scholarly journals Least Squares Estimation for Discretely Observed Stochastic Lotka–Volterra Model Driven by Small α -Stable Noises

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Chao Wei ◽  
Yan Wei ◽  
Yingying Zhou
Keyword(s):  
Population Dynamics ◽  
Least Squares ◽  
Random Environment ◽  
Schwarz Inequality ◽  
Volterra Model ◽  
Markov Inequality ◽  
Numerical Examples ◽  
Model Driven ◽  
Gronwall’S Inequality ◽  
Least Squares Estimators

Stochastic Lotka–Volterra model driven by small α -stable noises is used to describe population dynamics perturbed by random environment. However, parameters in the model are always unknown. The contrast function is given to obtain least squares estimators. The consistency and the rate of convergence of the least squares estimators are proved, and the asymptotic distribution of the estimators are derived by Markov inequality, Cauchy–Schwarz inequality, and Gronwall’s inequality. Some numerical examples are provided to verify the effectiveness of the estimators.

scholarly journals Stochastic Delay Population Dynamics under Regime Switching: Permanence and Asymptotic Estimation

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Zheng Wu ◽  
Hao Huang ◽  
Lianglong Wang
Keyword(s):  
Population Dynamics ◽  
Random Environment ◽  
Regime Switching ◽  
Matrix Method ◽  
Volterra Model ◽  
Function Technique ◽  
Stochastic Delay ◽  
Switching Diffusion ◽  
Asymptotic Estimation ◽  
Diffusion In Random Environment

This paper is concerned with a delay Lotka-Volterra model under regime switching diffusion in random environment. Permanence and asymptotic estimations of solutions are investigated by virtue of V-function technique, M-matrix method, and Chebyshev's inequality. Finally, an example is given to illustrate the main results.

scholarly journals A New Inverted Topp-Leone Distribution: Applications to the COVID-19 Mortality Rate in Two Different Countries

Axioms ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 25 ◽  
Author(s):  
Ehab Almetwally ◽  
Randa Alharbi ◽  
Dalia Alnagar ◽  
Eslam Hafez
Keyword(s):  
Statistical Model ◽  
Least Squares ◽  
Weighted Least Squares ◽  
Likelihood Estimation ◽  
Linear Representation ◽  
Rate Function ◽  
Estimation Methods ◽  
Unknown Parameters ◽  
Least Squares Estimators ◽  
New Distribution

This paper aims to find a statistical model for the COVID-19 spread in the United Kingdom and Canada. We used an efficient and superior model for fitting the COVID 19 mortality rates in these countries by specifying an optimal statistical model. A new lifetime distribution with two-parameter is introduced by a combination of inverted Topp-Leone distribution and modified Kies family to produce the modified Kies inverted Topp-Leone (MKITL) distribution, which covers a lot of application that both the traditional inverted Topp-Leone and the modified Kies provide poor fitting for them. This new distribution has many valuable properties as simple linear representation, hazard rate function, and moment function. We made several methods of estimations as maximum likelihood estimation, least squares estimators, weighted least-squares estimators, maximum product spacing, Crame´r-von Mises estimators, and Anderson-Darling estimators methods are applied to estimate the unknown parameters of MKITL distribution. A numerical result of the Monte Carlo simulation is obtained to assess the use of estimation methods. also, we applied different data sets to the new distribution to assess its performance in modeling data.

scholarly journals An Inverse Problem Involving a Viscous Eikonal Equation with Applications in Electrophysiology

2021 ◽  
Author(s):  
Karl Kunisch ◽  
Philip Trautmann
Keyword(s):  
Inverse Problem ◽  
Least Squares ◽  
Eikonal Equation ◽  
State Equation ◽  
High Accuracy ◽  
Well Posedness ◽  
Numerical Examples ◽  
Marquardt Method ◽  
Math Biol ◽  
Levenberg Marquardt

AbstractIn this work we discuss the reconstruction of cardiac activation instants based on a viscous Eikonal equation from boundary observations. The problem is formulated as a least squares problem and solved by a projected version of the Levenberg–Marquardt method. Moreover, we analyze the well-posedness of the state equation and derive the gradient of the least squares functional with respect to the activation instants. In the numerical examples we also conduct an experiment in which the location of the activation sites and the activation instants are reconstructed jointly based on an adapted version of the shape gradient method from (J. Math. Biol. 79, 2033–2068, 2019). We are able to reconstruct the activation instants as well as the locations of the activations with high accuracy relative to the noise level.

On the admissibility of restricted least squares estimators

1984 ◽  
Vol 13 (9) ◽  
pp. 1135-1146 ◽  
Author(s):  
Ron C. Mittelhammer ◽  
Roger K. Conway
Keyword(s):  
Least Squares ◽  
Least Squares Estimators

Autoregressive processes with infinite variance

1977 ◽  
Vol 14 (02) ◽  
pp. 411-415 ◽  
Author(s):  
E. J. Hannan ◽  
Marek Kanter
Keyword(s):  
Least Squares ◽  
Autoregressive Model ◽  
Infinite Variance ◽  
Autoregressive Processes ◽  
Stable Law ◽  
Least Squares Estimators ◽  
Data Points

The least squares estimators β i(N), j = 1, …, p, from N data points, of the autoregressive constants for a stationary autoregressive model are considered when the disturbances have a distribution attracted to a stable law of index α < 2. It is shown that N1/δ(β i(N) – β) converges almost surely to zero for any δ > α. Some comments are made on alternative definitions of the βi (N).

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