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Beta-normal distribution and its applications. (English) Zbl 1009.62516
Summary: This paper introduces a general class of distributions generated from the logit of the beta random variable. A special case of this family is the beta-normal distribution. The shape properties of the beta-normal distribution are discussed. Estimation of parameters of the beta-normal distribution by the maximum likelihood method is also discussed. The beta-normal distribution provides great flexibility in modeling not only symmetric heavy-tailed distributions, but also skewed and bimodal distributions. The flexibility of this distribution is illustrated by applying it to two empirical data sets and comparing the results to previously used methods.

MSC:
62E10 Characterization and structure theory of statistical distributions
62F10 Point estimation
62G30 Order statistics; empirical distribution functions
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[1] DOI: 10.1007/BF02409935 · JFM 51.0405.08 · doi:10.1007/BF02409935
[2] Good I.J., Biometrika 40 pp 237– (1953) · Zbl 0051.37103 · doi:10.1093/biomet/40.3-4.237
[3] Wise M.E., Statistical Distributions in Scientific Work 2 pp 241– (1975) · doi:10.1007/978-94-010-1845-6_18
[4] Ljubo M., Statistical Review 15 pp 257– (1965)
[5] DOI: 10.1214/aos/1176343003 · Zbl 0312.62038 · doi:10.1214/aos/1176343003
[6] DOI: 10.2307/1269343 · Zbl 0628.62019 · doi:10.2307/1269343
[7] DOI: 10.2307/1913469 · Zbl 0557.62098 · doi:10.2307/1913469
[8] DOI: 10.1086/296404 · doi:10.1086/296404
[9] Thurow L.C., The American Economic Review 60 pp 261– (1970)
[10] DOI: 10.1002/0471725234 · doi:10.1002/0471725234
[11] DOI: 10.1002/bimj.4710300714 · Zbl 04527432 · doi:10.1002/bimj.4710300714
[12] Eugene N., A Generalized Normal Distribution: Properties, Estimation and Applications (2001)
[13] Bose R.C., Biometrika 46 pp 433– (1959) · Zbl 0223.62059 · doi:10.1093/biomet/46.3-4.433
[14] DOI: 10.2307/4128 · doi:10.2307/4128
[15] Park T., Physio. Zool. 37 pp 97– (1964) · doi:10.1086/physzool.37.2.30152328
[16] Park T., Physio. Zool. 27 pp 177– (1954) · doi:10.1086/physzool.27.3.30152164
[17] Leslie P.H., Biometrika 49 pp 1– (1962) · Zbl 0103.37304 · doi:10.1093/biomet/49.1-2.1
[18] Moffa A.M., Genetics 87 pp 785– (1977)
[19] DOI: 10.1016/S0167-9473(98)00018-8 · Zbl 1042.62514 · doi:10.1016/S0167-9473(98)00018-8
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