The Experts below are selected from a list of 297 Experts worldwide ranked by ideXlab platform
Sanjeev K. Tomer - One of the best experts on this subject based on the ideXlab platform.
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A Review on Inverse Maxwell Distribution with Its Statistical Properties and Applications
Journal of Statistical Theory and Practice, 2020Co-Authors: Sanjeev K. Tomer, M. S. PanwarAbstract:In this article, we review the inverse Maxwell Distribution and establish its statistical properties including moments, descriptive measures and stochastic orderings. We derive complete sufficient statistic, minimum variance unbiased estimator and maximum likelihood estimator for the parameter. We obtain Bayes estimators of the parameter under non-informative (Jeffrey’s) as well as conjugate priors. We also provide confidence and highest posterior density intervals for the parameter. Two real data sets, GAGurine and Guinea pig data, have been considered for numerical illustrations. Finally, we discuss some areas of applications and further extensions of inverse Maxwell Distribution for the future research work.
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Robust Bayesian Analysis of Lifetime Data from Maxwell Distribution
Austrian Journal of Statistics, 2018Co-Authors: M. S. Panwar, Sanjeev K. TomerAbstract:In this paper, we consider robust Bayesian analysis of lifetime data from the Maxwell Distribution assuming an $\varepsilon$-contamination class of prior Distributions for the parameter. We obtain robust Bayes estimates of the parameter and mean lifetime under squared error and LINEX loss functions in presence of uncensored as well as Type-I progressively hybrid censored lifetime data. A real data set is analysed for numerical illustrations.
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estimation of stress strength reliability for Maxwell Distribution under progressive type ii censoring scheme
International Journal of Systems Assurance Engineering and Management, 2018Co-Authors: Sachin Chaudhary, Sanjeev K. TomerAbstract:This paper deals with the estimation of stress–strength reliability \(P=P[Y
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Estimation of stress–strength reliability for Maxwell Distribution under progressive type-II censoring scheme
International Journal of System Assurance Engineering and Management, 2018Co-Authors: Sachin Chaudhary, Sanjeev K. TomerAbstract:This paper deals with the estimation of stress–strength reliability \(P=P[Y
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Estimation of P[Y < X] for Maxwell Distribution
Journal of Statistics and Management Systems, 2017Co-Authors: Sachin Chaudhary, Jitendra Kumar, Sanjeev K. TomerAbstract:AbstractIn this paper we consider the estimation of R = P[Y < X], where both the random variables X and Y follow Maxwell Distributions with different scale parameters. We obtain the maximum likelihood estimator of R. We also provide asymptotic confidence intervals and bootstrap intervals for the same. The Bayes estimator of R is derived under square error loss function and Bayesian credible and HPD intervals are also obtained. The results are illustrated through simulation study and analysis of a real data set.
Manish Malik - One of the best experts on this subject based on the ideXlab platform.
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Reliability estimation in Maxwell Distribution with progressively Type-II censored data
Journal of Statistical Computation and Simulation, 2012Co-Authors: Hare Krishna, Manish MalikAbstract:There may be situations in which either the reliability data do not fit to popular lifetime models or the estimation of the parameters is not easy, while there may be other Distributions which are not popular but either they provide better goodness-of-fit or have a smaller number of parameters to be estimated, or they have both the advantages. This paper proposes the Maxwell Distribution as a lifetime model and supports its usefulness in the reliability theory through real data examples. Important Distributional properties and reliability characteristics of this model are elucidated. Estimation procedures for the parameter, mean life, reliability and failure-rate functions are developed. In view of cost constraints and convenience of intermediate removals, the progressively Type-II censored sample information is used in the estimation. The efficiencies of the estimates are studied through simulation. Apart from researchers and practitioners in the reliability theory, the study is also useful for scientist...
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Reliability estimation in Maxwell Distribution with Type‐II censored data
International Journal of Quality & Reliability Management, 2009Co-Authors: Hare Krishna, Manish MalikAbstract:Purpose – This paper seeks to focus on the study and estimation of reliability characteristics of Maxwell Distribution under Type‐II censoring scheme.Design/methodology/approach – Maximum likelihood estimation and Bayes estimation methods have been used for the estimation of reliability characteristics. Monte‐Carlo simulation is used to compare the efficiency of the estimates developed by these estimation methods.Findings – With prior information on the parameter of Maxwell Distribution, Bayes estimation provides better estimates of reliability characteristics; otherwise Maximum likelihood estimation is good enough to use for reliability practitioners.Practical implications – When items are costly, Type‐II censoring scheme can be used to save the cost of the experiment and the discussed methods provide the means to estimate the reliability characteristics of the proposed lifetime model under this scheme.Originality/value – The study is useful for researchers and practitioners in reliability theory and als...
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reliability estimation in Maxwell Distribution with type ii censored data
International Journal of Quality & Reliability Management, 2009Co-Authors: Hare Krishna, Manish MalikAbstract:Purpose – This paper seeks to focus on the study and estimation of reliability characteristics of Maxwell Distribution under Type‐II censoring scheme.Design/methodology/approach – Maximum likelihood estimation and Bayes estimation methods have been used for the estimation of reliability characteristics. Monte‐Carlo simulation is used to compare the efficiency of the estimates developed by these estimation methods.Findings – With prior information on the parameter of Maxwell Distribution, Bayes estimation provides better estimates of reliability characteristics; otherwise Maximum likelihood estimation is good enough to use for reliability practitioners.Practical implications – When items are costly, Type‐II censoring scheme can be used to save the cost of the experiment and the discussed methods provide the means to estimate the reliability characteristics of the proposed lifetime model under this scheme.Originality/value – The study is useful for researchers and practitioners in reliability theory and als...
Zhou Gang - One of the best experts on this subject based on the ideXlab platform.
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exponential convergence to the Maxwell Distribution of solutions of spatially inhomogeneous boltzmann equations
Reviews in Mathematical Physics, 2020Co-Authors: Zhou GangAbstract:We consider the rate of convergence of solutions of spatially inhomogeneous Boltzmann equations, with hard-sphere potentials, to some equilibriums, called Maxwellians. Maxwellians are spatially hom...
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Exponential Convergence to the Maxwell Distribution For Spatially Inhomogenous Boltzmann Equations
arXiv: Analysis of PDEs, 2016Co-Authors: Zhou GangAbstract:We consider the rate of convergence of solutions of spatially inhomogenous Boltzmann equations, with hard sphere potentials, to some equilibriums, called Maxwellians. Maxwellians are spatially homogenous static Maxwell velocity Distributions with different temperatures and mean velocities. We study solutions in weighted space $L^{1}(\mathbb{R}^{3}\times \mathbb{T}^3)$. We prove a conjecture of C. Villani: assume the solution is sufficiently localized and sufficiently smooth, then the solution, in $L^{1}$-space, converges to a Maxwellian, exponentially fast in time.
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Exponential Convergence to the Maxwell Distribution for Some Class of Boltzmann Equations
Communications in Mathematical Physics, 2012Co-Authors: Jürg Fröhlich, Zhou GangAbstract:We consider a class of nonlinear Boltzmann equations describing return to thermal equilibrium in a gas of colliding particles suspended in a thermal medium. We study solutions in the space \({L^{1}(\Gamma^{(1)},d\lambda),}\) where \({\Gamma^{(1)}=\mathbb{R}^{3} \times \mathbb{T}^3}\) is the one-particle phase space and \({d\lambda= d^3 v d^3 x}\) is the Liouville measure on Γ(1). Special solutions of these equations, called “Maxwellians,” are spatially homogenous static Maxwell velocity Distributions at the temperature of the medium. We prove that, for dilute gases, the solutions corresponding to smooth initial conditions in a weighted L1-space converge to a Maxwellian in \({L^{1}(\Gamma^{(1)},d\lambda)}\) , exponentially fast in time.
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Exponential Convergence to the Maxwell Distribution For Some Class of Boltzmann Equations
arXiv: Analysis of PDEs, 2010Co-Authors: Juerg Froehlich, Zhou GangAbstract:We consider a class of nonlinear Boltzmann equations describing return to thermal equilibrium in a gas of colliding particles suspended in a thermal medium. We study solutions in the space $L^{1}(\mathbb{R}^{3}\times \mathbb{T}^3).$ Special solutions of these equations, called "Maxwellians," are spatially homogenous static Maxwell velocity Distributions at the temperature of the medium. We prove that, for dilute gases, the solutions corresponding to smooth initial conditions in a weighted $L^{1}$-space converge to a Maxwellian in $L^{1},$ exponentially fast in time.
Hare Krishna - One of the best experts on this subject based on the ideXlab platform.
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Estimation in Maxwell Distribution with randomly censored data
Journal of Statistical Computation and Simulation, 2014Co-Authors: Hare Krishna, Vivekanand, Kapil KumarAbstract:In many practical situations, complete data are not available in lifetime studies. Many of the available observations are right censored giving survival information up to a noted time and not the exact failure times. This constitutes randomly censored data. In this paper, we consider Maxwell Distribution as a survival time model. The censoring time is also assumed to follow a Maxwell Distribution with a different parameter. Maximum likelihood estimators and confidence intervals for the parameters are derived with randomly censored data. Bayes estimators are also developed with inverted gamma priors and generalized entropy loss function. A Monte Carlo simulation study is performed to compare the developed estimation procedures. A real data example is given at the end of the study.
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Reliability estimation in Maxwell Distribution with progressively Type-II censored data
Journal of Statistical Computation and Simulation, 2012Co-Authors: Hare Krishna, Manish MalikAbstract:There may be situations in which either the reliability data do not fit to popular lifetime models or the estimation of the parameters is not easy, while there may be other Distributions which are not popular but either they provide better goodness-of-fit or have a smaller number of parameters to be estimated, or they have both the advantages. This paper proposes the Maxwell Distribution as a lifetime model and supports its usefulness in the reliability theory through real data examples. Important Distributional properties and reliability characteristics of this model are elucidated. Estimation procedures for the parameter, mean life, reliability and failure-rate functions are developed. In view of cost constraints and convenience of intermediate removals, the progressively Type-II censored sample information is used in the estimation. The efficiencies of the estimates are studied through simulation. Apart from researchers and practitioners in the reliability theory, the study is also useful for scientist...
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Reliability estimation in Maxwell Distribution with Type‐II censored data
International Journal of Quality & Reliability Management, 2009Co-Authors: Hare Krishna, Manish MalikAbstract:Purpose – This paper seeks to focus on the study and estimation of reliability characteristics of Maxwell Distribution under Type‐II censoring scheme.Design/methodology/approach – Maximum likelihood estimation and Bayes estimation methods have been used for the estimation of reliability characteristics. Monte‐Carlo simulation is used to compare the efficiency of the estimates developed by these estimation methods.Findings – With prior information on the parameter of Maxwell Distribution, Bayes estimation provides better estimates of reliability characteristics; otherwise Maximum likelihood estimation is good enough to use for reliability practitioners.Practical implications – When items are costly, Type‐II censoring scheme can be used to save the cost of the experiment and the discussed methods provide the means to estimate the reliability characteristics of the proposed lifetime model under this scheme.Originality/value – The study is useful for researchers and practitioners in reliability theory and als...
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reliability estimation in Maxwell Distribution with type ii censored data
International Journal of Quality & Reliability Management, 2009Co-Authors: Hare Krishna, Manish MalikAbstract:Purpose – This paper seeks to focus on the study and estimation of reliability characteristics of Maxwell Distribution under Type‐II censoring scheme.Design/methodology/approach – Maximum likelihood estimation and Bayes estimation methods have been used for the estimation of reliability characteristics. Monte‐Carlo simulation is used to compare the efficiency of the estimates developed by these estimation methods.Findings – With prior information on the parameter of Maxwell Distribution, Bayes estimation provides better estimates of reliability characteristics; otherwise Maximum likelihood estimation is good enough to use for reliability practitioners.Practical implications – When items are costly, Type‐II censoring scheme can be used to save the cost of the experiment and the discussed methods provide the means to estimate the reliability characteristics of the proposed lifetime model under this scheme.Originality/value – The study is useful for researchers and practitioners in reliability theory and als...
Sajid Ali - One of the best experts on this subject based on the ideXlab platform.
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Two-parameter Maxwell Distribution: Properties and different methods of estimation
Journal of Statistical Theory and Practice, 2016Co-Authors: Sanku Dey, Tanujit Dey, Sajid Ali, Madhuri S. MulekarAbstract:In this article we consider the problem of estimating location and scale parameters of the Maxwell Distribution from both frequentist and Bayesian points of view. Additionally, some properties of the Distribution, namely, stochastic ordering, Rényi and Shannon entropies, and order statistics, are derived. Behavior of the estimators from different frequentist approaches, namely, maximum likelihood, method of moments, least square’s, and weighted least square as well as Bayes estimators of parameters, is compared with respect to bias, mean squared errors, and the coverage percentage extracted from bootstrap confidence intervals. The existence and uniqueness of the maximum likelihood estimators are also discussed. The Bayes estimators and the associated credible intervals are obtained using importance sampling technique under squared error loss function. A gamma prior is used for the scale parameter and a uniform prior for the location parameter. An example with flood-level data is used to illustrate applicability of procedures discussed.
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Two-parameter Maxwell Distribution: Properties and different methods of estimation
Journal of Statistical Theory and Practice, 2016Co-Authors: Sanku Dey, Tanujit Dey, Sajid Ali, Madhuri S. MulekarAbstract:ABSTRACTIn this article we consider the problem of estimating location and scale parameters of the Maxwell Distribution from both frequentist and Bayesian points of view. Additionally, some properties of the Distribution, namely, stochastic ordering, Renyi and Shannon entropies, and order statistics, are derived. Behavior of the estimators from different frequentist approaches, namely, maximum likelihood, method of moments, least square’s, and weighted least square as well as Bayes estimators of parameters, is compared with respect to bias, mean squared errors, and the coverage percentage extracted from bootstrap confidence intervals. The existence and uniqueness of the maximum likelihood estimators are also discussed. The Bayes estimators and the associated credible intervals are obtained using importance sampling technique under squared error loss function. A gamma prior is used for the scale parameter and a uniform prior for the location parameter. An example with flood-level data is used to illustrate...
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Posterior Analysis for the Maxwell Model
2012Co-Authors: Muhammad Aslam, Syed Mohsin Ali Kazmi, Sajid AliAbstract:The Bayesian approach to analyze different statistical models has developed great interest among analysts. Posterior Distribution is the workbench of the Bayesian statisticians. It is obtained when prior information is combined with likelihood. Therefore the prior information is necessary for the Bayesian approach. The prior information is purely subjective assessment of an expert before any data have been observed. So here we consider different informative and non-informative priors and compare them to see which one is more suitable for our proposed model. The effort of current study is to explore the heterogeneous population using the Bayesian analysis for simple and mixture of the Maxwell Distribution when data is censored and uncensored. Various types of comparisons of prior Distributions for the parameter of the Maxwell Distribution and loss functions are illustrated. We also consider Type I mixture of the Maxwell Distribution which is member of the subclass of the exponential family. As an extension to this work, a comparisons of different loss functions are made. Moreover we have derived the limiting expressions for the Bayes estimators with their variances.
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on the bayesian estimation for two component mixture of Maxwell Distribution assuming type i censored data
2012Co-Authors: Syed Mohsin, Muhammad Aslam, Ali Kazmi, Sajid AliAbstract:Mixture models constitute a finite and infinite number of components that explain different datasets. However there are many situations where mixture models comprise an interesting sketch of different aspects. In this study we explore the idea of mixture density under Type I censoring scheme. We model a heterogeneous population by means of two components mixture of the Maxwell Distribution. The parameters of the Maxwell mixture are estimated and compared using the Bayes estimates under the square error loss function and precautionary loss function. A censored mixture data is simulated by probabilistic mixing for the computational purpose. Closed form expressions for the Bayes estimators and posterior risk are derived for the censored sample as well as for the complete sample. Some interesting comparison and properties of the estimates are observed and presented. A real life data application has also been discussed.
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A Note on the Maximum Likelihood Estimators for the Mixture of Maxwell Distributions Using Type-I Censored Scheme
The Open Statistics and Probability Journal, 2011Co-Authors: Syed Mohsin Ali Kazmi, Muhammad Aslam, Sajid AliAbstract:This article focuses on the study of mixture density under Type I censoring scheme by taking Maxwell distribu- tion as a life time model. In this paper we sculpt a heterogeneous population by means of two components mixture of the Maxwell Distribution. We derive the maximum likelihood estimators using type-I censored data and also their variances matrix. The problem with ML estimators is discussed. The Maple 13.0 code is also presented in appendix.