Abstract
In this paper we introduced Gompertz Gumbel II (GG II) distribution which generalizes the Gumbel II distribution. The new distribution is a flexible exponential type distribution which can be used in modeling real life data with varying degree of asymmetry. Unlike the Gumbel II distribution which exhibits a monotone decreasing failure rate, the new distribution is useful for modeling unimodal (Bathtub-shaped) failure rates which sometimes characterised the real life data. Structural properties of the new distribution namely, density function, hazard function, moments, quantile function, moment generating function, orders statistics, Stochastic Ordering, Renyi entropy were obtained. For the main formulas related to our model, we present numerical studies that illustrate the practicality of computational implementation using statistical software. We also present a Monte Carlo simulation study to evaluate the performance of the maximum likelihood estimators for the GGTT model. Three life data sets were used for applications in order to illustrate the flexibility of the new model.
Highlights
Let be a Lie algebra of all matrices of order
We work with finite-dimensional modules and finite-dimensional representation of
Choose integers, such that the inequality is satisfied. These partitions are quite important because they appear to be the core in constructing representations. These chosen integers are used to construct some index set
Summary
Let be a Lie algebra of all matrices of order. In this paper, we work with finite-dimensional modules and finite-dimensional representation of. Choose integers , , , such that the inequality is satisfied These partitions are quite important because they appear to be the core in constructing representations. L. Tsetlin gave an explicit construction of a basis for every simple finitedimensional module of. Tsetlin gave an explicit construction of a basis for every simple finitedimensional module of In their work, they gave all the irreducible representations of general linear algebra ( ). E. Ramirez provided a classification and explicit bases of tableaux of all irreducible generic Gelfand-Tsetlin modules for the Lie algebra [2]. This paper will show that the Gelfand-Tsetlin constructions given in the year [1] forms all the irreducible representations of special linear algebra by providing proofs to results.
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