.org/journal/am
http://dx.doi.org/10.4236/am.2014.521328

[9]   Chen, W.W.S. (2014) A Note on Finding Geodesic Equation of Two Parameter Weibull Distribution. Theoretical Mathematics & Applications, 4, 43-52.

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

[11]   Gradshteyn, I.S., Ryzhik, I.M. and Jeffrey, A. (1994) Table of Integrals, Series, and Products. 5th Edition, Academic Press.

Top