On the Ratio of two Independent Exponentiated Pareto Variables
DOI:
https://doi.org/10.17713/ajs.v39i4.253Abstract
In this paper we derive the distribution of the ratio of two independent exponentiated Pareto random variables, X and Y , and study its properties. We also find the UMVUE of Pr(X < Y ), and the UMVUE of its variance. As some of the expressions could not be expressed in closed forms, some special functions have been used to evaluate them.References
Abramowitz, M., and Stegun, I. A. (1972). Handbook of Mathematical Functions. New York: Dover Publications, Inc.
Ali, M., Pal, M., and Woo, J. (2005). Inference on P(Y
Ali, M. M., Pal, M., and Woo, J. (2007). Some exponentiated distributions. The Korean Communications in Statistics, 14, 93-109.
Ali, M. M., Pal, M., and Woo, J. (2009). Estimation of Pr(Y
Gradshteyn, I. S., and Ryzhik, I. M. (1965). Tables of Integral, Series, and Products. New York: Academic Press.
Gupta, R. C., Gupta, P. L., and Gupta, R. D. (1998). Modelling failure time data by Lehman alternatives. Communications in Statistics, Theory and Methods, 27, 887-904.
Gupta, R. D., and Kundu, D. (2001). Exponentiated exponential family: An alternative to Gamma and Weibull distributions. Biometrical Journal, 43, 117-130.
Pal, M., Ali, M. M., and Woo, J. (2005). Estimation and testing of P(Y>X) in twoparameter exponential distributions. Statistics, 39, 415-428.
Pal, M., Ali, M. M., and Woo, J. (2006). Exponentiated Weibull distribution. Statistica, 66, 139-148.
Raqab, M. Z., Madi, M. T., and Kundu, D. (2007). Estimation of P(Y
Watthanacheewakul, L., and Suwattee, P. (2010, March 17-19, 2010). Comparisons of several Pareto population means. In Proceedings of the International MultiConference of Engineers and Computer Scientists 2010 (Vol. III). Hong Kong.
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