Nonparametric Bayes Estimation of Distribution Functions and the Study of Probability Density Estimates.

1980 ◽  
Author(s):  
W. J. Padgett ◽  
R. L. Taylor ◽  
L. J. Wei
Keyword(s):  
Probability Density ◽  
Distribution Functions ◽  
Bayes Estimation ◽  
Nonparametric Bayes ◽  
Density Estimates ◽  
Estimation Of Distribution

Nonparametric Bayes estimation in repair models

2009 ◽  
Vol 139 (5) ◽  
pp. 1722-1733 ◽  
Author(s):  
Jayaram Sethuraman ◽  
Myles Hollander
Keyword(s):  
Bayes Estimation ◽  
Nonparametric Bayes ◽  
Repair Models

scholarly journals Estimating a Distribution Function at the Boundary

2020 ◽  
Vol 49 (1) ◽  
pp. 1-23
Author(s):  
Shunpu Zhang ◽  
Zhong Li ◽  
Zhiying Zhang
Keyword(s):  
Distribution Function ◽  
Kernel Estimation ◽  
Kernel Estimator ◽  
Distribution Functions ◽  
Practical Application ◽  
Real World Applications ◽  
Distribution Kernel ◽  
Estimation Of Distribution ◽  
Simulation Results ◽  
Boundary Correction

Estimation of distribution functions has many real-world applications. We study kernel estimation of a distribution function when the density function has compact support. We show that, for densities taking value zero at the endpoints of the support, the kernel distribution estimator does not need boundary correction. Otherwise, boundary correction is necessary. In this paper, we propose a boundary distribution kernel estimator which is free of boundary problem and provides non-negative and non-decreasing distribution estimates between zero and one. Extensive simulation results show that boundary distribution kernel estimator provides better distribution estimates than the existing boundary correction methods. For practical application of the proposed methods, a data-dependent method for choosing the bandwidth is also proposed.

scholarly journals Nonparametric bayes estimation of the reliability function of a coherent system

2021 ◽  
Vol 54 (2) ◽  
pp. 183-206
Author(s):  
AKM Fazlur Rahman ◽  
Edsel A. Pena
Keyword(s):  
Structure Function ◽  
Dirichlet Process ◽  
Synthetic Data ◽  
Reliability Function ◽  
Bayes Estimation ◽  
Coherent System ◽  
System Failure ◽  
Nonparametric Bayes ◽  
Lifetime Distributions ◽  
Safety Considerations

Complex coherent systems are the engines driving forward our technological world. A coherent system is composed of components, which could be modules or sub-systems, that interact with each other according to some structure function. For purposes of maintenance and safety considerations, it is of critical importance to gain knowledge of the distribution of the system lifetime, with this distribution being a function of the distributions of the components lifetimes. Since the monitoring of a system ceases upon system failure, at system failure some components will be failed, while others, depending on the structure function, will still be functioning with their lifetimes right-censored by the system lifetime. This paper deals with the estimation of the system lifetime distribution. The inferential framework is nonparametric Bayesian, with partition-based Dirichlet processes (PBDP) assigned as priors on the components lifetime distributions. PBDP are more general than the usual Dirichlet process (DP) priors and are particularly suited as priors in settings with censored data. The resulting estimator of the system life distribution, which is a function of the nonparametric Bayes estimators of the components lifetime distributions, is compared in terms of bias and variance with a product-limit type estimator proposed by Doss, et. al. (Ann. Statist., 1989), which can be obtained as a limit of the proposed estimator. These comparisons, which are facilitated through computer simulations, demonstrate that the proposed estimator possesses some robustness. The proposed estimator is illustrated using a synthetic data for a parallel system with five components.

scholarly journals On Estimation of Distribution Function Using Dual Auxiliary Information under Nonresponse Using Simple Random Sampling

2020 ◽  
Vol 2020 ◽  
pp. 1-13 ◽  
Author(s):  
Saddam Hussain ◽  
Mi Zichuan ◽  
Sardar Hussain ◽  
Anum Iftikhar ◽  
Muhammad Asif ◽  
...  
Keyword(s):  
Random Sampling ◽  
Mean Squared Error ◽  
Population Distribution ◽  
Auxiliary Information ◽  
Simple Random Sampling ◽  
Auxiliary Variable ◽  
Distribution Functions ◽  
Supplementary Information ◽  
Auxiliary Variables ◽  
Estimation Of Distribution

In this paper, we proposed two new families of estimators using the supplementary information on the auxiliary variable and exponential function for the population distribution functions in case of nonresponse under simple random sampling. The estimations are done in two nonresponse scenarios. These are nonresponse on study variable and nonresponse on both study and auxiliary variables. As we have highlighted above that two new families of estimators are proposed, in the first family, the mean was used, while in the second family, ranks were used as auxiliary variables. Expression of biases and mean squared error of the proposed and existing estimators are obtained up to the first order of approximation. The performances of the proposed and existing estimators are compared theoretically. On these theoretical comparisons, we demonstrate that the proposed families of estimators are better in performance than the existing estimators available in the literature, under the obtained conditions. Furthermore, these theoretical findings are braced numerically by an empirical study offering the proposed relative efficiencies of the proposed families of estimators.

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