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Decision Processes by Using Bivariate Normal Quantile Pairs pp 137–191Cite as

Application Paradigms

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Abstract

This chapter is the crux of the book. This chapter reveals the real power of BIVNOR which yields tables of biquantile pairs. The same are used to solve problems on joint condensed confidence interval, joint chance-constrained programming and for valid cum precise results haunting decision scientists and decision-makers for about seven decades. Thus, it is possible now to realize that a significant step of advancement has been taken in the direction of dependence and dynamism. This chapter has 15 sections of which first 14 chapters exhibit the application of biquantile pairs/equi-quantile values. Though the examples more often show the use of equi-quantile values, but those are biquantile pairs which are of greater importance than the former. This is because the same offers the scope for generating larger number of alternatives for decision-making at the same level of prefixed risk or confidence coefficient and for given or computed value of correlation coefficient.

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Notes

  1. 1.

    These are available from Table 8.1 Sheet 1, for positive correlation and Table 8.1 Sheet 3 for the negative correlation of Chap. 8. These are 1.9159 and 1.9599, respectively.

  2. 2.

    This is dealt in Sect. 4.11 (Chap. 4).

  3. 3.

    By using formula (4.42).

  4. 4.

    By using formula (4.45).

  5. 5.

    The equi-quantile value h = k = 2.187 is obtained by interpolation between two nearest values from the said Table 8.1 of Chap. 8 (taking the mean of BIGH values for PROB levels 0.98 and 0.97 and RHO = +0.7).

  6. 6.

    By Table 8.1 of Chap. 8.

  7. 7.

    And thereby using equi-quantile value from Table 8.1 of Chap. 8.

  8. 8.

    As given in Agricultural Research Data Book (2007).

  9. 9.

    As available from the Table 8.1 of Chap. 8.

  10. 10.

    Consequently equi-quantile value from the Table 8.1 of Chap. 8 corresponding to the estimate of correlation has been obtained by interpolation: for PROB = 0.95 and CORR = +0.974; BIGH = 1.7291 which is the required equi-quantile value, and SMHL = 1.65, by iteration.

    For Bonferroni’s joint confidence interval, Eq. (4.46) (in Chap. 4) has been applied by using univariate normal quantile value (=2.24) to get the same for the mean value of the data in Table 7.2.

  11. 11.

    As quoted by Rejda (2006) on p. 713.

  12. 12.

    From Table 8.1 of Chap. 8.

  13. 13.

    As stated in Table 8.1 of Chap. 8.

  14. 14.

    As shown in Table 8.2-67 of Chap. 8.

  15. 15.

    And, therefore, the repeated consultation of Table 8.2 of Chap. 8 was not required.

  16. 16.

    As discussed in Sect. 4.10 (Chap. 4).

  17. 17.

    Also discussed in Sect. 4.3 (Chap. 4).

  18. 18.

    The same could be changed by the expression (4.21) in Chap. 4.

  19. 19.

    From expressions (4.23) and (4.24), in Chap. 4.

  20. 20.

    From Table 8.1 of Chap. 8.

  21. 21.

    Such an action was natural, because nothing could be known then about the existence of the tables of biquantile pairs before the tables (as presented in Part II) get published.

  22. 22.

    As obtained through the use of Table 8.1 of Chap. 8.

  23. 23.

    See Table 8.2-136 of Chap. 8.

  24. 24.

    As obtainable from Table 8.1 of Chap. 8.

  25. 25.

    From Table 8.1 of Chap. 8.

  26. 26.

    As obtained from Table 8.2-52 of Table 8.2 of Chap. 8.

  27. 27.

    Such advantages are accruable only by the application of biquantile pairs available from the tables in Table 8.2 of Chap. 8.

  28. 28.

    As discussed in Chap. 4.

  29. 29.

    Through Table 8.2 of Chap. 8.

  30. 30.

    If the need arises to compute such a quantile pair or a finer value of probability and correlation, other than those available in Tables of Part II, one can find the same value either by two-way interpolation from appropriate grids of Table 8.1 of Chap. 8.

  31. 31.

    Through this book text and tables presented in Chap. 8.

  32. 32.

    Also in Sect. 4.8 (Chap. 4).

  33. 33.

    By interpolation from Table 8.1 of Chap. 8.

  34. 34.

    By interpolation from two adjacent values of Table 8.1.

  35. 35.

    By using Table 8.1 of Chap. 8.

  36. 36.

    For generation of random numbers/variables refer to Degpunar (1988) and Knuth (2000).

  37. 37.

    Obtained by interpolation from Table 8.1 of Chap. 8.

  38. 38.

    From Table 8.1 of Chap. 8.

  39. 39.

    Refer to Tables 8.2 in Chap. 8 and Table 9.9 of Chap. 9.

  40. 40.

    As discussed in Sect. 7.12.

  41. 41.

    As discussed in Sect. 1.2 (in Chap. 1).

  42. 42.

    As discussed in Sect. 1.2 (Chap. 1).

  43. 43.

    As envisaged in Sect. 1.2 (Chap. 1).

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  1. Department of Statistics, Birsa Agricultural University, Ranchi, Jharkhand, India

    N. C. Das

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Das, N.C. (2015). Application Paradigms. In: Decision Processes by Using Bivariate Normal Quantile Pairs. Springer, New Delhi. https://doi.org/10.1007/978-81-322-2364-1_7

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