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Idempotent Elements of Weak Projection Generalized Hypersubstitutions

transformations defined by generalized hy- persubstitutions, Sci. Math. Jpn. Online 6 (2002) 355-366. [5] K. Denecke and S.L. Wismath, Hyperidentities and Clones (Gordon and Breach science Publishers, 2000). [6] K. Denecke and S.L. Wismath, Universal Algebra and Applications in Theoretical Computer Science (Boca Raton: Chapman & Hall/CRC, 2002). [7] J. Koppitz and K. Denecke, M-Solid Varieties of Algebras (Springer Science+ Business Media, Inc., 2006). [8] S. Leeratanavalee, Structural properties of generalized

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On Marshall-Olkin Burr X family of distribution


Generalizing distributions is important for applied statisticians and recent literature has suggested several ways of extending well-known distributions. We propose a new class of distributions called the Marshall-Olkin Burr X family, which yields exible shapes for its density such as symmetrical, left-skewed, right-skewed and reversed-J shaped, and can have increasing, decreasing,constant, bathtub and upside-down bathtub hazard rates shaped. Some of its structural properties including quantile and generating functions, ordinary and incomplete moments, and mean deviations are obtained. One special model of this family, the Marshall- Olkin-Burr-Lomax distribution, is investigated in details. We also derive the density of the order statistics. The model parameters are estimated by the maximum likelihood method. For illustrative purposes, three applications to real life data are presented.

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