T-Distribution

2020 ◽  
Author(s):  
Keyword(s):  
T Distribution

MULTIVARIATE SKEW t -DISTRIBUTION

Statistics ◽  
2003 ◽  
Vol 37 (4) ◽  
pp. 1-1
Author(s):  
A. K. GUPTA
Keyword(s):  
T Distribution

Categorizing Exam Results: t-distribution

2017 ◽  
Vol 1 (11) ◽  
pp. 1-10
Author(s):  
Suresh Akella ◽  
◽  
Girija Akella ◽  
Keyword(s):  
T Distribution

Sebaran Peluang Acak Kontinu, Distribusi Normal, Distribusi Normal Baku, Distribusi T, Distribusi Chi Square, dan Distribusi F

2020 ◽  
Author(s):  
Ahmad Sudi Pratikno
Keyword(s):  
Hypothesis Test ◽  
Standard Normal Distribution ◽  
Process Data ◽  
Nominal Data ◽  
Chi Square ◽  
Stable Curve ◽  
Standard Normal ◽  
Research Findings ◽  
F Distribution ◽  
T Distribution

In statistics, there are various terms that may feel unfamiliar to researcher who is not accustomed to discussing it. However, despite all of many functions and benefits that we can get as researchers to process data, it will later be interpreted into a conclusion. And then researcher can digest and understand the research findings. The distribution of continuous random opportunities illustrates obtaining opportunities with some detection of time, weather, and other data obtained from the field. The standard normal distribution represents a stable curve with zero mean and standard deviation 1, while the t distribution is used as a statistical test in the hypothesis test. Chi square deals with the comparative test on two variables with a nominal data scale, while the f distribution is often used in the ANOVA test and regression analysis.

scholarly journals Adjustment models for multivariate geodetic time series with vector-autoregressive errors

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Boris Kargoll ◽  
Alexander Dorndorf ◽  
Mohammad Omidalizarandi ◽  
Jens-André Paffenholz ◽  
Hamza Alkhatib
Keyword(s):  
Least Squares Method ◽  
Functional Model ◽  
Expectation Maximization Algorithm ◽  
Two Dimensions ◽  
Vector Autoregressive ◽  
Wide Range ◽  
Engineering Geodesy ◽  
Cross Correlations ◽  
T Distribution ◽  
Multivariate T

Abstract In this contribution, a vector-autoregressive (VAR) process with multivariate t-distributed random deviations is incorporated into the Gauss-Helmert model (GHM), resulting in an innovative adjustment model. This model is versatile since it allows for a wide range of functional models, unknown forms of auto- and cross-correlations, and outlier patterns. Subsequently, a computationally convenient iteratively reweighted least squares method based on an expectation maximization algorithm is derived in order to estimate the parameters of the functional model, the unknown coefficients of the VAR process, the cofactor matrix, and the degree of freedom of the t-distribution. The proposed method is validated in terms of its estimation bias and convergence behavior by means of a Monte Carlo simulation based on a GHM of a circle in two dimensions. The methodology is applied in two different fields of application within engineering geodesy: In the first scenario, the offset and linear drift of a noisy accelerometer are estimated based on a Gauss-Markov model with VAR and multivariate t-distributed errors, as a special case of the proposed GHM. In the second scenario real laser tracker measurements with outliers are adjusted to estimate the parameters of a sphere employing the proposed GHM with VAR and multivariate t-distributed errors. For both scenarios the estimated parameters of the fitted VAR model and multivariate t-distribution are analyzed for evidence of auto- or cross-correlations and deviation from a normal distribution regarding the measurement noise.

scholarly journals A Robust SMC-PHD Filter for Multi-Target Tracking with Unknown Heavy-Tailed Measurement Noise

Sensors ◽  
2021 ◽  
Vol 21 (11) ◽  
pp. 3611
Author(s):  
Yang Gong ◽  
Chen Cui
Keyword(s):  
Target Tracking ◽  
Sequential Monte Carlo ◽  
Measurement Noise ◽  
Particle Simulation ◽  
Target Number ◽  
Student T Distribution ◽  
Multi Target Tracking ◽  
Heavy Tailed ◽  
Scale Matrix ◽  
T Distribution

In multi-target tracking, the sequential Monte Carlo probability hypothesis density (SMC-PHD) filter is a practical algorithm. Influenced by outliers under unknown heavy-tailed measurement noise, the SMC-PHD filter suffers severe performance degradation. In this paper, a robust SMC-PHD (RSMC-PHD) filter is proposed. In the proposed filter, Student-t distribution is introduced to describe the unknown heavy-tailed measurement noise where the degrees of freedom (DOF) and the scale matrix of the Student-t distribution are respectively modeled as a Gamma distribution and an inverse Wishart distribution. Furthermore, the variational Bayesian (VB) technique is employed to infer the unknown DOF and scale matrix parameters while the recursion estimation framework of the RSMC-PHD filter is derived. In addition, considering that the introduced Student- t distribution might lead to an overestimation of the target number, a strategy is applied to modify the updated weight of each particle. Simulation results demonstrate that the proposed filter is effective with unknown heavy-tailed measurement noise.

scholarly journals Robust Power System State Estimation Using t-Distribution Noise Model

2020 ◽  
Vol 14 (1) ◽  
pp. 771-781 ◽  
Author(s):  
Tengpeng Chen ◽  
Lu Sun ◽  
Keck-Voon Ling ◽  
Weng Khuen Ho
Keyword(s):  
Power System ◽  
State Estimation ◽  
Noise Model ◽  
System State ◽  
Power System State Estimation ◽  
T Distribution

Robust Curve Clustering Based on a Multivariate $t$-Distribution Model

2010 ◽  
Vol 21 (12) ◽  
pp. 1976-1984 ◽  
Author(s):  
Zhi Min Wang ◽  
Qing Song ◽  
Yeng Chai Soh ◽  
Kang Sim
Keyword(s):  
Distribution Model ◽  
Multivariate T Distribution ◽  
Curve Clustering ◽  
T Distribution ◽  
Multivariate T

scholarly journals Correction Note: Correction to "A Bivariate $t$ Distribution"

1967 ◽  
Vol 38 (5) ◽  
pp. 1594-1594
Author(s):  
M. M. Siddiqui
Keyword(s):  
T Distribution

Moments of random vectors with skew t distribution and their quadratic forms

2003 ◽  
Vol 63 (4) ◽  
pp. 417-423 ◽  
Author(s):  
Hyoung-Moon Kim ◽  
Bani K. Mallick
Keyword(s):  
Quadratic Forms ◽  
Random Vectors ◽  
T Distribution
Sign in / Sign up

Export Citation Format

Share Document