http://starc.stthomas.ac.in:8080/xmlui/xmlui/handle/123456789/31 Tue, 07 Apr 2026 08:21:23 GMT 2026-04-07T08:21:23Z http://http://starc.stthomas.ac.in:8080/xmlui:8080/xmlui/bitstream/id/773386de-0296-4ea4-935d-be15a0911e67/ http://starc.stthomas.ac.in:8080/xmlui/xmlui/handle/123456789/31 http://starc.stthomas.ac.in:8080/xmlui/xmlui/handle/123456789/426 On Complex Matrix-Variate Dirichlet Averages and Its Applications in Various Sub-Domains Thankamani, Princy; Sebastian, Nicy; Haubold, Hans J. This paper is about Dirichlet averages in the matrix-variate case or averages of functions over the Dirichlet measure in the complex domain. The classical power mean contains the harmonic mean, arithmetic mean and geometric mean (Hardy, Littlewood and Polya), which is generalized to the y-mean by de Finetti and hypergeometric mean by Carlson; see the references herein. Carlson’s hypergeometric mean averages a scalar function over a real scalar variable type-1 Dirichlet measure, which is known in the current literature as the Dirichlet average of that function. The idea is examined when there is a type-1 or type-2 Dirichlet density in the complex domain. Averages of several functions are computed in such Dirichlet densities in the complex domain. Dirichlet measures are defined when the matrices are Hermitian positive definite. Some applications are also discussed. Fri, 10 Nov 2023 00:00:00 GMT http://starc.stthomas.ac.in:8080/xmlui/xmlui/handle/123456789/426 2023-11-10T00:00:00Z http://starc.stthomas.ac.in:8080/xmlui/xmlui/handle/123456789/409 Topp-Leone Generated q-Weibull Distribution and its Applications Sebastian, Nicy; Joseph, Jeena; Santhosh, Sona In this paper, we introduce a new generated distribution called the Topp-Leone Generated q-Weibull(TLqW) Distribution. The described distribution’s many distributional attributes and reliability traits are covered. Some well-known special cases of the mentioned model are also listed. When the lifetimes follow this distribution, it is better to establish a new reliability test plan, which aids in picking the best choices. The maximum likelihood method is investigated for parameter estimation in models. Using actual data sets, we used empirical evidence to demonstrate the value and adaptability of the new model in the model building process. The new test plan is then used to demonstrate how it may be used for creating dependable software in commercial settings. Sat, 15 Apr 2023 00:00:00 GMT http://starc.stthomas.ac.in:8080/xmlui/xmlui/handle/123456789/409 2023-04-15T00:00:00Z http://starc.stthomas.ac.in:8080/xmlui/xmlui/handle/123456789/407 TYPE-1 BETA DISTRIBUTION AND ITS CONNECTIONS TO LIKELIHOOD RATIO TEST Sebastian, Nicy; Princy, T. In many cases involving hypothesis testing for parameters in multivariate Gaussian populations and certain other populations, likelihood ratio criteria, or their one-to-one functions, can be expressed in terms of the determinant of a real type-1 beta matrix. In geometrical probability problems, when the random points are type-1 beta distributed, the volume content of the parallellotope generated by these points is also associated with the determinant of a real type-1 beta matrix. These problems in the corresponding complex domain do not seem to have been discussed in the literature. It is well-known that the determinant of a real type-1 beta matrix can be written as a product of statistically independently distributed real scalar type-1 beta random variables. This paper addresses the general h-th moments of a scalar random variable, in either the real or complex domain, for any arbitrary h. The structure of these moments is quite general, and the paper provides exact distribution results, asymptotic gamma function results, and asymptotic normal results for both the real and complex domains Sun, 01 Dec 2024 00:00:00 GMT http://starc.stthomas.ac.in:8080/xmlui/xmlui/handle/123456789/407 2024-12-01T00:00:00Z http://starc.stthomas.ac.in:8080/xmlui/xmlui/handle/123456789/400 Applications of Burr III-Weibull quantile function in reliability analysis Deepthy, G. S.; Sebastian, Nicy; Chandra, N. This paper introduces a new family of distributions defined in terms of quantile function. The quantile function introduced here is the sum of quantile functions of life time distributions called Burr III and Weibull. Different distributional characteristics and reliability properties are included in the study. Method of Least Square and Method of L-moments are applied to estimate the parameters of the model. Two real life data sets are used to illustrate the performance of the model. Tue, 09 May 2023 00:00:00 GMT http://starc.stthomas.ac.in:8080/xmlui/xmlui/handle/123456789/400 2023-05-09T00:00:00Z