Mishra, Vishnu Narayan, Patel, Prashantkumar, and Mishra, Lakshmi Narayan
Subjects
APPROXIMATION theory, MATHEMATICAL functions, MATHEMATICAL models, INTEGRAL equations, MATHEMATICS
Abstract
In the present paper, we discuss the approximation properties of Durrmeyer-Stancu type variant of Jain operators with the modified forms of the Beta basis functions. We establish some direct results, which include the asymptotic formula, the error estimation in terms of the modulus of continuity and weighted approximation. Also, we construct a King modification of these operators which preserves the test functions e0 and e1. [ABSTRACT FROM AUTHOR]
In this paper, we study the uniform approximation of functions by Meyer-König and Zeller operators of max-product type in some weighted spaces. We estimate the rate of approximation in terms of a suitable modulus of continuity. [ABSTRACT FROM AUTHOR]
RAYLEIGH model, MONTE Carlo method, APPROXIMATION theory, NUMERICAL analysis, MATHEMATICS
Abstract
In this paper, we consider the problem of estimating the scale parameter of the inverse Rayleigh distribution based on general progressively Type-II censored samples and progressively Type-II censored samples. The pivotal quantity method is used to derive the estimator of the scale parameter. Besides, considering that the maximum likelihood estimator is tough to obtain for this distribution, we derive an explicit estimator of the scale parameter by approximating the likelihood equation with Taylor expansion. The interval estimation is also studied based on pivotal inference. Then we conduct Monte Carlo simulations and compare the performance of different estimators. We demonstrate that the pivotal inference is simpler and more effective. The further application of the pivotal quantity method is also discussed theoretically. Finally, two real data sets are analyzed using our methods. [ABSTRACT FROM AUTHOR]