On the Inverted Gamma Distribution
International Journal of Systems Science and Applied Mathematics
Volume 1, Issue 3, September 2016, Pages: 16-22
Received: Aug. 29, 2016;
Accepted: Sep. 14, 2016;
Published: Sep. 28, 2016
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Salah H. Abid, Mathematics Department, Education College, Al-Mustansiriya University, Baghdad, Iraq
Saja A. Al-Hassany, Mathematics Department, Education College, Al-Mustansiriya University, Baghdad, Iraq
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If a random variable follows a particular distribution then the distribution of the reciprocal of that random variable is called inverted distribution. In this paper we studied some issues related with inverted gamma distribution which is the reciprocal of the gamma distribution. We provide forms for the characteristic function, rth raw moment, skewness, kurtosis, Shannon entropy, relative entropy and Rényi entropy function. This paper deals also with the determination of R = P[Y < X] when X and Y are two independent inverted gamma distributions (IGD) with different scale parameters and different shape parameters. Different methods to estimate inverted gamma distribution parameters are studied, Maximum Likelihood estimator, Moments estimator, Percentile estimator, least square estimator and weighted least square estimator. An empirical study is conducted to compare among these methods.
Inverted Gamma Distribution, Characteristic Function, Stress-Strength, Shannon Entropy, Relative Entropy, Rényi Entropy, MLE, Percentile Estimator
To cite this article
Salah H. Abid,
Saja A. Al-Hassany,
On the Inverted Gamma Distribution, International Journal of Systems Science and Applied Mathematics.
Vol. 1, No. 3,
2016, pp. 16-22.
Copyright © 2016 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/
) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abdulah, E. and Elsalloukh, H. (2012) "The Epsilon Skew Inverted Gamma Distribution", JSM Proceeding, Biometrics Section. San Diago California: American Statistical Association.
Abdulah, E. and Elsalloukh, H. (2014) "Bimodal Class based on the Inverted Symmetrized Gamma Distribution with Applications", J. Stat. Appl. Pro. 3, No. 1, 1-7.
Ali, M. & Woo, J. & Pal, M. and Wahed, A. (2008) "Some Skew-Symmetric Double Inverted Distributions", International Journal of Statistical Sciences, Vol. 7, pp 1-12.
Giron, F. and Castello, D. (2001) "A note on the convolution of inverted-gamma distributions with applications to the Behrens-Fisher distribution", Rev. R. Acad. Cien. Serie A. Mat, VOL. 95 (1), pp. 39. 44.
Kao J (1959). A graphical estimation of mixed Weibull parameters in life testing electron tubes, Technometrics, 1, 389-407.
Li, T & Peng, L. and Sun, H. (2008( "The Geometric Structure of the Inverse Gamma Distribution", Beitr age zur Algebra und Geometrie Contributions to Algebra and Geometry Volume 49, No. 1, 217-225.
Llera, A. and Beckmann, C. (2016) "Estimating an Inverse Gamma distribution", Technical report, Radboud University Nijmegen, Donders Institute for Brain Cognition and Behavior.
Swain J, Venkatraman S and Wilson J (1988). Least squares estimation of distribution function in Johnson's translation system, Journal of Statistical Computation and Simulation, 29, 271-297.
Witkovsky, V. (2001) "Computing the distribution of a linear combination of inverted gamma variables", Kybernetika 37 (1), p. 79-90.
Woo, J. (2012) "Inference on Reliability in the Gamma and Inverted Gamma Distributions", PJSOR, Vol. 8, No. 3, pages 635-643, Special Volume In Honour of Distinguished Professor Dr. Mir Masoom Ali.