scholarly journals A new class of estimators for the shape parameter of a Pareto model

2020 ◽  
Author(s):  
Ayana Mateus ◽  
Frederico Caeiro
Keyword(s):  
Shape Parameter ◽  
New Class ◽  
Pareto Model ◽  
Class Of Estimators

scholarly journals A New Class of Estimators Based on a General Relative Loss Function

Mathematics ◽  
2021 ◽  
Vol 9 (10) ◽  
pp. 1138
Author(s):  
Tao Hu ◽  
Baosheng Liang
Keyword(s):  
Loss Function ◽  
Asymptotically Normal ◽  
New Class ◽  
Statistical Inferences ◽  
Relative Loss ◽  
Special Cases ◽  
Class Of Estimators ◽  
Box Cox Transformation ◽  
Loss Estimator ◽  
Prostate Cancer Study

Motivated by the relative loss estimator of the median, we propose a new class of estimators for linear quantile models using a general relative loss function defined by the Box–Cox transformation function. The proposed method is very flexible. It includes a traditional quantile regression and median regression under the relative loss as special cases. Compared to the traditional linear quantile estimator, the proposed estimator has smaller variance and hence is more efficient in making statistical inferences. We show that, in theory, the proposed estimator is consistent and asymptotically normal under appropriate conditions. Extensive simulation studies were conducted, demonstrating good performance of the proposed method. An application of the proposed method in a prostate cancer study is provided.

scholarly journals Restructured class of estimators for population mean using an auxiliary variable under simple random sampling scheme

2020 ◽  
Vol 16 (1) ◽  
pp. 61-75
Author(s):  
S. Baghel ◽  
S. K. Yadav
Keyword(s):  
Random Sampling ◽  
Simple Random Sampling ◽  
Auxiliary Variable ◽  
Sampling Scheme ◽  
Order Of Approximation ◽  
Study Variable ◽  
Population Mean ◽  
First Order ◽  
New Class ◽  
Class Of Estimators

AbstractThe present paper provides a remedy for improved estimation of population mean of a study variable, using the information related to an auxiliary variable in the situations under Simple Random Sampling Scheme. We suggest a new class of estimators of population mean and the Bias and MSE of the class are derived upto the first order of approximation. The least value of the MSE for the suggested class of estimators is also obtained for the optimum value of the characterizing scaler. The MSE has also been compared with the considered existing competing estimators both theoretically and empirically. The theoretical conditions for the increased efficiency of the proposed class, compared to the competing estimators, is verified using a natural population.

A new class of estimators of finite population mean in sample surveys

2016 ◽  
Vol 46 (6) ◽  
pp. 2630-2637
Author(s):  
Housila P. Singh ◽  
Surya Kant Pal ◽  
Ramkrishna S. Solanki
Keyword(s):  
Finite Population ◽  
Sample Surveys ◽  
Population Mean ◽  
New Class ◽  
Class Of Estimators

scholarly journals The Bayesian Inference of Pareto Models Based on Information Geometry

Entropy ◽  
2020 ◽  
Vol 23 (1) ◽  
pp. 45
Author(s):  
Fupeng Sun ◽  
Yueqi Cao ◽  
Shiqiang Zhang ◽  
Huafei Sun
Keyword(s):  
Bayesian Inference ◽  
Loss Function ◽  
Geodesic Distance ◽  
Jeffreys Prior ◽  
Sea Clutter ◽  
New Class ◽  
Parameter Estimations ◽  
Pareto Model ◽  
Bayesian Estimations

Bayesian methods have been rapidly developed due to the important role of explicable causality in practical problems. We develope geometric approaches to Bayesian inference of Pareto models, and give an application to the analysis of sea clutter. For Pareto two-parameter model, we show the non-existence of α-parallel prior in general, hence we adopt Jeffreys prior to deal with the Bayesian inference. Considering geodesic distance as the loss function, an estimation in the sense of minimal mean geodesic distance is obtained. Meanwhile, by involving Al-Bayyati’s loss function we gain a new class of Bayesian estimations. In the simulation, for sea clutter, we adopt Pareto model to acquire various types of parameter estimations and the posterior prediction results. Simulation results show the advantages of the Bayesian estimations proposed and the posterior prediction.

scholarly journals On a New Construction of Generalized q-Bernstein Polynomials Based on Shape Parameter λ

Symmetry ◽  
2021 ◽  
Vol 13 (10) ◽  
pp. 1919
Author(s):  
Qing-Bo Cai ◽  
Reşat Aslan
Keyword(s):  
Error Estimation ◽  
Shape Parameter ◽  
Bernstein Polynomials ◽  
Modulus Of Smoothness ◽  
Basis Functions ◽  
Approximation Properties ◽  
Bernstein Basis ◽  
New Class ◽  
New Construction ◽  
Bernstein Basis Functions

This paper deals with several approximation properties for a new class of q-Bernstein polynomials based on new Bernstein basis functions with shape parameter λ on the symmetric interval [−1,1]. Firstly, we computed some moments and central moments. Then, we constructed a Korovkin-type convergence theorem, bounding the error in terms of the ordinary modulus of smoothness, providing estimates for Lipschitz-type functions. Finally, with the aid of Maple software, we present the comparison of the convergence of these newly constructed polynomials to the certain functions with some graphical illustrations and error estimation tables.

A new class of estimators of a “scale” second order parameter

Extremes ◽  
2007 ◽  
Vol 9 (3-4) ◽  
pp. 193-211 ◽  
Author(s):  
Frederico Caeiro ◽  
M. Ivette Gomes
Keyword(s):  
Order Parameter ◽  
Second Order ◽  
New Class ◽  
Class Of Estimators ◽  
Second Order Parameter
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