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A Note on the Ratio of Two Normally Distributed Variables

Author

Listed:
  • Jack Hayya

    (The Pennsylvania State University, University Park, Pennsylvania)

  • Donald Armstrong

    (Bechtel Power Corporation, Houston, Texas)

  • Nicolas Gressis

    (Indiana University, Bloomington, Indiana)

Abstract

This note is a continuation of a previous paper on normal approximations of standard forms. The standard form treated here is the ratio of two normally distributed variables. It is found that a suitable transformation of this ratio is approximately normally distributed provided that the coefficient of variation of the denominator is less than 0.39.

Suggested Citation

  • Jack Hayya & Donald Armstrong & Nicolas Gressis, 1975. "A Note on the Ratio of Two Normally Distributed Variables," Management Science, INFORMS, vol. 21(11), pages 1338-1341, July.
    • Handle: RePEc:inm:ormnsc:v:21:y:1975:i:11:p:1338-1341
    DOI: 10.1287/mnsc.21.11.1338
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    Cited by:

    1. Melanie Lefevre, 2011. "Willingness-to-pay for Local Milk-based Dairy Product in Senegal," CREPP Working Papers 1108, Centre de Recherche en Economie Publique et de la Population (CREPP) (Research Center on Public and Population Economics) HEC-Management School, University of Liège.
    2. Anderson, Jock R. & Doran, Howard E., 1978. "Some Properties of Simple Functions of Random Variables," Review of Marketing and Agricultural Economics, Australian Agricultural and Resource Economics Society, vol. 46(01), pages 1-11, April.
    3. Liu, Bin & Gao, Jianbo, 2019. "Understanding the non-Gaussian distribution of revealed comparative advantage index and its alternatives," International Economics, Elsevier, vol. 158(C), pages 1-11.
    4. K.P. Tran & P. Castagliola & G. Celano, 2016. "The performance of the Shewhart-RZ control chart in the presence of measurement error," International Journal of Production Research, Taylor & Francis Journals, vol. 54(24), pages 7504-7522, December.
    5. Peng Wang & Siqi Xu & Yi‐Xin Wang & Baolin Wu & Wing Kam Fung & Guimin Gao & Zhijiang Liang & Nianjun Liu, 2021. "Penalized Fieller's confidence interval for the ratio of bivariate normal means," Biometrics, The International Biometric Society, vol. 77(4), pages 1355-1368, December.
    6. Eloísa Díaz-Francés & Francisco Rubio, 2013. "On the existence of a normal approximation to the distribution of the ratio of two independent normal random variables," Statistical Papers, Springer, vol. 54(2), pages 309-323, May.
    7. Burlacu, Radu & Fontaine, Patrice & Jimenez-Garcès, Sonia & Seasholes, Mark S., 2012. "Risk and the cross section of stock returns," Journal of Financial Economics, Elsevier, vol. 105(3), pages 511-522.
    8. Pandey, Sushil & Piggott, Roley R. & MacAulay, T. Gordon, 1982. "The Elasticity Of Aggregate Australian Agricultural Supply: Estimates And Policy Implications," Australian Journal of Agricultural Economics, Australian Agricultural and Resource Economics Society, vol. 26(3), pages 1-18, December.
    9. Willem van Jaarsveld & Alan Scheller-Wolf, 2015. "Optimization of Industrial-Scale Assemble-to-Order Systems," INFORMS Journal on Computing, INFORMS, vol. 27(3), pages 544-560, August.
    10. Kim Phuc Tran & Philippe Castagliola & Giovanni Celano, 2018. "Monitoring the ratio of population means of a bivariate normal distribution using CUSUM type control charts," Statistical Papers, Springer, vol. 59(1), pages 387-413, March.
    11. Kourtis, Apostolos, 2014. "On the distribution and estimation of trading costs," Journal of Empirical Finance, Elsevier, vol. 28(C), pages 104-117.
    12. Yanqing Wang & Suojin Wang & Raymond J. Carroll, 2015. "The direct integral method for confidence intervals for the ratio of two location parameters," Biometrics, The International Biometric Society, vol. 71(3), pages 704-713, September.
    13. Lukas Leitner, 2024. "Imprecision in the Estimation of Willingness to Pay Using Subjective Well-Being Data," Journal of Happiness Studies, Springer, vol. 25(7), pages 1-40, October.
    14. Hee Mok Park & Puneet Manchanda, 2015. "When Harry Bet with Sally: An Empirical Analysis of Multiple Peer Effects in Casino Gambling Behavior," Marketing Science, INFORMS, vol. 34(2), pages 179-194, March.
    15. Andrew Daly & Stephane Hess & Kenneth Train, 2012. "Assuring finite moments for willingness to pay in random coefficient models," Transportation, Springer, vol. 39(1), pages 19-31, January.

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