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.

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Chen, W. (2015) On Finding Geodesic Equation of Two Parameters Logistic Distribution. Applied Mathematics, 6, 2169-2174. doi: 10.4236/am.2015.612189.

Conflicts of Interest

The authors declare no conflicts of interest.

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.

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