Doctoral Theses

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    Estimation of stress-strength reliability from exponentiated Fréchet distribution
    (Springer, 2016) Rao, G. S; Rosaiah, K; Babu, M. S
    In this paper, we are mainly concerned in estimating the reliability R = P(Y < X) in the exponentiated Fréchet distribution, recently proposed by Nadarajah and Kotz (2006), Acta Appl Math 92:97–111. The model arises as a generalization of the standard Fréchet distribution in the same way the exponentiated exponential distribution introduced by Gupta et al. (1998), Commun Stat Theory Methods 27:887–904. The maximum likelihood estimator and its asymptotic distribution are used to construct an asymptotic confidence interval of R. Assuming that the common scale and shape parameters are known, the maximum likelihood estimator, uniformly minimum variance unbiased estimator of R are discussed. Different methods and the corresponding confidence intervals are compared using Monte Carlo simulation. Using real data, we illustrate the procedure.
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    Generalized anisotropic compact star models via embedding of dimensions
    (The University of Dodoma, 2022) Mathias, Alberto Kimbuya
    The generalized anisotropic stellar models to the Einstein-Maxwell field equations are generated. The Karmarkar condition and an equation of state are used with the Einstein-Maxwell field equations to investigate various physical properties and behaviour of compact stars. The embedding approach provides a relationship between gravitational potentials. The general forms for the gravitational potentials, theme asure of anisotropy and the electric field intensity are specified on physical grounds to generate exact solutions to the Einstein-Maxwellfield equations. Thenon-linear Einstein Maxwellfield equations are transformed by adopting the Durgapaland Bannerji transformations. The approach of merging the Karmakar condition and an equation of state adopted in this study generates charged anisotropic models with astrophysical significance. The generated classes of charged anisotropic solutions reduce to several uncharged models with isotropic behaviour as special cases. Charged anisotropic models with embedding and an equation of state that reduce to neutral isotropic models are missing in the existing literature. The graphical representations for the generated models are presented to describe the structure and properties of relativistic compact stars. The detailed physical analysis on the results shows that the gravitational potentials and matter variables are well behaved. The stars are found to be stable under adiabatic indexes, all energy conditions are satisfied the regularity condition is not violated, forces under equilibrium conditions are balanced, and the matching conditions are satisfied at the boundary of the relativistic star.
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    Generalized models to the einstein-maxwell field equations for space-time symmetries with conformal motions
    (The University of Dodoma, 2022) Jape, Jonas William
    New generalized solutions of the Einstein-Maxwell field equations for charged anisotropic stellar spheres are generated. The Einstein-Maxwell field equations are investigated in the presence of the conformal Killing vector and a linear equation of state. The conformal Killing vector provides an equation relating the gravitational potentials. New general forms for the gravitational potentials, a measure of anisotropy, and electric field intensity are specified on physical grounds to generate exact solutions related to compact stars. The generalized solutions with conformal symmetry and a linear equation of state gener ated in this study reduce to several charged/uncharged and anisotropic/isotropic solutions generated by various researchers in the past with approaches other than conformal sym metry. Charged anisotropic models with conformal symmetry and an equation of state that reduce to neutral isotropic models as special cases are missing in the literature. The detailed physical analysis reveals that the gravitational potentials and matter variables are well behaved. The interior and exterior metrics are matched smoothly at the stellar boundary, the gravitational potentials are free from physical and geometric singularities, the energy conditions are satisfied, the mass-radius ratio and surface red shifts are found to be within acceptable limits with the existing literature, and the natural physical forces balance at equilibrium. The models are also stable from gravitational collapse.