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A Flexible Method For Empirically Estimating Probability Functions

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  • Taylor, C. Robert

Abstract

This paper presents a hyperbolic trigonometric (HT) transformation procedure for empirically estimating a cumulative probability distribution function (cdf), from which the probability density function (pdf) can be obtained by differentiation. Maximum likelihood (ML) is the appropriate estimation technique, but a particularly appealing feature of the HT transformation as opposed to other zero-one transformations is that the transformed cdf can be fitted with ordinary least squares (OLS) regression. Although OLS estimates are biased and inconsistent, they are usually very close to ML estimates; thus use of OLS estimates as starting values greatly facilitates use of numerical search procedures to obtain ML estimates. ML estimates have desirable asymptotic properties. The procedure is no more difficult to use than unconstrained nonlinear regression. Advantages of the procedure as compared to alternative procedures for fitting probability functions are discussed in the manuscript. Use of the conditional method is illustrated by application to two sets of yield response data.

Suggested Citation

  • Taylor, C. Robert, 1984. "A Flexible Method For Empirically Estimating Probability Functions," Western Journal of Agricultural Economics, Western Agricultural Economics Association, vol. 9(1), pages 1-11, July.
    • Handle: RePEc:ags:wjagec:32377
    DOI: 10.22004/ag.econ.32377
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    2. VanTassell, L. W. & Richardson, J. W. & Conner, J. R., 1987. "Incorporating Environmental Uncertainties In A Ranch Simulation," 1987 Annual Meeting, August 2-5, East Lansing, Michigan 269979, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
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    4. Sanneh, Njundu & Moffitt, L. Joe & Lass, Daniel A., 2001. "Stochastic Efficiency Analysis Of Community-Supported Agriculture Core Management Options," Journal of Agricultural and Resource Economics, Western Agricultural Economics Association, vol. 26(2), pages 1-14, December.
    5. Novak, Frank S. & Schnitkey, Gary D., 1994. "The Effects Of Including Bankruptcy On Dynamic Investment Decisions," Journal of Agricultural and Resource Economics, Western Agricultural Economics Association, vol. 19(2), pages 1-12, December.
    6. Burt, Oscar R. & Taylor, C. Robert, 1988. "Reduction Of State Variable Dimension In Stochastic Dynamic Optimization Models Which Use Time-Series Data," Working Papers 225814, University of California, Davis, Department of Agricultural and Resource Economics.
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    9. Moss, Charles B. & Shonkwiler, J. S., 1991. "Modeling Yield With Stochastic Trend And Nonnormal Errors," 1991 Annual Meeting, August 4-7, Manhattan, Kansas 271165, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    10. Kinwa-Muzinga, Annie & Mazzocco, Michael A., 2000. "Preferred Price Paths Of Biotechnology-Derived Products: Time And Portfolio Affects," Transitions in Agbiotech: Economics of Strategy and Policy, June 24-25, 1999, Washington, D.C. 26031, Regional Research Project NE-165 Private Strategies, Public Policies, and Food System Performance.
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    12. Coble, Keith H. & Zuniga, Manuel & Heifner, Richard, 2003. "Evaluation of the interaction of risk management tools for cotton and soybeans," Agricultural Systems, Elsevier, vol. 75(2-3), pages 323-340.
    13. Pierre, Raphael & Spreen, Thomas H. & Moss, Charles B., 2006. "Invasive Species and Biosecurity: Cost of Monitoring and Controlling Mediterranean Fruit Flies in Florida," Journal of Agricultural and Applied Economics, Cambridge University Press, vol. 38(2), pages 337-343, August.
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    15. Kizer, Michael A. & Stoecker, Arthur L. & Carreira, Rita I. & Hattey, Jeffory A., 2004. "Management Strategies To Mitigate Environmental Impact Of Weather Uncertainty In Effluent Application To Irrigated Corn In Semiarid Regions," 2004 Annual meeting, August 1-4, Denver, CO 20110, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    16. Kim, Kwansoo & Chavas, Jean-Paul, 2003. "Technological change and risk management: an application to the economics of corn production," Agricultural Economics, Blackwell, vol. 29(2), pages 125-142, October.
    17. Funk, Robert D. & Mjelde, James W. & Hons, Frank M. & Saladino, Vince A., 1999. "An Economic Analysis Of A Corn-Soybean Crop Rotation Under Various Input Combinations In South Central Texas," Journal of Agricultural and Applied Economics, Southern Agricultural Economics Association, vol. 31(1), pages 1-13, April.
    18. Antle, John M., 1989. "The Measurement Of Economic Variability With Pooled Data: Conceptual And Methodological Issues," 1989 Quantifying Long Run Agricultural Risks and Evaluating Farmer Responses to Risk Meeting, April 9-12, 1989, Sanibel Island, Florida 271522, Regional Research Projects > S-232: Quantifying Long Run Agricultural Risks and Evaluating Farmer Responses to Risk.
    19. Winsten, Jonathan R. & Stokes, Jeffrey R., 2004. "The efficacy of controlling phosphorus loading: the case of management-intensive grazing," Agricultural Systems, Elsevier, vol. 79(3), pages 283-303, March.
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