The Cramer—Rao Inequality to Improve the Resolution of the Least-Squares Method in Track Fitting [PDF]
Instruments, 2020 The Cramer−Rao−Frechet inequality is reviewed and extended to track fitting. A diffused opinion attributes to this inequality the limitation of the resolution of the track fits with the number N of observations.
Gregorio Landi, Giovanni E. Landi
doaj +6 more sources
Fisher and Shannon Functionals for Hyperbolic Diffusion [PDF]
Entropy, 2023 The complexity measure for the distribution in space-time of a finite-velocity diffusion process is calculated. Numerical results are presented for the calculation of Fisher’s information, Shannon’s entropy, and the Cramér–Rao inequality, all of which ...
Manuel O. Cáceres +2 more
doaj +2 more sources
Annals of Statistics, 1977 Sufficient conditions for the Cramer-Rao inequality are formulated which do not impose any requirement on the estimator and which are independent of the choice of the densities. A hereditary property is proved for these conditions and the attainability of the lower bound is studied.
Václav Fabian
exaly +4 more sources
Information theory and thermal properties of an extended cosine hyperbolic potential model [PDF]
Scientific ReportsThis study presents the information-theoretic measures and molar thermodynamic properties for an extended cosine hyperbolic potential. The analytic expressions for the Fisher information in both position and momentum spaces are derived.
Chou-Yi Hsu +6 more
doaj +2 more sources
Information theory and thermodynamic properties for a combined potential model [PDF]
Scientific ReportsYukawa potential and Hulthẻn potential are very useful potential models with applications in different areas of physics. The present study examined theoretic measure and thermodynamic properties of energy levels and wave functions for a combination of ...
C. A. Onate +4 more
doaj +2 more sources
Determination of probability density, position and momentum uncertainties, and information theoretic measures using a class of inversely quadratic Yukawa potential [PDF]
Scientific ReportsThis study utilizes the Nikiforov-Uvarov method to solve the Schrödinger equation for the class of inversely quadratic Yukawa potential (CIQYP), deriving both the energy equation and the normalized wave function. Shannon entropy and Fisher information in
Etido P. Inyang +5 more
doaj +2 more sources
Necessary and Sufficient Conditions for Inequalities of Cramer-Rao Type
Annals of Statistics, 1974 For a random variable $X$ with possible distributions indexed by a parameter $\theta$, and for real-valued $T = T(X)$ and $V = V(X, \theta)$ with $\operatorname{Var} T < \infty$ and $0 < \operatorname{Var} V < \infty$, Schwarz's inequality gives $\operatorname{Var} T \geqq \{\operatorname{Cov} (T, V)\}^2/\operatorname{Var} V$.
exaly +4 more sources
Malliavin calculus in statistical inference: Cramer-Rao lower bound for fuzzy random variables [PDF]
تصمیم گیری و تحقیق در عملیات, 2020 The Cramer-Rao lower bound is obtained by using integration by parts and the Cauchy-Schwarz inequality. The integration by parts formulas of Malliavin calculus plays a role in this study. The point estimation problem is very crucial and has a wide range
Hossein Jafari, Mohammad Javad Ebadi
doaj +1 more source
Information entropic measures for a trigonometric inversely quadratic plus Coulombic Hyperbolic Potential [PDF]
Songklanakarin Journal of Science and Technology (SJST), 2022 In this study, the analytical solution of the Schrödinger equation for the Trigonometric Inversely Quadratic plus Coulombic Hyperbolic Potential via the methodology of the supersymmetric approach was obtained.
Clement Atachegbe Onate +2 more
doaj +1 more source
Entropy production and fluctuation theorems in a continuously monitored optical cavity at zero temperature [PDF]
Quantum, 2022 Fluctuation theorems allow one to make generalised statements about the behaviour of thermodynamic quantities in systems that are driven far from thermal equilibrium. In this article we use Crooks' fluctuation theorem to understand the entropy production
Michael J. Kewming, Sally Shrapnel
doaj +1 more source