scholarly journals On the Calculation of Variances and Credibilities by Experience Rating

1977 ◽  
Vol 9 (1-2) ◽  
pp. 203-207 ◽  
Author(s):  
K. Loimaranta
Keyword(s):  
Iterative Process ◽  
Linear Equations ◽  
The Other ◽  
Likelihood Principle ◽  
Experience Rating ◽  
Maximum Likelihood Principle ◽  
Image Position ◽  
The Mathematical Model ◽  
Non Linear Equations ◽  
General Method

By experience rating the main problem is to estimate the credibilities. We have for the credibility αk the famous formula)but it is often troublesome to find suitable estimates for the variances and . In the present paper a general method to estimate them from the actual statistics is given.A disadvantage of the method is that good estimates require relatively extensive statistical material. If one of the variances is known, the method can be easily modified to give the other variance from statistics of moderate size.The method is based on the Maximum Likelihood principle and leads to a system of non-linear equations. The equations can be solved by an iterative process, easily programmable for computers.The mathematical model underlying the experience rating problem differs in our case lightly from the usual one.

A System of Linear Equations with an Infinity of Unknowns

1924 ◽  
Vol 22 (3) ◽  
pp. 282-286
Author(s):  
E. C. Titchmarsh
Keyword(s):  
Present Note ◽  
Linear Equations ◽  
The Other ◽  
System Of Linear Equations ◽  
Other Hand ◽  
Image Position ◽  
Monotonic Character

I have collected in the present note some theorems regarding the solution of a certain system of linear equations with an infinity of unknowns. The general form of the equations isthe numbers a1, a2, … c1, c2, … being given. Equations of this type are of course well known; but in studying them it is generally assumed that the series depend for convergence on the convergence-exponent of the sequences involved, e.g. that and are convergent. No assumptions of this kind are made here, and in fact the series need not be absolutely convergent. On the other hand rather special assumptions are made with regard to the monotonic character of the sequences an and cn.

Excess molar volumes of the (cyclohexane + pentane, or hexane, or heptane, or octane, or nonane) systems at the temperature 298.15 K

2007 ◽  
Vol 61 (6) ◽  
Author(s):  
J. Balán ◽  
L. Morávková ◽  
J. Linek
Keyword(s):  
Maximum Likelihood ◽  
Fourth Order ◽  
Excess Molar Volumes ◽  
The Other ◽  
Likelihood Principle ◽  
Molar Volumes ◽  
Maximum Likelihood Principle ◽  
Vibrating Tube Densimeter ◽  
Kister Equation

AbstractThe densities of the (cyclohexane + pentane, or hexane, or heptane, or octane, or nonane) systems were measured at the temperature 298.15 K by means of a vibrating-tube densimeter. Their respective excess molar volumes were calculated and correlated using the fourth-order Redlich—Kister equation, with the maximum likelihood principle being applied in the determination of the adjustable parameters. The values of excess molar volumes were negative for the cyclohexane + pentane system, whereas they were positive for the other systems with the values increasing with the number of carbon atoms in the respective alkane molecules.

Mathematical Modeling for the Accumulation of Cadmium, Zinc and Arsenic from the Soil in the Case of Bulrush Plant Type

2020 ◽  
Vol 70 (12) ◽  
pp. 4576-4583
Keyword(s):  
Mathematical Model ◽  
Linear Equations ◽  
Mathematic Model ◽  
Plant Type ◽  
High Accumulation ◽  
Plant Samples ◽  
Accumulation Capacity ◽  
The Mathematical Model ◽  
Non Linear Equations ◽  
Soil Interface

This paper proposes a tridimensional mathematical model of the accumulation of cadmium, arsenic and zinc from the soil in the case of bulrush plant type (the soil and plant samples was taken from two points along the Bistriţa River, belonging to the Siret hydrographic basin). The variable measures taken into consideration when carrying out the experiments and realizing the mathematical model are the distance from the water-soil interface from which the plant samples were taken and the content of cadmium, arsenic and zinc in the soil. The mathematical model was elaborated and tested by means of the TableCurve 3D program used for generating linear and non-linear equations. A reduced accumulation capacity of arsenic from the soil was registered. A high accumulation of cadmium from the soil was registered, in the case of bulrush plant type (765÷875 % higher than in the soil). The correlation coefficient of the mathematic model was between 0.94-0.99. Keywords: cadmium, arsenic, zinc, mathematic model, accumulation, Typha Latifola’s

scholarly journals Methods for fitting equations with two or more non-linear parameters

1976 ◽  
Vol 157 (2) ◽  
pp. 489-492 ◽  
Author(s):  
I A Nimmo ◽  
G L Atkins
Keyword(s):  
Experimental Data ◽  
Least Squares ◽  
Linear Equations ◽  
Simultaneous Equations ◽  
The Other ◽  
Parameter Estimates ◽  
Non Linear ◽  
Non Linear Equations

1. Descriptions are given of two ways for fitting non-linear equations by least-squares criteria to experimental data. One depends on solving a set of non-linear simultaneous equations, and the other on Taylor's theorem. 2. It is shown that better parameter estimates result when an equation with two or more non-linear parameters is fitted to all the sets of data simultaneously than when it is fitted to each set in turn.

The effect of rotation on the simpler modes of motion of a liquid in an elliptic paraboloid

1965 ◽  
Vol 22 (3) ◽  
pp. 529-545 ◽  
Author(s):  
F. K. Ball
Keyword(s):  
Linear Equations ◽  
The Other ◽  
List Type ◽  
Elliptic Paraboloid ◽  
The Earth ◽  
Positive Sense ◽  
Rotation Of The Earth ◽  
The Waves ◽  
Negative Sense ◽  
Non Linear Equations

The six simplest modes of motion are considered and three rotational effects investigated:The effect of the rotation of the earth.The effect of the rotation of the container.The effect of the rotation of the liquid within the container.The first two are shown to be equivalent for motion in a paraboloid, and the last two are also equivalent when the paraboloid iscircular. In the case of an elliptic paraboloid the last is rather more difficult and one must first derive a solution of the non-linear equations representing ‘elliptic rotation’ and then consider deviations from it.The changes in frequency consequent on the rotation are derived in all three cases for all six modes. In the case of the earth's rotation the disposition and character of the amphidromic (nodal) points and the amphidromic waves that rotate round these points are investigated in detail. One mode is particularly interesting because it has four amphidromic points, the waves rotate in a positive sense around two of these and in a negative sense round the other two.

Existence Theorems for Some Non-Linear Equations of Evolution

1970 ◽  
Vol 22 (4) ◽  
pp. 726-745 ◽  
Author(s):  
John C. Clements
Keyword(s):  
Differential Operators ◽  
Existence Theorems ◽  
Linear Equations ◽  
Global Solutions ◽  
The Real ◽  
Partial Differential Operators ◽  
Non Linear ◽  
Image Position ◽  
Vector Valued Function ◽  
Non Linear Equations

In recent years considerable attention has been focused on non-linear hyperbolic differential equations with the object of establishing the existence of global solutions. It is our aim here to establish the existence of weak solutions of boundary value problems for non-linear equations of the form(1-1)where d is a real constant called the damping coefficient, u(t) is a vector-valued function defined on a subinterval of the real line into a space of complex-valued functions u(x) defined on a bounded domain Ω in the real Euclidean space EN of N dimensions, ut(t) ≡ du(t)/dt, and A(t) is the family of partial differential operators of order 2m (m = 1, 2, …) on Ω given in generalized divergence form by(1-2)with

scholarly journals A master exceptional field theory

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Guillaume Bossard ◽  
Axel Kleinschmidt ◽  
Ergin Sezgin
Keyword(s):  
Field Theory ◽  
Gauge Invariance ◽  
Sigma Model ◽  
Linear Equations ◽  
Field Theories ◽  
Gauge Invariant ◽  
Non Linear ◽  
Non Linear Equations

Abstract We construct a pseudo-Lagrangian that is invariant under rigid E11 and transforms as a density under E11 generalised diffeomorphisms. The gauge-invariance requires the use of a section condition studied in previous work on E11 exceptional field theory and the inclusion of constrained fields that transform in an indecomposable E11-representation together with the E11 coset fields. We show that, in combination with gauge-invariant and E11-invariant duality equations, this pseudo-Lagrangian reduces to the bosonic sector of non-linear eleven-dimensional supergravity for one choice of solution to the section condi- tion. For another choice, we reobtain the E8 exceptional field theory and conjecture that our pseudo-Lagrangian and duality equations produce all exceptional field theories with maximal supersymmetry in any dimension. We also describe how the theory entails non-linear equations for higher dual fields, including the dual graviton in eleven dimensions. Furthermore, we speculate on the relation to the E10 sigma model.

scholarly journals stochprofML: stochastic profiling using maximum likelihood estimation in R

2021 ◽  
Vol 22 (1) ◽  
Author(s):  
Lisa Amrhein ◽  
Christiane Fuchs
Keyword(s):  
Maximum Likelihood ◽  
Cell Fate ◽  
Likelihood Estimation ◽  
R Package ◽  
Cell Populations ◽  
Simulation Studies ◽  
Likelihood Principle ◽  
Maximum Likelihood Principle ◽  
Molecular Expression ◽  
Mixed Samples

Abstract Background Tissues are often heterogeneous in their single-cell molecular expression, and this can govern the regulation of cell fate. For the understanding of development and disease, it is important to quantify heterogeneity in a given tissue. Results We present the R package stochprofML which uses the maximum likelihood principle to parameterize heterogeneity from the cumulative expression of small random pools of cells. We evaluate the algorithm’s performance in simulation studies and present further application opportunities. Conclusion Stochastic profiling outweighs the necessary demixing of mixed samples with a saving in experimental cost and effort and less measurement error. It offers possibilities for parameterizing heterogeneity, estimating underlying pool compositions and detecting differences between cell populations between samples.

scholarly journals Framework for Reconstruction of Pseudo Quad Polarimetric Imagery from General Compact Polarimetry

2021 ◽  
Vol 13 (3) ◽  
pp. 530
Author(s):  
Junjun Yin ◽  
Jian Yang
Keyword(s):  
Linear Equations ◽  
Estimation Method ◽  
Data Sets ◽  
Reconstruction Procedure ◽  
Component Decomposition ◽  
Reconstruction Methods ◽  
Sar Imagery ◽  
Key Aspects ◽  
Non Linear Equations ◽  
Reconstruction Model

Pseudo quad polarimetric (quad-pol) image reconstruction from the hybrid dual-pol (or compact polarimetric (CP)) synthetic aperture radar (SAR) imagery is a category of important techniques for radar polarimetric applications. There are three key aspects concerned in the literature for the reconstruction methods, i.e., the scattering symmetric assumption, the reconstruction model, and the solving approach of the unknowns. Since CP measurements depend on the CP mode configurations, different reconstruction procedures were designed when the transmit wave varies, which means the reconstruction procedures were not unified. In this study, we propose a unified reconstruction framework for the general CP mode, which is applicable to the mode with an arbitrary transmitted ellipse wave. The unified reconstruction procedure is based on the formalized CP descriptors. The general CP symmetric scattering model-based three-component decomposition method is also employed to fit the reconstruction model parameter. Finally, a least squares (LS) estimation method, which was proposed for the linear π/4 CP data, is extended for the arbitrary CP mode to estimate the solution of the system of non-linear equations. Validation is carried out based on polarimetric data sets from both RADARSAT-2 (C-band) and ALOS-2/PALSAR (L-band), to compare the performances of reconstruction models, methods, and CP modes.

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