Parameter estimation of Gumbel distribution using Quasi-Newton Broyden Fletcher Goldfarb Shanno (BFGS) method and its application on data of daily precipitation in Purworejo regency

The BFGS method is one of the most efficient quasi-Newton methods for solving small- and medium-size unconstrained optimization problems. For the sake of exploring its more interesting properties, a modified two-parameter scaled BFGS method is stated in this paper. The intention of the modified scaled BFGS method is to improve the eigenvalues structure of the BFGS update. In this method, the first two terms and the last term of the standard BFGS update formula are scaled with two different positive parameters, and the new value of yk is given. Meanwhile, Yuan-Wei-Lu line search is also proposed. Under the mentioned line search, the modified two-parameter scaled BFGS method is globally convergent for nonconvex functions. The extensive numerical experiments show that this form of the scaled BFGS method outperforms the standard BFGS method or some similar scaled methods.

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Time-variant parameter estimation of a nonlinear system using a quasi-newton method

IFAC Proceedings Volumes ◽

10.1016/s1474-6670(17)56653-7 ◽

1999 ◽

Vol 32 (2) ◽

pp. 3826-3831

Author(s):

Wenhuan Yu ◽

Dongyi Liu

Keyword(s):

Parameter Estimation ◽

Nonlinear System ◽

Newton Method ◽

Quasi Newton

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Parameter Estimation with Least-Squares Method for the Inverse Gaussian distribution Model Using Simplex and Quasi-Newton Optimization Methods

Journal of Applied Mathematics and Computation ◽

10.26855/jamc.2018.10.002 ◽

2018 ◽

Vol 2 (11) ◽

Author(s):

Khizar Hayat Khan ◽

Keyword(s):

Parameter Estimation ◽

Least Squares ◽

Gaussian Distribution ◽

Least Squares Method ◽

Optimization Methods ◽

Inverse Gaussian Distribution ◽

Distribution Model ◽

Inverse Gaussian ◽

Quasi Newton ◽

Gaussian Distribution Model

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Quasi-Newton methods for parameter estimation in functional differential equations

10.1109/cdc.1988.194422 ◽

2003 ◽

Cited By ~ 3

Author(s):

D.W. Brewer

Keyword(s):

Parameter Estimation ◽

Differential Equations ◽

Functional Differential Equations ◽

Newton Methods ◽

Functional Differential ◽

Quasi Newton

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Maximum-Likelihood Parameter Estimation of a Generalized Gumbel Distribution

10.21236/ada207994 ◽

1989 ◽

Author(s):

Jr Hall ◽

Lehnigk Charles E. ◽

Viswanath Siegfried H. ◽

Guttalu R.

Keyword(s):

Parameter Estimation ◽

Maximum Likelihood ◽

Gumbel Distribution

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Parameter estimation of a two-layer soil model using Quasi-Newton methods

2018 Simposio Brasileiro de Sistemas Eletricos (SBSE) ◽

10.1109/sbse.2018.8395665 ◽

2018 ◽

Author(s):

Raphael Batista ◽

Marcos Roberto de Araujo ◽

Rodney Rezende Saldanha

Keyword(s):

Parameter Estimation ◽

Newton Methods ◽

Soil Model ◽

Quasi Newton

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Quasi-Newton Stochastic Optimization Algorithm for Parameter Estimation of a Stochastic Model of the Budding Yeast Cell Cycle

IEEE/ACM Transactions on Computational Biology and Bioinformatics ◽

10.1109/tcbb.2017.2773083 ◽

2019 ◽

Vol 16 (1) ◽

pp. 301-311 ◽

Cited By ~ 4

Author(s):

Minghan Chen ◽

Brandon D. Amos ◽

Layne T. Watson ◽

John J. Tyson ◽

Young Cao ◽

...

Keyword(s):

Cell Cycle ◽

Parameter Estimation ◽

Stochastic Model ◽

Stochastic Optimization ◽

Yeast Cell ◽

Optimization Algorithm ◽

Budding Yeast ◽

Stochastic Optimization Algorithm ◽

Quasi Newton ◽

Budding Yeast Cell Cycle

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Random Scaling of Quasi-Newton BFGS Method to Improve the O(N2)-operation Approximation of Covariance-matrix Inverse in Gaussian Process

2007 IEEE 22nd International Symposium on Intelligent Control ◽

10.1109/isic.2007.4450928 ◽

2007 ◽

Author(s):

Yunong Zhang ◽

W. E. Leithead ◽

D. J. Leith

Keyword(s):

Gaussian Process ◽

Covariance Matrix ◽

Bfgs Method ◽

Matrix Inverse ◽

Quasi Newton

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A Sparse Quasi-Newton Method Based on Automatic Differentiation for Solving Unconstrained Optimization Problems

Symmetry ◽

10.3390/sym13112093 ◽

2021 ◽

Vol 13 (11) ◽

pp. 2093

Author(s):

Huiping Cao ◽

Xiaomin An

Keyword(s):

Unconstrained Optimization ◽

Newton Method ◽

Automatic Differentiation ◽

Optimization Problems ◽

Symmetric Matrix ◽

Matrix Completion ◽

Bfgs Method ◽

Limited Memory ◽

Unconstrained Optimization Problems ◽

Quasi Newton

In our paper, we introduce a sparse and symmetric matrix completion quasi-Newton model using automatic differentiation, for solving unconstrained optimization problems where the sparse structure of the Hessian is available. The proposed method is a kind of matrix completion quasi-Newton method and has some nice properties. Moreover, the presented method keeps the sparsity of the Hessian exactly and satisfies the quasi-Newton equation approximately. Under the usual assumptions, local and superlinear convergence are established. We tested the performance of the method, showing that the new method is effective and superior to matrix completion quasi-Newton updating with the Broyden–Fletcher–Goldfarb–Shanno (BFGS) method and the limited-memory BFGS method.

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Estimating extreme dry spell risk in Ichkeul Lake Basin (Northern Tunisia): a comparative analysis of annual maxima series with a Gumbel distribution

Proceedings of the International Association of Hydrological Sciences ◽

10.5194/piahs-383-241-2020 ◽

2020 ◽

Vol 383 ◽

pp. 241-248

Author(s):

Majid Mathlouthi ◽

Fethi Lebdi

Keyword(s):

Daily Precipitation ◽

Gumbel Distribution ◽

Lake Basin ◽

Climatic Variable ◽

Rainfall Events ◽

Northern Tunisia ◽

Dry Spell ◽

Ichkeul Lake ◽

Threshold Amount ◽

Annual Maximum Series

Abstract. This paper analyses a 42 year time series of daily precipitation in Ichkeul Lake Basin (northern Tunisia) in order to predict extreme dry-spell risk. Dry events are considered as a sequence of dry days separated by rainfall events from each other. Thus the rainy season is defined as a series of rainfall and subsequent dry events. Rainfall events are defined as the uninterrupted sequence of rainy days, when at last on one day more than a threshold amount of rainfall has been observed. A comparison of observed and estimated maximum dry events (42 year return period) showed that Gumbel distribution fitted to annual maximum series gives better results than the exponential (E) distribution combined with partial duration series (PDS). Indeed, the classical Gumbel approach slightly underestimated the empirical duration of dry events. The AMS–G approach was successfully applied in the study of extreme hydro-climatic variable values. The results reported here could be applied in estimating climatic drought risks in other geographical areas.

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