×
Pardo, M. C.; Pardo, J. A.

Statistical applications of order \(\alpha\)-\(\beta\) weighted information energy. (English) Zbl 0837.62005

Appl. Math., Praha 40, No. 4, 305-317 (1995).
Summary: A statistic using the concept of order \(\alpha\)-\(\beta\) weighted information energy introduced by R. K. Tuteja and S. Chaudhary [Inf. Sci. 66, No. 1/2, 53-61 (1992; Zbl 0753.94008)] is considered and its asymptotic distribution in a stratified random sampling is obtained. Some special cases are also discussed.

MSC:

62B10 Statistical aspects of information-theoretic topics
62E20 Asymptotic distribution theory in statistics

Keywords:

order alpha-beta weighted information energy; stratified random sampling

Citations:

Zbl 0753.94008
Cite Review PDF
Full Text: DOI EuDML

References:

[1] N.I. Aggarwal, C.F. Picard: Functional equations and information measures with preference. Kybernetika 14 (1978), 174-181. · Zbl 0385.94008
[2] M. Belis, G. Guiasu: A quantitative-qualitative measure of information in cybernetic systems. IEEE Trans. Inform. Theory 14 (1968), 593-594.
[3] D.A.S. Fraser: Nonparametric Methods in Statistics. John Wiley, New York, 1957. · Zbl 0077.12903
[4] M.A. Gil: A note on stratification and gain in precision in estimating diversity from large samples. Communications in Statistics. Theory and Methods 18 (1989), no. 4, 1521-1526. · Zbl 0696.62261 · doi:10.1080/03610928908829983
[5] M.A. Gil: On the asymptotic optimum allocation in estimating inequality from complete data. Kybernetika 28 (1992), 325-337. · Zbl 0771.62083
[6] S. Guiasu: The least weighted deviation. Information Sciences 53 (1991), 271-284. · Zbl 0705.62015 · doi:10.1016/0020-0255(91)90040-2
[7] F. Gurdial, F. Pesson: On useful information of order \(\alpha \). JCISS 3 (1973), 158-162.
[8] J. Havrda, F. Charvát: Quantification method of classification processes: Concepts of structural entropy. Kybernetika 3 (1967), 30-35. · Zbl 0178.22401
[9] D.S. Hooda: A non-additive generalized measure of relative useful information. Pure App. Math. Sci. 22 (1984), no. 1, 2, 143-151. · Zbl 0541.94009
[10] P.L. Kannappan: On some functional equations for additive and nonadditive measures. Stochastica 1 (1980), 15-22. · Zbl 0468.39003
[11] S. Kotz, N.M. Johnson, D.W. Boid: Series representation of quadratic forms in normal variables. I. Central Case. AMS (1967), 823-837. · Zbl 0146.40906 · doi:10.1214/aoms/1177698877
[12] K.V. Mardia, J.T. Kent, J.M. Bibby: Multivariate Analysis. Academic Press, 1982. · Zbl 0432.62029
[13] M. Mohan, J. Mitter: On bounds of useful information measures. Information and Control 39 (1978), 233-236. · Zbl 0416.94004
[14] O. Onicescu: Energie informationelle. C. R. Acad. Sci. Paris, Ser. A 263 (1966), 841-842. · Zbl 0143.41206
[15] J.A. Pardo: Caracterización axiomática de la energía informacional util. Estadística Española 108 (1985), 107-116.
[16] J.A. Pardo: On the asymptotic distribution of useful Shannon entropy in a stratified sampling. Metron, LI (1993), no. 1,2, 119-137. · Zbl 0829.62009
[17] J.A. Pardo, M.L. Vicente: Asymptotic distribution of the useful informational energy. Kybernetika 30 (1994), no. 1, 87-99. · Zbl 0850.62126
[18] L. Pardo: Energía informacional util. Trabajos de Estadística e investigación operativa 32 (1981), no. 2, 85-94.
[19] L. Pardo: The order \(\alpha \) information energy gain in sequential design of experiments. Proceedings Third European Young Statisticians Meeting, 1983, pp. 140-147.
[20] L. Pardo, D. Morales, V. Quesada: Plan de muestreo secuencial basado en la energía informacional para una población exponencial. Trabajos de Estadística e I.O. 36 (1985), 233-242.
[21] L. Pardo: Order \(\alpha \) weighted information energy. Information Science 40 (1986), 155-164. · Zbl 0629.94007 · doi:10.1016/0020-0255(86)90005-8
[22] L. Pardo: La energía informacional en el muestreo secuencial: Aplicación a las poblaciones normales. Real Academia de Ciencias Exactas, Físicas y Naturales de Madrid LXXXI (1987), 103-115.
[23] L. Pardo, M.L. Menéndez, J.A. Pardo: A sequential selection method of a fixed number of fuzzy information systems based on the information energy gain. Fuzzy Sets and Systems 25 (1988), 97-105. · Zbl 0642.94053 · doi:10.1016/0165-0114(88)90103-0
[24] L. Pardo, M.L. Menéndez: Applications of the informational energy to the design and comparison of regression experiment in a bayesian context. Journal of Combinatiorics, Information & System Sciences 14 (1989), no. 4, 163-171. · Zbl 0900.62044
[25] A. Pérez: Sur l’energie informationelle de M. Octavio Onicescu. Rev. Roumaine Math. Pures Appli. 12 (1966), 1341-1347.
[26] C.F. Picard: Graphs et Questionnaires. Gauthier-Villars, Paris, 1972.
[27] C.F. Picard: Weighted probabilistic information measures. J. Comb. & Syst. Sci. 4 (1979), 343-356. · Zbl 0447.94011
[28] J.N.K. Rao, A.J. Scott: The analysis of categorical data from complex sample surveys: chi-squared tests for goodness of fit and independence in two way tables. J. Amer. Stat. Assoc. 76 (1981), 221-230. · Zbl 0473.62010 · doi:10.2307/2287815
[29] C.E. Shannon: The Mathematical theory of communications. Bell System Techn. J. 27 (1948), 379-423. · Zbl 1154.94303
[30] B.D. Sharma, J. Mitter, M. Mohan: On measures of useful information. Information and Control 39 (1978), 123-136. · Zbl 0389.94004 · doi:10.1016/S0019-9958(78)90671-X
[31] B.D. Sharma, R.P. Shings: On generating information measures with preference. JCISS 8 (1983), 61-72. · Zbl 0622.94009
[32] B.D. Sharma, I.J. Taneja: Entropy of type \((\alpha ,\beta )\) and other generalized measures in information theory. Metrika 22 (1975), 205-215. · Zbl 0328.94012 · doi:10.1007/BF01899728
[33] R.P. Singh: On information measure of type \((\alpha ,\beta )\) with preference. Caribb. J. Math. 2 (1983), no. 1 & 2, 25-37. · Zbl 0531.94007
[34] A. Theodorescu: Energie informationnelle et notions apparentes. Trabajos de Estadística e Investigación Operativa 28 (1977), 183-206. · Zbl 0437.94001
[35] R.K. Tuteja, S. Chaudhary: Order \(\alpha \)-\(\beta \) weighted information energy. Information Sciences 66 (1992), 53-61. · Zbl 0753.94008 · doi:10.1016/0020-0255(92)90087-O
[36] I. Vajda: Axiomatic definition of energy of complete and incomplete probability schemes. Bull. Math. Soc. Sci. Math. Roum. 11 (1967), 197-203. · Zbl 0157.48901
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.