APPLICATIONS OF TWO NON-CENTRAL HYPERGEOMETRIC DISTRIBUTIONS OF BIASED SAMPLING STATISTICAL MODELS

2021 ◽  
Vol 4 (4) ◽  
pp. 415-424
Author(s):  
A. A. Issa ◽  
K. O. Adetunji ◽  
T. Alanamu ◽  
E. J. Adefila ◽  
K. A. Muhammed
Keyword(s):  
Statistical Models ◽  
Research Work ◽  
Hypergeometric Distribution ◽  
Biased Sampling ◽  
Inversion Method ◽  
Urn Model ◽  
Fisher Distribution ◽  
Direct Inversion ◽  
Mean And Variance ◽  
Hypergeometric Distributions

Statistical models of biased sampling of two non-central hypergeometric distributions Wallenius' and Fisher's distribution has been extensively used in the literature, however, not many of the logic of hypergeometric distribution have been investigated by different techniques. This research work examined the procedure of the two non-central hypergeometric distributions and investigates the statistical properties which includes the mean and variance that were obtained. The parameters of the distribution were estimated using the direct inversion method of hyper simulation of biased urn model in the environment of R statistical software, with varying odd ratios (w) and group sizes (mi). It was discovered that the two non - central hypergeometric are approximately equal in mean, variance and coefficient of variation and differ as odds ratios (w) becomes higher and differ from the central hypergeometric distribution with ω = 1. Furthermore, in univariate situation we observed that Fisher distribution at (ω = 0.2, 0.5, 0.7, 0.9) is more consistent than Wallenius distribution, although central hypergeometric is more consistent than any of them. Also, in multinomial situation, it was observed that Fisher distribution is more consistent at (ω = 0.2, 0.5), Wallenius distribution at (ω = 0.7, 0.9) and central hypergeometric at (ω = 0.2)    

A Comparative Study of Direct and Iterative Inversion Approaches to Determine the Spatial Shear Modulus Distribution of Elastic Solids

2019 ◽  
Vol 11 (10) ◽  
pp. 1950097 ◽  
Author(s):  
Zhi Liu ◽  
Yanli Sun ◽  
Jianwei Deng ◽  
Dongmei Zhao ◽  
Yue Mei ◽  
...  
Keyword(s):  
Shear Modulus ◽  
Comparative Study ◽  
Inversion Method ◽  
Noise Levels ◽  
Elastic Solids ◽  
Direct Inversion ◽  
Advantages And Disadvantages ◽  
Iterative Inversion ◽  
Very High ◽  
Selection Of

This paper presents a comparative study of two typical inverse algorithms, i.e., direct and iterative inversion methods, to reconstruct the shear modulus distribution of linearly elastic solids. Both approaches are based on the finite element framework and compared utilizing both the simulated and experimental data. The reconstruction results demonstrate that both approaches are capable of identifying the nonhomogeneous shear modulus distribution of solids well. It can also be found that the direct inversion method is much faster than the iterative inversion method, whereas the iterative inversion method is capable of yielding better shear modulus ratio between the stiff inclusion and the soft background even with very high noise levels. Afterwards, a thorough comparison on the advantages and disadvantages of these two approaches has been performed. This comparative study provides useful information on the selection of the proper inverse scheme in estimating nonhomogeneous elastic property distribution of soft solids nondestructively.

A Quantum Approach Using Stochastic Simulation and Schrodinger with Multi-Layer Learning for Finding Features from Dataset

2020 ◽  
Vol 17 (6) ◽  
pp. 2514-2518
Author(s):  
Kapil Prashar ◽  
Rajneesh Talwar ◽  
Chander Kant
Keyword(s):  
Quantum Computing ◽  
Mathematical Models ◽  
Stochastic Simulation ◽  
Statistical Models ◽  
State Of The Art ◽  
Research Work ◽  
Current Approach ◽  
Suggested Model ◽  
Quantum Approach ◽  
Multiple State

Quantum computing relies on the quantity of the mechanical phenomenon, such as interference and overlap. It aims to solve issues which are not realistically possible on computers. The research work introduces the new quantum-based model from a provided dataset for forecasting the infection. This technique is beneficial in describing the association among different statistical models. Our study has resulted in highest precision than ever applied technique, which was differentiated and calculated from the defined dataset and results. Such suggested strategies were evaluated and reviewed against multiple state-of-the-art methods to demonstrate efficacy. The qualitative and graphical results are provided for the verification of the current approach. The suggested model is more robust than existing mathematical models due to the findings.

Perturbation method of analysis of crystal truncation rod data

2005 ◽  
Vol 38 (2) ◽  
pp. 299-305 ◽  
Author(s):  
I. K. Robinson ◽  
M. Tabuchi ◽  
S. Hisadome ◽  
R. Oga ◽  
Y. Takeda
Keyword(s):  
Perturbation Method ◽  
Diffraction Pattern ◽  
Model Calculation ◽  
Lattice Strain ◽  
Inversion Method ◽  
Layered Semiconductor ◽  
Direct Inversion ◽  
Crystal Truncation Rod ◽  
Semiconductor Heterostructure ◽  
Perturbation Approximation

A new method of direct inversion of crystal truncation rod (CTR) data is demonstrated for the analysis of layered semiconductor heterostructure materials. This method is based on approximations that are valid when the electron density deviations and lattice strain are small in the regions of the sample close to a well defined surface. The CTR diffraction pattern can then be regarded as a perturbation with respect to that of an ideal surface. The direct inversion method is shown to work for the analysis of a series of InP/GaInAs/InP heterostructures. The ability to recover strain information is demonstrated with a model calculation. The beginning of breakdown of the perturbation approximation is seen and explained in both cases.

Optimizing Sampling Design for Herring Spawn Surveys in the Strait of Georgia, B.C.

1985 ◽  
Vol 42 (11) ◽  
pp. 1806-1814 ◽  
Author(s):  
J. F. Schweigert ◽  
C. W. Haegele ◽  
M. Stocker
Keyword(s):  
Sampling Design ◽  
Systematic Sampling ◽  
Biased Sampling ◽  
Ratio Estimator ◽  
Two Stage ◽  
Stage Design ◽  
Strait Of Georgia ◽  
Egg Density ◽  
Mean And Variance ◽  
The Mean

Three estimators for two-stage sampling designs assuming unequal sized primaries (transects) were compared. The ratio estimator was found to provide the most consistent estimates of the mean and variance and so was used for estimating optimal sample design. Preliminary results from some biased sampling during 1976 and 1978 provided guidelines for the 1981 study designed to derive an optimal sampling design. Inconsistent results from the two areas surveyed during 1981 prevented general conclusions, but a corroborating resurvey of one area in 1983 suggested that a sampling intensity of five samples per 100 m of transect and transects every 250–400 m along the length of the spawn should result in estimates of the mean egg density with a standard error no greater than 25%. Systematic sampling is logistically preferable to random sampling and can be incorporated into the two-stage design described herein which should be used in future spawn surveys designed to estimate spawning escapement.

Forward Scattering and Volterra Renormalization for Acoustic Wavefield Propagation in Vertically Varying Media

2016 ◽  
Vol 20 (2) ◽  
pp. 353-373 ◽  
Author(s):  
Jie Yao ◽  
Anne-Cécile Lesage ◽  
Fazle Hussain ◽  
Donald J. Kouri
Keyword(s):  
Scattering Theory ◽  
Incidence Angle ◽  
Neumann Series ◽  
Forward Scattering ◽  
Acoustic Medium ◽  
Inversion Method ◽  
Angle Of Incidence ◽  
Direct Inversion ◽  
Reference Medium ◽  
Density Perturbations

AbstractWe extend the full wavefield modeling with forward scattering theory and Volterra Renormalization to a vertically varying two-parameter (velocity and density) acoustic medium. The forward scattering series, derived by applying Born-Neumann iterative procedure to the Lippmann-Schwinger equation (LSE), is a well known tool for modeling and imaging. However, it has limited convergence properties depending on the strength of contrast between the actual and reference medium or the angle of incidence of a plane wave component. Here, we introduce the Volterra renormalization technique to the LSE. The renormalized LSE and related Neumann series are absolutely convergent for any strength of perturbation and any incidence angle. The renormalized LSE can further be separated into two sub-Volterra type integral equations, which are then solved noniteratively. We apply the approach to velocity-only, density-only, and both velocity and density perturbations. We demonstrate that this Volterra Renormalization modeling is a promising and efficient method. In addition, it can also provide insight for developing a scattering theory-based direct inversion method.

Limit theorems for general size distributions

1981 ◽  
Vol 18 (1) ◽  
pp. 139-147 ◽  
Author(s):  
Wen-Chen Chen
Keyword(s):  
Limit Theorems ◽  
Local Limit Theorem ◽  
Random Variables ◽  
Local Limit ◽  
Negative Integer ◽  
Urn Model ◽  
Special Cases ◽  
Mean And Variance ◽  
Bose Einstein ◽  
General Size

Let X1, X2, · ··, Xn, · ·· be independent and identically distributed non-negative integer-valued random variables with finite mean and variance. For any positive integer n and m we consider the random vector i.e., L has the same distribution as the conditional distribution of (X1, · ··, Xm) given the condition It is easy to see that our model includes the classical urn model, the Bose–Einstein urn model and the Pólya urn model as special cases. For any non-negative integer s define G(s) = the number of Li′s such that Li = s, and U = the number of Li′s such that Li is an even number; in this paper we study the asymptotic behaviour of the random variables considered above. Some central limit theorems and a multinormal local limit theorem are proved.

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