scholarly journals The Jolly-Seber-Tag-Loss model with group heterogeneity

1969 ◽  
pp. 30-43
Author(s):  
Selina Beatriz Gonzalez ◽  
Dr. Laura Cowen
Keyword(s):  
Maximum Likelihood Estimators ◽  
Parameter Estimates ◽  
Population Parameters ◽  
R Software ◽  
Loss Model ◽  
Tag Loss ◽  
Subsequent Time ◽  
Group Heterogeneity ◽  
Newton Raphson ◽  
Raphson Method

Mark-recapture experiments are performed to estimate population parameters such as survival probabilities. Animals are captured, tagged, released, and recaptured at subsequent time periods in order to obtain parameter information. The Jolly-Seber-Tag-Loss (JSTL) model (Cowen & Schwarz, 2006) requires some individuals to be double tagged in order to account for the possibility of animals losing their tags. The Jolly-Seber-Tag-Loss model does not, however, consider the possibility of parameters being different among different groups of individuals, that is, group heterogeneity (for example, males may have higher capture probabilities than females). Our research extends the Jolly-Seber-Tag-Loss model to account for this possibility of group heterogeneity among parameters. We use a Newton-Raphson method to obtain maximum likelihood estimators and R software to create a program that estimates population parameters from tag histories. Our simulation study concludes that when group heterogeneity exists, accounting for this group heterogeneity results in more accurate parameter estimates than the original JSTL model. We present the group heterogeneous JSTL (g-hJSTL) for this purpose.

Application of Extreme Value Statistics to Annual Maximum Magnitudes in Jordan Employing a Mixture Distribution

1999 ◽  
Vol 15 (4) ◽  
pp. 711-724 ◽  
Author(s):  
Abdallah I. Husein Malkawi ◽  
Fayez A. Abdulla ◽  
Samer A. Barakat ◽  
Mohanned S. Al-Sheriadeh
Keyword(s):  
Maximum Likelihood ◽  
Simplex Method ◽  
Mixture Distribution ◽  
Maximum Likelihood Estimators ◽  
Extreme Value ◽  
Annual Maximum ◽  
Maximum Earthquake Magnitude ◽  
Newton Raphson ◽  
Maximum Earthquake ◽  
Raphson Method

The concept of extreme value mixture distribution (EVmix) has been implemented in this study to estimate maximum earthquake magnitude occurrence. The EVmix model is applied to annual maximum earthquake magnitude occurrence in Jordan and conterminous regions spanning over the period 1918 to 1997. The maximum likelihood method, in conjunction with the two optimization methods, was employed for determining the statistical parameters of the Gumbel's asymptotic distribution, i.e., GI, and the extreme value distributions EVIII and EVmix. The Simplex method of Nelder and Mead (1965) was found to be more successful in obtaining the maximum likelihood estimators of the three given distributions than the Newton-Raphson method. The difficulties inherent to the Newton-Raphson method were overcome by the Simplex method. It is shown in this study that the EVmix model fits the observed annual maxima far better than GI and EVIII models. In addition, the maximum likelihood estimators obtained using the Simplex method were used to calculate the earthquake risk for a given return period and a design lifetime of structures.

Group heterogeneity in the Jolly–Seber-Tag-Loss model

2014 ◽  
Vol 17 ◽  
pp. 3-16 ◽  
Author(s):  
Yuan Xu ◽  
Laura L.E. Cowen ◽  
Caleb Gardner
Keyword(s):  
Loss Model ◽  
Tag Loss ◽  
Group Heterogeneity

Using Approximation Non-Bayesian Computation with Fuzzy Data to Estimation Inverse Weibull Parameters and Reliability Function

2018 ◽  
pp. 397
Author(s):  
Nadia Hashim Al-Noor ◽  
Shurooq A.K. Al-Sultany
Keyword(s):  
Maximum Likelihood ◽  
Expectation Maximization ◽  
Mean Squared Error ◽  
Maximum Likelihood Estimators ◽  
Reliability Function ◽  
Fuzzy Data ◽  
Monte Carlo Simulation Study ◽  
Weibull Parameters ◽  
Squared Error ◽  
Newton Raphson

        In real situations all observations and measurements are not exact numbers but more or less non-exact, also called fuzzy. So, in this paper, we use approximate non-Bayesian computational methods to estimate inverse Weibull parameters and reliability function with fuzzy data. The maximum likelihood and moment estimations are obtained as non-Bayesian estimation. The maximum likelihood estimators have been derived numerically based on two iterative techniques namely “Newton-Raphson” and the “Expectation-Maximization” techniques. In addition, we provide compared numerically through Monte-Carlo simulation study to obtained estimates of the parameters and reliability function in terms of their mean squared error values and integrated mean squared error values respectively.

Axisymmetric flow near the critical point on the moving boundary

2010 ◽  
Vol 7 ◽  
pp. 182-190
Author(s):  
I.Sh. Nasibullayev ◽  
E.Sh. Nasibullaeva
Keyword(s):  
Fluid Flow ◽  
Finite Difference ◽  
Boundary Conditions ◽  
Numerical Solution ◽  
Axial Velocity ◽  
Moving Boundary ◽  
Axisymmetric Flow ◽  
Boundary Motion ◽  
Newton Raphson ◽  
Raphson Method

In this paper the investigation of the axisymmetric flow of a liquid with a boundary perpendicular to the flow is considered. Analytical equations are derived for the radial and axial velocity and pressure components of fluid flow in a pipe of finite length with a movable right boundary, and boundary conditions on the moving boundary are also defined. A numerical solution of the problem on a finite-difference grid by the iterative Newton-Raphson method for various velocities of the boundary motion is obtained.

A Generalized Compositional Approach for Reservoir Simulation

1983 ◽  
Vol 23 (05) ◽  
pp. 727-742 ◽  
Author(s):  
Larry C. Young ◽  
Robert E. Stephenson
Keyword(s):  
Enhanced Recovery ◽  
Gas Condensate ◽  
Reservoir Modeling ◽  
Pressure Equation ◽  
Compositional Modeling ◽  
Fluid Property ◽  
Black Oil ◽  
Fluid Properties ◽  
Newton Raphson ◽  
Raphson Method

A procedure for solving compositional model equations is described. The procedure is based on the Newton Raphson iteration method. The equations and unknowns in the algorithm are ordered in such a way that different fluid property correlations can be accommodated leadily. Three different correlations have been implemented with the method. These include simplified correlations as well as a Redlich-Kwong equation of state (EOS). The example problems considered area conventional waterflood problem,displacement of oil by CO, andthe displacement of a gas condensate by nitrogen. These examples illustrate the utility of the different fluid-property correlations. The computing times reported are at least as low as for other methods that are specialized for a narrower class of problems. Introduction Black-oil models are used to study conventional recovery techniques in reservoirs for which fluid properties can be expressed as a function of pressure and bubble-point pressure. Compositional models are used when either the pressure. Compositional models are used when either the in-place or injected fluid causes fluid properties to be dependent on composition also. Examples of problems generally requiring compositional models are primary production or injection processes (such as primary production or injection processes (such as nitrogen injection) into gas condensate and volatile oil reservoirs and (2) enhanced recovery from oil reservoirs by CO or enriched gas injection. With deeper drilling, the frequency of gas condensate and volatile oil reservoir discoveries is increasing. The drive to increase domestic oil production has increased the importance of enhanced recovery by gas injection. These two factors suggest an increased need for compositional reservoir modeling. Conventional reservoir modeling is also likely to remain important for some time. In the past, two separate simulators have been developed and maintained for studying these two classes of problems. This result was dictated by the fact that compositional models have generally required substantially greater computing time than black-oil models. This paper describes a compositional modeling approach paper describes a compositional modeling approach useful for simulating both black-oil and compositional problems. The approach is based on the use of explicit problems. The approach is based on the use of explicit flow coefficients. For compositional modeling, two basic methods of solution have been proposed. We call these methods "Newton-Raphson" and "non-Newton-Raphson" methods. These methods differ in the manner in which a pressure equation is formed. In the Newton-Raphson method the iterative technique specifies how the pressure equation is formed. In the non-Newton-Raphson method, the composition dependence of certain ten-ns is neglected to form the pressure equation. With the non-Newton-Raphson pressure equation. With the non-Newton-Raphson methods, three to eight iterations have been reported per time step. Our experience with the Newton-Raphson method indicates that one to three iterations per tune step normally is sufficient. In the present study a Newton-Raphson iteration sequence is used. The calculations are organized in a manner which is both efficient and for which different fluid property descriptions can be accommodated readily. Early compositional simulators were based on K-values that were expressed as a function of pressure and convergence pressure. A number of potential difficulties are inherent in this approach. More recently, cubic equations of state such as the Redlich-Kwong, or Peng-Robinson appear to be more popular for the correlation Peng-Robinson appear to be more popular for the correlation of fluid properties. SPEJ p. 727

scholarly journals Correction to: Efficient analysis of welding thermal conduction using the Newton–Raphson method, implicit method, and their combination

2020 ◽  
Author(s):  
Zhongyuan Feng ◽  
Ninshu Ma ◽  
Wangnan Li ◽  
Kunio Narasaki ◽  
Fenggui Lu
Keyword(s):  
Thermal Conduction ◽  
Implicit Method ◽  
Newton Raphson ◽  
Raphson Method

A Correction to this paper has been published: https://doi.org/10.1007/s00170-020-06437-w

scholarly journals Fractional Newton–Raphson Method Accelerated with Aitken’s Method

Axioms ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 47
Author(s):  
A. Torres-Hernandez ◽  
F. Brambila-Paz ◽  
U. Iturrarán-Viveros ◽  
R. Caballero-Cruz
Keyword(s):  
Fractional Derivative ◽  
Iterative Methods ◽  
Fractional Integral ◽  
Order Of Convergence ◽  
Fractional Operators ◽  
Speed Of Convergence ◽  
Newton Raphson ◽  
Raphson Method

In the following paper, we present a way to accelerate the speed of convergence of the fractional Newton–Raphson (F N–R) method, which seems to have an order of convergence at least linearly for the case in which the order α of the derivative is different from one. A simplified way of constructing the Riemann–Liouville (R–L) fractional operators, fractional integral and fractional derivative is presented along with examples of its application on different functions. Furthermore, an introduction to Aitken’s method is made and it is explained why it has the ability to accelerate the convergence of the iterative methods, in order to finally present the results that were obtained when implementing Aitken’s method in the F N–R method, where it is shown that F N–R with Aitken’s method converges faster than the simple F N–R.

scholarly journals Comparing Different Approaches for Solving Large Scale Power-Flow Problems With the Newton-Raphson Method

IEEE Access ◽  
2021 ◽  
Vol 9 ◽  
pp. 56604-56615
Author(s):  
Manolo D'orto ◽  
Svante Sjoblom ◽  
Lung Sheng Chien ◽  
Lilit Axner ◽  
Jing Gong
Keyword(s):  
Power Flow ◽  
Large Scale ◽  
Flow Problems ◽  
Newton Raphson ◽  
Raphson Method
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