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A link between two-sided power and asymmetric Laplace distributions: with applications to mean and variance approximations

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  • Kotz, Samuel
  • van Dorp, J. René
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    Abstract

    Motivated by our investigations of refinements of the project evaluation and review technique (PERT), we have developed a reparameterization of the asymmetric Laplace distribution and found it to be a useful tool for extending and improving various three-point approximations of continuous distributions (pioneered by Pearson and Tukey (Biometrika 52(3/4) (1965) 533)) by specifying the values of two quantiles and the mode.

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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 71 (2005)
    Issue (Month): 4 (March)
    Pages: 383-394

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    Handle: RePEc:eee:stapro:v:71:y:2005:i:4:p:383-394

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    Related research

    Keywords: Lower and upper quantiles Bounded support Triangular distribution Beta distribution;

    References

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    1. Donald L. Keefer & William A. Verdini, 1993. "Better Estimation of PERT Activity Time Parameters," Management Science, INFORMS, vol. 39(9), pages 1086-1091, September.
    2. Hon-Shiang Lau & Amy Hing-Ling Lau & Chrwan-Jyh Ho, 1998. "Improved Moment-Estimation Formulas Using More Than Three Subjective Fractiles," Management Science, INFORMS, vol. 44(3), pages 346-351, March.
    3. Kamburowski, J., 1997. "New validations of PERT times," Omega, Elsevier, vol. 25(3), pages 323-328, June.
    4. C. Perry & I. D. Greig, 1975. "Estimating the Mean and Variance of Subjective Distributions in PERT and Decision Analysis," Management Science, INFORMS, vol. 21(12), pages 1477-1480, August.
    5. Hinkley, David V. & Revankar, Nagesh S., 1977. "Estimation of the Pareto law from underreported data : A further analysis," Journal of Econometrics, Elsevier, vol. 5(1), pages 1-11, January.
    6. Joseph J. Moder & E. G. Rodgers, 1968. "Judgment Estimates of the Moments of Pert Type Distributions," Management Science, INFORMS, vol. 15(2), pages B76-B83, October.
    7. Donald L. Keefer & Samuel E. Bodily, 1983. "Three-Point Approximations for Continuous Random Variables," Management Science, INFORMS, vol. 29(5), pages 595-609, May.
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    Cited by:
    1. C. García & J. García Pérez & J. Dorp, 2011. "Modeling heavy-tailed, skewed and peaked uncertainty phenomena with bounded support," Statistical Methods and Applications, Springer, vol. 20(4), pages 463-486, November.

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