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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(01), pages 1-11, July.
    • Handle: RePEc:ags:wjagec:32377
    DOI: 10.22004/ag.econ.32377
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    References listed on IDEAS

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    1. Antle, John M, 1983. "Testing the Stochastic Structure of Production: A Flexible Moment-based Approach," Journal of Business & Economic Statistics, American Statistical Association, vol. 1(3), pages 192-201, July.
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    Citations

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    Cited by:

    1. Russell Tronstad & C. Robert Taylor, 1989. "Effects of the 1986 Tax Reform Act on Grain Marketing Decisions: A Case Study of Winter Wheat Producers," Review of Agricultural Economics, Agricultural and Applied Economics Association, vol. 11(2), pages 309-320.
    2. 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.
    3. 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(01), pages 1-13, April.
    4. Coble, Keith H. & Heifner, Richard G. & Zuniga, Manuel, 2000. "Implications Of Crop Yield And Revenue Insurance For Producer Hedging," Journal of Agricultural and Resource Economics, Western Agricultural Economics Association, vol. 25(2), pages 1-21, December.
    5. 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.
    6. 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.
    7. Moss, Charles B. & Shonkwiler, J. S., "undated". "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).
    8. Coble, Keith H. & Heifner, Richard, 1998. "The Effect of Crop or Revenue Insurance on Optimal Hedging," 1981-1999 Conference Archive 285727, NCR-134/ NCCC-134 Applied Commodity Price Analysis, Forecasting, and Market Risk Management.
    9. Shukla, Sumedha & Arora, Gaurav & Agarwal, Sandip Kumar, 2025. "Evaluating the role of mixed-cropping for managing production risks on small farms: An application of BetaIV framework for input-conditional crop yield density estimation," 2025 AAEA & WAEA Joint Annual Meeting, July 27-29, 2025, Denver, CO 361060, Agricultural and Applied Economics Association.
    10. Ayenew, Habtamu Yesigat & Sauer, Johannes & Abate-Kassa, Getachew, 2015. "Expossure To Risk And Risk Management In Smallholder Agriculture," 55th Annual Conference, Giessen, Germany, September 23-25, 2015 209211, German Association of Agricultural Economists (GEWISOLA).
    11. repec:isu:genstf:201701010800006248 is not listed on IDEAS
    12. 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.
    13. 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.
    14. 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.
    15. 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.
    16. VanTassell, L. W. & Richardson, J. W. & Conner, J. R., "undated". "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).
    17. 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).
    18. Carreira, R.I. & Stoecker, A.L. & Epplin, F.M. & Hattey, J.A. & Kizer, M.A., 2006. "Subsurface Drip Irrigation Versus Center-Pivot Sprinkler for Applying Swine Effluent to Corn," Journal of Agricultural and Applied Economics, Cambridge University Press, vol. 38(3), pages 645-658, December.
    19. repec:ags:rrsr94:307864 is not listed on IDEAS
    20. Lambart, David K. & Harris, Thomas R., "undated". "Multi-Period Rangeland Investment Analysis with Safety-First constraints and Uncertain Data," 1991 Annual Meeting, August 4-7, Manhattan, Kansas 271157, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    21. 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.
    22. 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.

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