Random spherical triangles I: Geometrical background

1989 ◽  
Vol 21 (3) ◽  
pp. 570-580
Author(s):  
Huiling Le
Keyword(s):  
Mathematical Model ◽  
Shape Space ◽  
Companion Paper ◽  
Statistical Properties ◽  
Data Sets ◽  
Riemannian Structure ◽  
Geometric Structures ◽  
Fundamental Properties ◽  
Random Mechanism ◽  
Spherical Triangles

In this paper we identify the shape space Σ(S2, k) for k labelled points on the sphere S2 that gives a mathematical model applicable to data sets whose elements are, or can be represented by, configurations of labelled sequences of points on S2 and for which the fundamental properties of interest are the shapes of these configurations, and we examine the geometric structures on the space, especially the riemannian structure on Σ(S2, 3). In a companion paper (pp. 581–594) we investigate the statistical properties of such shapes when the k points are generated by a random mechanism.

Random spherical triangles I: Geometrical background

1989 ◽  
Vol 21 (03) ◽  
pp. 570-580 ◽  
Author(s):  
Huiling Le
Keyword(s):  
Mathematical Model ◽  
Shape Space ◽  
Companion Paper ◽  
Statistical Properties ◽  
Data Sets ◽  
Riemannian Structure ◽  
Geometric Structures ◽  
Fundamental Properties ◽  
Random Mechanism ◽  
Spherical Triangles

In this paper we identify the shape space Σ(S 2, k) for k labelled points on the sphere S 2 that gives a mathematical model applicable to data sets whose elements are, or can be represented by, configurations of labelled sequences of points on S2 and for which the fundamental properties of interest are the shapes of these configurations, and we examine the geometric structures on the space, especially the riemannian structure on Σ(S 2, 3). In a companion paper (pp. 581–594) we investigate the statistical properties of such shapes when the k points are generated by a random mechanism.

scholarly journals The Odd Log-Logistic Poisson Inverse Rayleigh Distribution: Statistical Properties and Applications

2020 ◽  
pp. 775-787
Author(s):  
Ibrahim Elbatal
Keyword(s):  
Maximum Likelihood ◽  
Simulation Study ◽  
Maximum Likelihood Estimators ◽  
Real Data ◽  
Rayleigh Distribution ◽  
Statistical Properties ◽  
Data Sets ◽  
New Model ◽  
Fundamental Properties

In this work, a new extension of the Inverse Rayleigh model is proposed and studied. We derive some of its fundamental properties. We assess the performance of the maximum likelihood estimators via a simulation study. The importance of the new model is shown via two applications to real data sets. The new model is better fit than other important competitive models based on two real data sets.

scholarly journals The Flexible Burr X-G Family: Properties, Inference, and Applications in Engineering Science

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 474
Author(s):  
Abdulhakim A. Al-Babtain ◽  
Ibrahim Elbatal ◽  
Hazem Al-Mofleh ◽  
Ahmed M. Gemeay ◽  
Ahmed Z. Afify ◽  
...  
Keyword(s):  
Numerical Simulations ◽  
Exponential Distribution ◽  
Real Data ◽  
Exponential Model ◽  
Statistical Properties ◽  
Engineering Science ◽  
Data Sets ◽  
Engineering Sciences ◽  
General Statistical ◽  
Anderson Darling

In this paper, we introduce a new flexible generator of continuous distributions called the transmuted Burr X-G (TBX-G) family to extend and increase the flexibility of the Burr X generator. The general statistical properties of the TBX-G family are calculated. One special sub-model, TBX-exponential distribution, is studied in detail. We discuss eight estimation approaches to estimating the TBX-exponential parameters, and numerical simulations are conducted to compare the suggested approaches based on partial and overall ranks. Based on our study, the Anderson–Darling estimators are recommended to estimate the TBX-exponential parameters. Using two skewed real data sets from the engineering sciences, we illustrate the importance and flexibility of the TBX-exponential model compared with other existing competing distributions.

scholarly journals New class of Lindley distributions: properties and applications

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Duha Hamed ◽  
Ahmad Alzaghal
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Simulation Study ◽  
Likelihood Estimation ◽  
Statistical Properties ◽  
Data Sets ◽  
Lifetime Data ◽  
Unknown Parameters ◽  
Lindley Distribution ◽  
New Class

AbstractA new generalized class of Lindley distribution is introduced in this paper. This new class is called the T-Lindley{Y} class of distributions, and it is generated by using the quantile functions of uniform, exponential, Weibull, log-logistic, logistic and Cauchy distributions. The statistical properties including the modes, moments and Shannon’s entropy are discussed. Three new generalized Lindley distributions are investigated in more details. For estimating the unknown parameters, the maximum likelihood estimation has been used and a simulation study was carried out. Lastly, the usefulness of this new proposed class in fitting lifetime data is illustrated using four different data sets. In the application section, the strength of members of the T-Lindley{Y} class in modeling both unimodal as well as bimodal data sets is presented. A member of the T-Lindley{Y} class of distributions outperformed other known distributions in modeling unimodal and bimodal lifetime data sets.

scholarly journals Localization of Windows and Doors in 3d Point Clouds of Facades

2014 ◽  
Vol II-3 ◽  
pp. 87-94 ◽  
Author(s):  
W. Nguatem ◽  
M. Drauschke ◽  
H. Mayer
Keyword(s):  
Bayes Factor ◽  
Likelihood Function ◽  
Parallel Implementation ◽  
Point Clouds ◽  
Search Space ◽  
Shape Space ◽  
Data Sets ◽  
3D Point Clouds ◽  
Spline Curves ◽  
Search Routine

In this paper, we present a fully automatic approach to localize the outlines of facade objects (windows and doors) in 3D point clouds of facades. We introduce an approach to search for the main facade wall and locate the facade objects within a probabilistic framework. Our search routine is based on Monte Carlo Simulation (MC-Simulation). Templates containing control points of curves are used to approximate the possible shapes of windows and doors. These are interpolated using parametric B-spline curves. These templates are scored in a sliding window style over the entire facade using a likelihood function in a probabilistic matching procedure. This produces many competing results for which a two layered model selection based on Bayes factor is applied. A major thrust in our work is the introduction of a 2D shape-space of similar shapes under affine transform in this architectural scene. This transforms the initial parametric B-splines curves representing the outlines of objects to curves of affine similarity in a strongly reduced dimensionality thus facilitating the generation of competing hypotheses within the search space. A further computational speedup is achieved through the clustering of the search space to disjoint regions, thus enabling a parallel implementation. We obtain state-of-the results on self-acquired data sets. The robustness of our algorithm is evaluated on 3D point clouds from image matching and LiDAR data of diverse quality.

scholarly journals Two-Parameter Nwikpe (TPAN) Distribution with Application

2021 ◽  
pp. 56-67
Author(s):  
Barinaadaa John Nwikpe ◽  
Isaac Didi Essi
Keyword(s):  
Goodness Of Fit ◽  
Continuous Distribution ◽  
Real Life ◽  
Moment Generating Function ◽  
Statistical Properties ◽  
Likelihood Method ◽  
Data Sets ◽  
Method Of Moment ◽  
Two Parameter ◽  
New Distribution

A new two-parameter continuous distribution called the Two-Parameter Nwikpe (TPAN) distribution is derived in this paper. The new distribution is a mixture of gamma and exponential distributions. A few statistical properties of the new probability distribution have been derived. The shape of its density for different values of the parameters has also been established.  The first four crude moments, the second and third moments about the mean of the new distribution were derived using the method of moment generating function. Other statistical properties derived include; the distribution of order statistics, coefficient of variation and coefficient of skewness. The parameters of the new distribution were estimated using maximum likelihood method. The flexibility of the Two-Parameter Nwikpe (TPAN) distribution was shown by fitting the distribution to three real life data sets. The goodness of fit shows that the new distribution outperforms the one parameter exponential, Shanker and Amarendra distributions for the data sets used for this study.

scholarly journals A New Right-Skewed Upside Down Bathtub Shaped Heavy-tailed Distribution and its Applications

2021 ◽  
Vol 19 (1) ◽  
Author(s):  
Sandeep Kumar Maurya ◽  
Sanjay K Singh ◽  
Umesh Singh
Keyword(s):  
Maximum Likelihood ◽  
Real Data ◽  
Statistical Properties ◽  
New Right ◽  
Data Sets ◽  
Proposed Model ◽  
Heavy Tailed Distribution ◽  
Heavy Tailed

A one parameter right skewed, upside down bathtub type, heavy-tailed distribution is derived. Various statistical properties and maximum likelihood approaches for estimation purpose are studied. Five different real data sets with four different models are considered to illustrate the suitability of the proposed model.

scholarly journals Maximum Product of Spacing Parameter Estimation of Gompertz Rayleigh Distribution and Application to Rainfall Datasets

2021 ◽  
pp. 41-59
Author(s):  
Hussein Ahmad Abdulsalam ◽  
Sule Omeiza Bashiru ◽  
Alhaji Modu Isa ◽  
Yunusa Adavi Ojirobe
Keyword(s):  
Goodness Of Fit ◽  
Negative Binomial ◽  
Likelihood Estimation ◽  
Statistical Properties ◽  
Rainfall Data ◽  
Parameter Estimates ◽  
Data Sets ◽  
Unknown Parameters ◽  
Exponentiated Weibull ◽  
Integrated Hazard

Gompertz Rayleigh (GomR) distribution was introduced in an earlier study with few statistical properties derived and parameters estimated using only the most common traditional method, Maximum Likelihood Estimation (MLE). This paper aimed at deriving more statistical properties of the GomR distribution, estimating the three unknown parameters via a competitive method, Maximum Product of Spacing (MPS) and evaluating goodness of fit using rainfall data sets from Nigeria, Malaysia and Argentina. Properties of statistical distributions including distribution of smallest and largest order statistics, cumulative or integrated hazard function, odds function, rth non-central moments, moment generating function, mean, variance and entropy measures for GomR distribution were explicitly derived. The fitted data sets reveal the flexibility of GomR distribution over other distributions been compared with. Simulation study was used to evaluate the consistency, accuracy and unbiasedness of the GomR distribution parameter estimates obtained from the method of MPS. The study found that GomR distribution could not provide a better fit for Argentine rainfall data but it was the best distribution for the rainfall data sets from Nigeria and Malaysia in comparison with the distributions; Generalized Weibull Rayleigh (GWR), Exponentiated Weibull Rayleigh (EWR), Type (II) Topp Leone Generalized Inverse Rayleigh (TIITLGIR), Kumarawamy Exponential Inverse Raylrigh (KEIR), Negative Binomial Marshall-Olkin Rayleigh (NBMOR) and Exponentiated Weibull (EW). Furthermore, the estimates from MPSE were consistent as the sample size increases but not as efficient as those from MLE.

scholarly journals ASSESSING LIDAR TRAINING DATA QUANTITIES FOR CLASSIFICATION MODELS

2021 ◽  
Vol XLVI-4/W4-2021 ◽  
pp. 101-106
Author(s):  
O. Majgaonkar ◽  
K. Panchal ◽  
D. Laefer ◽  
M. Stanley ◽  
Y. Zaki
Keyword(s):  
Point Cloud ◽  
Classification Performance ◽  
Training Data ◽  
Lidar Data ◽  
Data Sets ◽  
Classification Models ◽  
Fundamental Properties ◽  
Point Cloud Classification ◽  
The Impact ◽  
Insight Into

Abstract. Classifying objects within aerial Light Detection and Ranging (LiDAR) data is an essential task to which machine learning (ML) is applied increasingly. ML has been shown to be more effective on LiDAR than imagery for classification, but most efforts have focused on imagery because of the challenges presented by LiDAR data. LiDAR datasets are of higher dimensionality, discontinuous, heterogenous, spatially incomplete, and often scarce. As such, there has been little examination into the fundamental properties of the training data required for acceptable performance of classification models tailored for LiDAR data. The quantity of training data is one such crucial property, because training on different sizes of data provides insight into a model’s performance with differing data sets. This paper assesses the impact of training data size on the accuracy of PointNet, a widely used ML approach for point cloud classification. Subsets of ModelNet ranging from 40 to 9,843 objects were validated on a test set of 400 objects. Accuracy improved logarithmically; decelerating from 45 objects onwards, it slowed significantly at a training size of 2,000 objects, corresponding to 20,000,000 points. This work contributes to the theoretical foundation for development of LiDAR-focused models by establishing a learning curve, suggesting the minimum quantity of manually labelled data necessary for satisfactory classification performance and providing a path for further analysis of the effects of modifying training data characteristics.

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