Bivariate Normal Distribution and Heuristic-Algorithm of BIVNOR for Generating Biquantile Pairs

N. C. Das ()
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N. C. Das: Birsa Agricultural University, Department of Statistics

Chapter Chapter 4 in Decision Processes by Using Bivariate Normal Quantile Pairs, 2015, pp 61-90 from Springer

Abstract: Abstract As it is the key chapter on software development, it begins with a characterization of bivariate normal distribution by Ludeman (Random processes, filtering, estimation and detection, Wiley India, New Delhi, 2010). That is followed by a brief presentation of the various properties of bivariate normal distribution and its applications by Essenwagner (Applied statistics in atmospheric science, part A. Frequencies and curve fitting, Elsevier, New York, 1976). Thereafter, Owen’s (1956) computational scheme for numerical integration of the bivariate normal integral is presented stepwise. The envisaged algorithm is to make iterative use of this scheme. It is very well realized that unlike univariate normal, which has a unique quantile value for a given probability level, its bivariate extension would have multiple (or infinite) quantile pairs for the same probability level. Apart from this, there arose other problems in their generation, which were sorted out and strategies to meet such problems were listed and used in perfecting the same algorithm. This was followed by finding the role of equi-quantile value BIGH for each probability level and correlation value as the initial point of such iterative scheme for the entire computational horizon of four hundred grids. In fact, the approach adopted is entirely innovative and of great economic and other consequences. Such action resulted in expansion of decision alternatives for the given or estimated correlation value without any change in probability (risk) level. Methods of forming simultaneous (joint) confidence intervals have emanated by using such biquantile pairs, having a definite edge over the existing Bonferroni’s joint confidence interval. Multiplicity of biquantile pairs offers a scope even for multiple joint confidence intervals for the same confidence probability. That could yield larger number of decision alternatives and hence the scope of choice amongst them by the decision maker on some criterion function. Those who are interested only in application of quantile pairs may skip Sect. 4.1, but they also should read its concluding part.

Keywords: Algorithm-BIVNOR; Biquantile pairs; Bivariate extension; Bivariate quantile; Chance constrained; Certainty equivalent; Confidence cover; Hueristic algorithm; Inverse problem; Owen’s-T; Gupta’s BIGH; Moran’s expression; Sheppard’s table; Trivariate case (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/978-81-322-2364-1_4

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