Mathematics And Statistics - Research Publications

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    A Novel Bivariate Generalized Weibull Distribution with Properties and Applications
    (Taylor and Francis Ltd., 2023-09-09T00:00:00) Pathak, Ashok Kumar; Arshad, Mohd; J. Azhad, Qazi; Khetan, Mukti; Pandey, Arvind
    Univariate Weibull distribution is a well known lifetime distribution and has been widely used in reliability and survival analysis. In this paper, we introduce a new family of bivariate generalized Weibull (BGW) distributions, whose univariate marginals are exponentiated Weibull distribution. Different statistical quantiles like marginals, conditional distribution, conditional expectation, product moments, correlation and a measure component reliability are derived. Various measures of dependence and statistical properties along with aging properties are examined. Further, the copula associated with BGW distribution and its various important properties are also considered. The methods of maximum likelihood and Bayesian estimation are employed to estimate unknown parameters of the model. A Monte Carlo simulation and real data study are carried out to demonstrate the performance of the estimators and results have proven the effectiveness of the distribution in real-life situations. � 2023 Taylor & Francis Group, LLC.
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    A Bivariate Teissier Distribution: Properties, Bayes Estimation and Application
    (Springer, 2023-08-29T00:00:00) Sharma, Vikas Kumar; Singh, Sudhanshu Vikram; Pathak, Ashok Kumar
    This article presents a bivariate extension of the Teissier distribution, whose univariate marginal distributions belong to the exponentiated Teissier family. Analytic expressions for the different statistical quantities such as conditional distribution, joint moments, and quantile function are explicitly derived. For the proposed distribution, the concepts of reliability and dependence measures are also explored in details. Both the maximum likelihood technique and the Bayesian approach are utilised in the process of parameter estimation for the proposed distribution with unknown parameters. Several numerical experiments are reported to study the performance of the classical and Bayes estimators for varying sample size. Finally, a bivariate data is fitted using the proposed distribution to show its applicability over the bivariate exponential, Rayleigh, and linear exponential distributions in real-life situations. � 2023, Indian Statistical Institute.
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    Stability analysis of neutral delay fractional differential equations with Erdelyi�Kober fractional integral boundary conditions
    (Elsevier B.V., 2023-08-11T00:00:00) Bedi, Pallavi; Kumar, Anoop; Khan, Aziz; Abdeljawad, Thabet
    The primary focus of this article is to provide sufficient conditions for the Ulam�Hyers stability of neutral delay fractional differential equations involving Hilfer fractional derivatives and Erdelyi�Kober fractional integral boundary conditions. The fixed point approach is utilized to prove the existence and uniqueness of mild solutions for the proposed problem. In the end, the derived results are validated through an illustrative example. � 2023 The Author(s)
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    Transmission dynamics of a novel fractional model for the Marburg virus and recommended actions
    (Springer Science and Business Media Deutschland GmbH, 2023-08-02T00:00:00) Singh, Jaskirat Pal; Abdeljawad, Thabet; Baleanu, Dumitru; Kumar, Sachin
    Marburg virus disease is a particularly virulent illness that causes hemorrhagic fever and has a fatality rate of up to 88%. It belongs to the same family of pathogens as the Ebola virus. The disease was first identified in 1967 as a result of two significant epidemics that happened concurrently in Marburg, hence the name Marburg, Frankfurt, both in Germany, and Belgrade, Serbia. This work proposes a unique fractional model for the Marburg virus based on the Atangana�Baleanu derivative in the Caputo sense. For the model, two equilibrium states have been founded: endemic equilibrium and disease-free equilibrium. If R< 1 , Castillo�s method and the next-generation matrix are used to demonstrate the disease-free equilibrium�s asymptotic global stability. When R> 1 , the endemic equilibrium point is locally asymptotically stable, according to the linearization. The model�s basic reproduction rates for both humans and bats are calculated using the parameter values. Fixed point theory is used to demonstrate the solution�s existence and uniqueness. Number of infected bats should be controlled and interaction with just recovered individuals should be avoided as these are the main contributors in the infection rate. These recommended actions will make the infected persons in the humans disappear, as demonstrated by the model�s numerical simulations. � 2023, The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature.
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    Modeling Bivariate Data Using Linear Exponential and Weibull Distributions as Marginals
    (De Gruyter Open Ltd, 2023-08-04T00:00:00) Arshad, Mohd; Pathak, Ashok Kumar; Azhad, Qazi J.; Khetan, Mukti
    Modeling bivariate data with different marginals is an important problem and have numerous applications in diverse disciplines. This paper introduces a new family of bivariate generalized linear exponential Weibull distribution having generalized linear and exponentiated Weibull distributions as marginals. Some important quantities like conditional distributions, conditional moments, product moments and bivariate quantile functions are derived. Concepts of reliability and measures of dependence are also discussed. The methods of maximum likelihood and Bayesian estimation are considered to estimate model parameters. Monte Carlo simulation experiments are performed to demonstrate the performance of the estimators. Finally, a real data application is also discussed to demonstrate the usefulness of the proposed distribution in real-life situations. � 2023 Mathematical Institute Slovak Academy of Sciences.
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    First Chen Inequality for General Warped Product Submanifolds of a Riemannian Space Form and Applications; [Premi�re in�galit� de Chen pour des produits tordus de sous-vari�t�s d�un espace forme riemannien et applications]
    (ISTE Group, 2023-06-15T00:00:00) Mustafa, Abdulqader; �zel, Cenap; Pigazzini, Alexander; Kaur, Ramandeep; Shanker, Gauree
    In this paper, the first Chen inequality is proved for general warped product submanifolds in Riemannian space forms, this inequality involves intrinsic invariants (?-invariant and sectional curvature) controlled by an extrinsic one (the mean curvature vector), which provides an answer for Chen�s Problem 1 relating to establish simple relationships between the main extrinsic invariants and the main intrinsic invariants of a submanifold. As a geometric application, this inequality is applied to derive a necessary condition for the immersed submanifold to be minimal in Riemannian space forms, which presents a partial answer for the well-known problem proposed by S.S. Chern, Problem 2. For further research directions, we address a couple of open problems; namely Problem 3 and Problem 4. � 2023 ISTE OpenScience � Published by ISTE Ltd. London, UK.
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    General form of axially symmetric stationary metric: exact solutions and conservation laws in vacuum fields
    (Institute of Physics, 2023-06-24T00:00:00) Jyoti, Divya; Kumar, Sachin
    The invariant non-static solutions of Einstein�s vacuum field equations, corresponding to the most general form of axially symmetric stationary line element that represents a non conformally flat semi-Riemannian spacetime in cylindrical coordinates, are investigated. Lie symmetry method is used for symmetry reduction as well as for obtaining exact solutions in terms of arbitrary functions. The conservation laws are obtained for vacuum equations in axially symmetric gravitational fields. The solutions of Lewis metric and Chandrasekhar metric, are derived from the obtained solutions. By considering the possibilities of arbitrary functions, the graphical behaviour of the solutions is also shown. � 2023 IOP Publishing Ltd.
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    Highly dispersive W�shaped and other optical solitons with quadratic�cubic nonlinearity: Symmetry analysis and new Kudryashov's method
    (Elsevier Ltd, 2023-06-24T00:00:00) Yadav, Ravindra; Malik, Sandeep; Kumar, Sachin; Sharma, Rajesh; Biswas, Anjan; Y?ld?r?m, Yakup; Gonz�lez-Gaxiola, O.; Moraru, Luminita; Alghamdi, Abdulah A.
    Lie symmetry analysis is utilized in this paper to explore the properties of highly dispersive optical solitons that exhibit quadratic�cubic self-phase modulation. The use of Lie symmetry analysis enables the reduction of the governing partial differential equation to an ordinary differential equation, which is then integrated using an enhanced Kudryashov's approach to obtain solitons with the model. The analysis presented in this paper does not explicitly discuss the formation and dynamics of soliton radiation. � 2023
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    Moderation effects of serotype on dengue severity across pregnancy status in Mexico
    (BioMed Central Ltd, 2023-03-26T00:00:00) Annan, Esther; Nguyen, Uyen-Sa D. T.; Trevi�o, Jes�s; Wan Yaacob, Wan Fairos; Mangla, Sherry; Pathak, Ashok Kumar; Nandy, Rajesh; Haque, Ubydul
    Background: Pregnancy increases a woman�s risk of severe dengue. To the best of our knowledge, the moderation effect of the dengue serotype among pregnant women has not been studied in Mexico. This study explores how pregnancy interacted with the dengue serotype from 2012 to 2020 in Mexico. Method: Information from 2469 notifying health units in Mexican municipalities was used for this cross-sectional analysis. Multiple logistic regression with interaction effects was chosen as the final model and sensitivity analysis was done to assess potential exposure misclassification of pregnancy status. Results: Pregnant women were found to have higher odds of severe dengue [1.50 (95% CI 1.41, 1.59)]. The odds of dengue severity varied for pregnant women with DENV-1 [1.45, (95% CI 1.21, 1.74)], DENV-2 [1.33, (95% CI 1.18, 1.53)] and DENV-4 [3.78, (95% CI 1.14, 12.59)]. While the odds of severe dengue were generally higher for pregnant women compared with non-pregnant women with DENV-1 and DENV-2, the odds of disease severity were much higher for those infected with the DENV-4 serotype. Conclusion: The effect of pregnancy on severe dengue is moderated by the dengue serotype. Future studies on genetic diversification may potentially elucidate this serotype-specific effect among pregnant women in Mexico. � 2023, The Author(s).
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    Existence of solutions by fixed point theorem of general delay fractional differential equation with p-Laplacian operator
    (American Institute of Mathematical Sciences, 2023-02-27T00:00:00) Kaushik, Kirti; Kumar, Anoop; Khan, Aziz; Abdeljawad, Thabet
    In this manuscript, the main objective is to analyze the existence, uniqueness,(EU) and stability of positive solution for a general class of non-linear fractional differential equation (FDE) with fractional differential and fractional integral boundary conditions utilizing ?p-Laplacian operator. To continue, we will apply Green�s function to determine the suggested FDE�s equivalent integral form. The Guo-Krasnosel�skii fixed point theorem and the properties of the p-Laplacian operator are utilized to derive the existence results. Hyers-Ulam (HU) stability is additionally evaluated. Further, an application is presented to validate the effectiveness of the result. � 2023 the Author(s), licensee AIMS Press.