scholarly journals Partial Histogram Bayes Learning Algorithm for Classification Applications

2018 ◽  
Vol 7 (4.11) ◽  
pp. 126
Author(s):  
Haider O. Lawend ◽  
Anuar M. Muad ◽  
Aini Hussain
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Learning Algorithm ◽  
Gaussian Function ◽  
Real Data ◽  
Distribution Functions ◽  
Factors Affecting ◽  
Probability Distribution Functions ◽  
Large Memory

This paper presents a proposed supervised classification technique namely partial histogram Bayes (PHBayes) learning algorithm. Conventional classifier based on Gaussian function has limitation when dealing with different probability distribution functions and requires large memory for large number of instance. Alternatively, histogram based classifiers are flexible for different probability density function. The aims of PHBayes are to handle large number of instances in datasets with lesser memory requirement, and fast in training and testing phases. The PHBayes depends on portion of the observed histogram that is similar to the probability density function. PHBayes was analyzed using synthetic and real data. Several factors affecting classification accuracy were considered. The PHBayes was compared with other established classifiers and demonstrated higher accurate classification, lesser memory even when dealing with large number of instance, and faster in training and testing phases.  

scholarly journals On a new distribution based on the arccosine function

2021 ◽  
Author(s):  
Christophe Chesneau ◽  
Lishamol Tomy ◽  
Jiju Gillariose
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Hazard Rate ◽  
Survival Function ◽  
Real Data ◽  
Cumulative Distribution ◽  
Data Sets ◽  
Power Functions ◽  
New Distribution

AbstractThis note focuses on a new one-parameter unit probability distribution centered around the inverse cosine and power functions. A special case of this distribution has the exact inverse cosine function as a probability density function. To our knowledge, despite obvious mathematical interest, such a probability density function has never been considered in Probability and Statistics. Here, we fill this gap by pointing out the main properties of the proposed distribution, from both the theoretical and practical aspects. Specifically, we provide the analytical form expressions for its cumulative distribution function, survival function, hazard rate function, raw moments and incomplete moments. The asymptotes and shape properties of the probability density and hazard rate functions are described, as well as the skewness and kurtosis properties, revealing the flexible nature of the new distribution. In particular, it appears to be “round mesokurtic” and “left skewed”. With these features in mind, special attention is given to find empirical applications of the new distribution to real data sets. Accordingly, the proposed distribution is compared with the well-known power distribution by means of two real data sets.

scholarly journals A Probability Density Function Generator Based on Deep Learning

2018 ◽  
Author(s):  
Chi-Hua Chen ◽  
Fangying Song ◽  
Feng-Jang Hwang ◽  
Ling Wu
Keyword(s):  
Deep Learning ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Probability Distributions ◽  
Real Data ◽  
Learning Model ◽  
Cumulative Distribution ◽  
Function Generator ◽  
Deep Learning Model

To generate a probability density function (PDF) for fitting probability distributions of real data, this study proposes a deep learning method which consists of two stages: (1) a training stage for estimating the cumulative distribution function (CDF) and (2) a performing stage for predicting the corresponding PDF. The CDFs of common probability distributions can be adopted as activation functions in the hidden layers of the proposed deep learning model for learning actual cumulative probabilities, and the differential equation of trained deep learning model can be used to estimate the PDF. To evaluate the proposed method, numerical experiments with single and mixed distributions are performed. The experimental results show that the values of both CDF and PDF can be precisely estimated by the proposed method.

Event Location with Sparse Data: When Probabilistic Global Search is Important

2020 ◽  
Author(s):  
Stephen Arrowsmith ◽  
Junghyun Park ◽  
Il-Young Che ◽  
Brian Stump ◽  
Gil Averbuch
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Arrival Time ◽  
Real Data ◽  
Parameter Estimates ◽  
Model Parameter ◽  
Event Location ◽  
Seismic Location ◽  
Probability Density Function Pdf

Abstract Locating events with sparse observations is a challenge for which conventional seismic location techniques are not well suited. In particular, Geiger’s method and its variants do not properly capture the full uncertainty in model parameter estimates, which is characterized by the probability density function (PDF). For sparse observations, we show that this PDF can deviate significantly from the ellipsoidal form assumed in conventional methods. Furthermore, we show how combining arrival time and direction-of-arrival constraints—as can be measured by three-component polarization or array methods—can significantly improve the precision, and in some cases reduce bias, in location solutions. This article explores these issues using various types of synthetic and real data (including single-component seismic, three-component seismic, and infrasound).

scholarly journals Qualitative Properties of Randomized Maximum Entropy Estimates of Probability Density Functions

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 548
Author(s):  
Yuri S. Popkov
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Maximum Entropy ◽  
Density Function ◽  
Lagrange Multipliers ◽  
Real Data ◽  
Model Parameters ◽  
Lake Area ◽  
Data Set ◽  
Maximum Entropy Estimation

The problem of randomized maximum entropy estimation for the probability density function of random model parameters with real data and measurement noises was formulated. This estimation procedure maximizes an information entropy functional on a set of integral equalities depending on the real data set. The technique of the Gâteaux derivatives is developed to solve this problem in analytical form. The probability density function estimates depend on Lagrange multipliers, which are obtained by balancing the model’s output with real data. A global theorem for the implicit dependence of these Lagrange multipliers on the data sample’s length is established using the rotation of homotopic vector fields. A theorem for the asymptotic efficiency of randomized maximum entropy estimate in terms of stationary Lagrange multipliers is formulated and proved. The proposed method is illustrated on the problem of forecasting of the evolution of the thermokarst lake area in Western Siberia.

scholarly journals Flexible Power-Normal Models with Applications

Mathematics ◽  
2021 ◽  
Vol 9 (24) ◽  
pp. 3183
Author(s):  
Guillermo Martínez-Flórez ◽  
Diego I. Gallardo ◽  
Osvaldo Venegas ◽  
Heleno Bolfarine ◽  
Héctor W. Gómez
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Gaussian Model ◽  
Real Data ◽  
Simulation Studies ◽  
New Model ◽  
Asymmetric Model

The main object of this paper is to propose a new asymmetric model more flexible than the generalized Gaussian model. The probability density function of the new model can assume bimodal or unimodal shapes, and one of the parameters controls the skewness of the model. Three simulation studies are reported and two real data applications illustrate the flexibility of the model compared with traditional proposals in the literature.

Uncertainty Analysis of Planar Robots With Joint Clearance

1998 ◽  
Author(s):  
Jianmin Zhu ◽  
Kwun-Lon Ting
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Distribution Functions ◽  
Joint Clearance ◽  
Performance Quality ◽  
The Impact ◽  
Random Nature ◽  
Deviation Zone ◽  
Planar Robots

Abstract Joint clearance in mechanisms and robots leads to uncertainty in function deviation. Unlike the impact of the link tolerance on the performance quality, the uncertain effect of the joint clearance to the performance can not be eliminated by calibration because of the random nature. In this paper, based on the probability theory, a general probability density function for the output of planar robots is established for any probability density function of joint clearance. The result is demonstrated by a uniform distribution in the joint clearance and a table of the resulting functions is presented. These distribution functions and the table provide a convenient way to obtain the probability value for a planar robot to position its end point within a desired deviation zone and to determine the joint clearance value based on the concerned shape of tolerance zone and the specified probability value of repeatability.

scholarly journals Inaccuracies of Measuring Methods and Their Influence on the Regression Function

1984 ◽  
Vol 11 (3) ◽  
pp. 243-247
Author(s):  
W. Sauer
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Linear Function ◽  
Gaussian Function ◽  
Regression Function ◽  
Quality Parameters ◽  
Electronic Components ◽  
Measuring Process ◽  
Exact Relationship

The quality parameters of electronic components and devices usually depend on the parameters of the materials. In many cases one does not know the theoretical relationship between the parameters, and therefore one makes technological experiments and measures the values of the parameters. Usually it is necessary to take several measuring points and calculate from this the unknown relationship between the parameters.The simplest equation that one can use is the linear function. In this case the theoretical probability density function is a Gaussian-function. Otherwise it is necessary to assume that the linear function is an approximation.When the measuring process has an inaccuracy, then one can show that the increase of the linear function is smaller and it is necessary to estimate a factor of correction to calculate the theoretical or exact relationship.

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