A Method for Computing Initial Approximations for a 3-parameter Exponential Function

Kikawa, C.R.; Shatalov, M. Y.; Kloppers, P. Hendrik

doi:10.9734/psij/2015/16503

Cited by 4 publications

(1 citation statement)

References 7 publications

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“…The unknown regression parameters are then estimated using the ordinary least squares (OLS) methods. The employed frame-work was first proposed by [19] and has been used in the estimation of exponential functions; see [23]. We propose a version of this frame-work and use it to estimate the Gaussian distribution parameters.…”

Section: Methodsmentioning

confidence: 99%

On the Estimation of a Univariate Gaussian Distribution: A Comparative Approach

Kikawa¹,

Shatalov²,

Kloppers³

et al. 2015

OJS

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Estimation of the unknown mean, μ and variance, σ 2 of a univariate Gaussian distribution () N 2 , µ σ given a single study variable x is considered. We propose an approach that does not require initialization of the sufficient unknown distribution parameters. The approach is motivated by linearizing the Gaussian distribution through differential techniques, and estimating, μ and σ 2 as regression coefficients using the ordinary least squares method. Two simulated datasets on hereditary traits and morphometric analysis of housefly strains are used to evaluate the proposed method (PM), the maximum likelihood estimation (MLE), and the method of moments (MM). The methods are evaluated by re-estimating the required Gaussian parameters on both large and small samples. The root mean squared error (RMSE), mean error (ME), and the standard deviation (SD) are used to assess the accuracy of the PM and MLE; confidence intervals (CIs) are also constructed for the ME estimate. The PM compares well with both the MLE and MM approaches as they all produce estimates whose errors have good asymptotic properties, also small CIs are observed for the ME using the PM and MLE. The PM can be used symbiotically with the MLE to provide initial approximations at the expectation maximization step.

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Section: Methodsmentioning

confidence: 99%

On the Estimation of a Univariate Gaussian Distribution: A Comparative Approach

Kikawa¹,

Shatalov²,

Kloppers³

et al. 2015

OJS

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Optimal interatomic potentials using modified method of least squares: Optimal form of interatomic potentials

Surulere,

Shatalov,

Olayiwola

2023

Open Physics

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The problem of optimization of interatomic potentials is formulated and solved by means of generalization of the Morse, Kaxiras–Pandey, and Rydberg potentials. The interatomic potentials are treated as solutions of some second-order ordinary differential equations which will be classified and analyzed. The most appropriate analytic form of the understudied potentials will be proposed based on a one-dimensional search for the parameter, γ \gamma , which is the power of the interatomic distance, r r . The optimal analytic form will also be proposed for metals such as gold, copper, aluminium, titanium, and the silver–copper alloy. The method of least squares will be used to estimate the potential parameters. Phenomenological potentials such as the classical Rydberg, classical Morse, generalized Morse, Kaxiras–Pandey, and classical Lennard–Jones will be studied, and new potentials based on the combination of some of the aforementioned potentials will also be proposed. Metrics such as the goal function values, will be used to identify which optimal value of the parameter, γ \gamma , is most appropriate to introduce into the preferred interatomic potential for interaction between atoms.

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A Comparative Investigation of Complex Conjugate Eigenvalues of Generalized Morse and Classical Lennard-Jones Potential for Metal Atoms

et al. 2020

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Background: The knowledge of parameter estimation for interatomic potentials is useful in the computation of the vibrational structure of van der Waals molecules. Methods: On the estimation of the Generalized Morse and Classical Lennard-Jones potential energy functions, complex conjugates eigenvalues may be obtained. Different approaches can be used to solve this resulting problem. A method that uses the objective least squares function method to estimate parameters of the interatomic potentials is employed. Results: Numerical simulation of the systems using metal atoms yields complex conjugates eigenvalues at some initial point. Conclusion: Other approaches of solving the complex conjugates eigenvalues problem are discussed comprehensively.

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A Method for Computing Initial Approximations for a 3-parameter Exponential Function

Cited by 4 publications

References 7 publications

On the Estimation of a Univariate Gaussian Distribution: A Comparative Approach

On the Estimation of a Univariate Gaussian Distribution: A Comparative Approach

Optimal interatomic potentials using modified method of least squares: Optimal form of interatomic potentials

A Comparative Investigation of Complex Conjugate Eigenvalues of Generalized Morse and Classical Lennard-Jones Potential for Metal Atoms

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