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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
Authors
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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Abstract
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.
Keywords
Inverted Gamma Distribution, Characteristic Function, Stress-Strength, Shannon Entropy, Relative Entropy, Rényi Entropy, MLE, Percentile Estimator
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. doi: 10.11648/j.ijssam.20160103.11
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