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On stochastic linear inequalities

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Trabajos de Estadistica

Summary

The author, in this unorthodox paper, discusses come actual problems of theory and methods of linear programming. He defines a compound matrix as a common property to all cases ofmatrix games: games theory. input-output analysis, theory of statistical decision and others; namely, mathematical programming. He uses the weak inequality as superior to the equality. He explains the classifications of elements of activity ma'rix as constants, random variables and statistics. He shows a nonparametric interval solution, instead of usual deterministic point solution, for one class of maximum mixture problems, when the data are «statistics». He proves that it is bounded and only two solutions are needed. He introduces a confidence interval solution if some data are only estimates, which obey the Poisson law. A numerical example as a demonstration of this technique and a survey of useful references are added.

Resumen

En este trabajo el autor discute algunos probemas actuales referentes a la teoría y a los métodos usados en programación lineal. Define para ello Matriz Compuesta como una propiedad común a todas las clases de juegos matriciales: Teoría de juegos, Teoría de decisión Estadística, etc.; esto es, programación matemática. En todo ello usa las desigualdades débiles como preferibles a las igualdades y clasifica los elementos de la matriz de actividad en constantes, variables aleatorias y estadísticos. Para cierta clase de problemas referentes a mezclas (cuyos datos son estadísticos), en lugar de la solución puntual clásica halla un intervalo no paramétrico. Demuestra además que está acotado y que sólo son necesarias dos soluciones. Introduce a continuación como solución un intervalo confidencial si algunos datos son sólo estimaciones, el cual intervalo sigue la ley de Poisson. Como aplicación de esta técnica se hace un ejemplo numérico. Al final del trabajo se encuentra abundante y útil bibliografía.

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Authors and Affiliations

  1. Marquefte University, Milwaukee, USA

    J. Talacko

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  1. J. Talacko
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Abstract (552–15) of this paper has been presented at the 552 meeting of the American Mathematical Society, at the Northwesern University, Evanston, Illinois, November 29, 1958.

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Talacko, J. On stochastic linear inequalities. Trabajos de Estadistica 10, 89–112 (1959). https://doi.org/10.1007/BF03003986

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