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Spherical probable error (Spe) and its estimation

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Summary

The problem of determining an estimate which may throw some light on the accuracy of a weapon system directed against an attacking aircraft has long been recognized. Although efficient methods are well known to the mathematicians, the personnal assigned to the execution may not know and therefore, may not utilize the raw data to form an efficient estimate. Particularly, its importance is to be realized when the data are not complete. This lead the author to suggest the concept of “Spherical Probable Error” (SPE) [Singh, 1962]. This is the three-dimensional analogue of the probable error of a single variate.

In this paper the derivation of SPE is given and various methods of its estimation are discussed from comparison point of view. Also results are obtained when the data are not complete but censored either on one or both tails an account of certain reasons. Various tables are given to obtain easily the unbiasing factors, variance of estimates and relative efficiencies of different estimates, etc.

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References

  • Chapman, D. G., H. Robbins: Minimum Variance estimation without regularity assumptions. Ann. Math. Stat.22, 1951, p. 581–586.

    MathSciNet  Google Scholar 

  • Cohen, A. C.: Radial error. J. Amer. Stat. Ass.59, 1955, p. 1122–1135.

    Article  Google Scholar 

  • Kendall, M. G.: The advancement theory of statistics.1, 1948, p. 42, 228, London.

  • Nair, U. S.: The standard error ofGini’s mean difference. Biometrika,28, 1936, p. 428.

    MATH  Google Scholar 

  • Pearson, E. S., H. O. Hartley: Biometrika Tables for Statisticians.1, Cambridge 1954.

  • Singh, N.: Estimation of parameters of a multivariate normal population from truneated and censored samples. J. Royal. Stat. Soc.,22, 1960, B 2, p. 307–11.

    MATH  Google Scholar 

  • -- Spherical Probable error. Nature, 1962.

  • Varma, R. S.: Some functions which are self-reciprocal in the Hankel Transform. Proc. London Math. Soc. (2),42, 1937, p. 9–17.

    Article  Google Scholar 

  • ——: Extensions of some self-reciprocal functions. J. Ind. Math. Soc. (N. S.)2, 1937, p. 269–275.

    Google Scholar 

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Authors and Affiliations

  1. Defence Science Laboratory, Delhi, India

    N. Singh

  2. Department of Mathematics, Monash University, 3168, Clayton, Victoria, Australia

    N. Singh

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  1. N. Singh
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Singh, N. Spherical probable error (Spe) and its estimation. Metrika 15, 149–163 (1970). https://doi.org/10.1007/BF02613568

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  • DOI: https://doi.org/10.1007/BF02613568

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