scholarly journals Multivariate Generalization of the Confluent Hypergeometric Function Kind 1 Distribution

2008 ◽  
Vol 2008 ◽  
pp. 1-13
Author(s):  
Daya K. Nagar ◽  
Fabio Humberto Sepúlveda-Murillo
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Hypergeometric Function ◽  
Confluent Hypergeometric Function ◽  
Multivariate Distribution ◽  
Multivariate Generalization ◽  
Probability Density Function Pdf

The confluent hypergeometric function kind 1 distribution with the probability density function (pdf) proportional tox_−1F11(α;β;−x),  x>0occurs as the distribution of the ratio of independent gamma and beta variables. In this article, a multivariate generalization of this distribution is defined and derived. Several pertinent properties of this multivariate distribution are discussed that shed some light on the nature of the distribution.

scholarly journals Dynamic Reliability Analysis Method of Degraded Mechanical Components Based on Process Probability Density Function of Stress

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Peng Gao ◽  
Liyang Xie
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Solar Array ◽  
Dynamic Reliability ◽  
Reliability Models ◽  
Practical Engineering ◽  
Mechanical Components ◽  
Reliability Computation ◽  
Probability Density Function Pdf

It is necessary to develop dynamic reliability models when considering strength degradation of mechanical components. Instant probability density function (IPDF) of stress and process probability density function (PPDF) of stress, which are obtained via different statistical methods, are defined, respectively. In practical engineering, the probability density function (PDF) for the usage of mechanical components is mostly PPDF, such as the PDF acquired via the rain flow counting method. For the convenience of application, IPDF is always approximated by PPDF when using the existing dynamic reliability models. However, it may cause errors in the reliability calculation due to the approximation of IPDF by PPDF. Therefore, dynamic reliability models directly based on PPDF of stress are developed in this paper. Furthermore, the proposed models can be used for reliability assessment in the case of small amount of stress process samples by employing the fuzzy set theory. In addition, the mechanical components in solar array of satellites are chosen as representative examples to illustrate the proposed models. The results show that errors are caused because of the approximation of IPDF by PPDF and the proposed models are accurate in the reliability computation.

scholarly journals A new subgrid-scale representation of hydrometeor fields using a multivariate PDF

2016 ◽  
Author(s):  
Brian M. Griffin ◽  
Vincent E. Larson
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Vertical Velocity ◽  
Lognormal Distribution ◽  
Large Eddy Simulations ◽  
Subgrid Scale ◽  
Microphysical Process ◽  
Large Eddy ◽  
Probability Density Function Pdf

Abstract. The subgrid-scale representation of hydrometeor fields is important for calculating microphysical process rates. In order to represent subgrid-scale variability, the Cloud Layers Unified By Binormals (CLUBB) parameterization uses a multivariate Probability Density Function (PDF). In addition to vertical velocity, temperature, and moisture fields, the PDF includes hydrometeor fields. Previously, each hydrometeor field was assumed to follow a multivariate single lognormal distribution. Now, in order to better represent the distribution of hydrometeors, two new multivariate PDFs are formulated and introduced. The new PDFs represent hydrometeors using either a delta-lognormal or a delta-double-lognormal shape. The two new PDF distributions, plus the previous single lognormal shape, are compared to histograms of data taken from Large-Eddy Simulations (LES) of a precipitating cumulus case, a drizzling stratocumulus case, and a deep convective case. Finally, the warm microphysical process rates produced by the different hydrometeor PDFs are compared to the same process rates produced by the LES.

PROBABILITY DENSITY FUNCTION CONTROL OF QUANTUM SYSTEMS

2011 ◽  
Vol 25 (17) ◽  
pp. 2289-2297 ◽  
Author(s):  
YI-FAN XING ◽  
JUN WU
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Quantum Control ◽  
Quantum Systems ◽  
Quantum Model ◽  
Control Engineering ◽  
Control Of Quantum Systems ◽  
Probability Density Function Pdf ◽  
Specific Control

This paper proposes a new method of controlling quantum systems via probability density function (PDF) control. Based on the quantum model from the PDF perspective, two specific control algorithms are proposed for the general case and limited input energy, respectively. Unlike traditional quantum control methods, this method directly controls the probability distribution of the quantum state. It provides an alternative method for quantum control engineering.

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 Research on Algorithm of Extracting PPG Signal for Detecting Atrial Fibrillation based on Probability Density Function

2015 ◽  
Vol 9 (1) ◽  
pp. 179-184 ◽  
Author(s):  
Kang Liang ◽  
Ying Sun ◽  
Fuying Tian ◽  
Shenghua Ye
Keyword(s):  
Atrial Fibrillation ◽  
Phase Space ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Normal Sinus Rhythm ◽  
New Method ◽  
Diagram Method ◽  
Normal Sinus ◽  
Probability Density Function Pdf

The paper introduced a new method based on probability density function (PDF) and phase space diagram method for photoplethysmography (PPG) signal extracting. In the paper, PPG information was generated from human fingertips by smartphones. The pulse wave period was then separated and reconstructed into probability density function (PDF) by the phase space diagram algorithm. The difference between normal sinus rhythm (NSR) and atrial fibrillation (AF) was finally found by skewness of the PDF. The results of the present study demonstrates that the new method is vividly viable for detecting AF on the smartphone.

Sign in / Sign up

Export Citation Format

Share Document