Quadratic error of an unbiased estimate of the probability density of sufficient statistics of the normal distribution

1988 ◽  
Vol 41 (1) ◽  
pp. 805-809 ◽  
Author(s):  
R. A. Abdulev ◽  
L. G. Simonova
Keyword(s):  
Normal Distribution ◽  
Probability Density ◽  
Unbiased Estimate ◽  
Quadratic Error ◽  
Sufficient Statistics

Sufficient statistics and minimum variance estimates

1949 ◽  
Vol 45 (2) ◽  
pp. 213-218 ◽  
Author(s):  
C. Radhakrishna Rao
Keyword(s):  
Probability Density ◽  
Unbiased Estimate ◽  
Minimum Variance ◽  
Sufficient Statistics ◽  
Image Position ◽  
Variance Estimates

Let the probability density of observations be denoted by φ(x | θ), where x stands for the variables and θ for the parameters. A function t of the observations is called an unbiased estimate of the function ψ(θ) of the parameters ifwhere dx stands for the product of differentials.

Understanding single-slit experiments on the basis of Galton board experiments

2021 ◽  
Vol 34 (3) ◽  
pp. 265-267
Author(s):  
Chong Wang
Keyword(s):  
Normal Distribution ◽  
Probability Density ◽  
Least Action ◽  
Neighboring Particle ◽  
Large Particles ◽  
Pass Through ◽  
Particle Group ◽  
Slit Experiment

In a single-slit experiment conducted for microparticles, the well-aligned rough structure of the slit wall can be viewed as a Galton board. Thus, when microparticles pass through the single slit, both the particle probability density (PPD) and particle direction of motion have a normal distribution. Therefore, when the distance between the slit and the receiving film becomes large, particles with different directions of motion will separate into different particle groups. By the nature of a normal distribution, the PPD for any particle group should also be normal-distributed. Obviously, between any two neighboring particle groups, there should be a valley in the PPD and thus the particle groups are observed as discrete fringes. All phenomena observed in the single-slit experiment can be explained reasonably well from the above viewpoint. In particular, analysis shows that the PPD can be described by the square of the modulus of the average least action of particles at a given location.

A novel mobile agent-based distributed evidential expectation maximization algorithm for uncertain sensor networks

2020 ◽  
pp. 014233122096958
Author(s):  
Mohiyeddin Mozaffari ◽  
Behrouz Safarinejadian ◽  
Mokhtar Shasadeghi
Keyword(s):  
Sensor Networks ◽  
Probability Density Function ◽  
Probability Density ◽  
Convergence Analysis ◽  
Density Function ◽  
Mobile Agent ◽  
Expectation Maximization ◽  
Convergence Criterion ◽  
Sufficient Statistics ◽  
Agent Based

In this paper, a novel mobile agent-based distributed evidential expectation maximization (MADEEM) algorithm is presented for sensor networks. The proposed algorithm is used for probability density function estimation and data clustering in the presence of uncertainties in sensor measurements. It is assumed that the sensor measurements are statistically modeled by a common Gaussian mixture model. The proposed algorithm maximizes a new generalized likelihood criterion in an iterative and distributed manner. For this purpose, mobile agents compute some local sufficient statistics by using local measurements of each sensor node. After the local computations, the global sufficient statistics are updated. At the end of iterations, the parameters of the probability density function are updated by using the global sufficient statistics. The mentioned process will be continued until the convergence criterion is satisfied. Convergence analysis of the proposed algorithm is also presented in this paper. After the convergence analysis, the simulation results show the promising performance of the proposed algorithm. Finally, the last part of the paper is devoted to the concluding remarks.

Research Lifetime of Oil Film Bearing on High-Speed Wire Mill Based on Reliability Analysis

2011 ◽  
Vol 402 ◽  
pp. 358-361
Author(s):  
Shi Bo Jiang ◽  
Jie Liu ◽  
Jun Lin Ten
Keyword(s):  
Probability Density Function ◽  
Normal Distribution ◽  
Probability Density ◽  
Reliability Analysis ◽  
Density Function ◽  
High Speed ◽  
Statistical Data ◽  
Wire Mill ◽  
Oil Film ◽  
Wear Life

Based on the prerequisite that oil- film Bearing wear extent obey normal distribution，This paper come to reliability account formula through wear extent probability density function，deduce the wear life account formula of oil- film Bearing. based on detailed statistical data, calculate the lifetime of oil film bearing in High Speed Wire Rod finishing block, and forward the method how to raise the lifetime of oil- film Bearing.

Inverse probability and sufficient statistics

1949 ◽  
Vol 45 (2) ◽  
pp. 225-229
Author(s):  
V. S. Huzurbazar
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Statistical Estimation ◽  
Sufficient Statistics ◽  
Inverse Probability ◽  
General Terms ◽  
Fiducial Probability ◽  
Posterior Probability Density ◽  
Posterior Probability Density Function

1. It is an interesting fact that in many problems of statistical estimation the results given by the theory of inverse probability (as modified by Jeffreys) are indistinguishable from those given by the methods of ‘fiducial probability’ or ‘confidence intervals’. The derivation of some of the important inverse distributions by Jeffreys(3) arouses one's curiosity. It seems that when this agreement is noticed there are usually sufficient statistics for parameters in the distribution. The object of this note is to throw some light, in general terms, on the similarity in form between the posterior probability-density function of the parameters and the probability-density function of the distribution when it admits sufficient statistics. For convenience the following notation in Jeffreys's probability logic is used below:P(q | p) is the probability of a proposition q on data p.

scholarly journals Probability Density Functions for Prediction Using Normal and Exponential Distribution

2021 ◽  
pp. 40-52
Author(s):  
Kunio Takezawa
Keyword(s):  
Probability Density Function ◽  
Normal Distribution ◽  
Probability Density ◽  
Density Function ◽  
Exponential Distribution ◽  
Predictive Ability ◽  
Probability Density Functions ◽  
Density Functions ◽  
Specific Distribution ◽  
Using Data

When data are found to be realizations of a specific distribution, constructing the probability density function based on this distribution may not lead to the best prediction result. In this study, numerical simulations are conducted using data that follow a normal distribution, and we examine whether probability density functions that have shapes different from that of the normal distribution can yield larger log-likelihoods than the normal distribution in the light of future data. The results indicate that fitting realizations of the normal distribution to a different probability density function produces better results from the perspective of predictive ability. Similarly, a set of simulations using the exponential distribution shows that better predictions are obtained when the corresponding realizations are fitted to a probability density function that is slightly different from the exponential distribution. These observations demonstrate that when the form of the probability density function that generates the data is known, the use of another form of the probability density function may achieve more desirable results from the standpoint of prediction.

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