scholarly journals On Beta Exponentiated Moment Exponential Distribution with Mathematical Characteristics and Application to Engineering Sectors

2021 ◽  
pp. 35-57
Author(s):  
Zafar Iqbal ◽  
Muhammad Rashad ◽  
Iram Rauf ◽  
Muhammad Salman
Keyword(s):  
Special Functions ◽  
Linear Equations ◽  
Likelihood Estimation ◽  
Entropy Measure ◽  
Reliability Measures ◽  
Lorenz Curves ◽  
Mathematical Properties ◽  
Method Of Maximum Likelihood ◽  
Non Linear Equations ◽  
Mathematical Characteristics

A new BEME distribution known as beta Exponentiated moment exponential (BEME) distribution is proposed. We provide here some shape properties, moments in the form of special functions, mean deviations of BEME distribution. We derive mathematical properties of the BEME distribution including the reliability measures, the Bonferroni and the Lorenz curves, rth order statistics, measures of uncertainty: the Shannon entropy measure and the s-entropy measure. The parameters of the BEME distribution are estimated by the method of maximum likelihood estimation and estimated non-linear equations for these estimates are presented. The application of BEME distribution is explored in three different fields of engineering.

scholarly journals The Nadarajah Haghighi Topp Leone-G Family of Distributions ‎with Mathematical Properties and Applications

2019 ◽  
Vol 15 (4) ◽  
pp. 849
Author(s):  
Hesham Reyad‎ ◽  
Mahmoud Ali Selim ◽  
Soha Othman
Keyword(s):  
Information Matrix ◽  
Quantile Function ◽  
Model Parameters ◽  
Lorenz Curves ◽  
New Class ◽  
New Family ◽  
Mathematical Properties ◽  
Probability Weighted Moments ◽  
Statistics And Probability ◽  
Method Of Maximum Likelihood

Based on the Nadarajah Haghighi distribution and the Topp Leone-G family in view of the T-X family, we introduce a new generator of continuous distributions with three extra parameters called the Nadarajah Haghighi Topp Leone-G family. Three sub-models of the new class are discussed. Main mathematical properties of the new family are investigated such as; quantile function, raw and incomplete moments, Bonferroni and Lorenz curves, moment and probability generating functions, stress-strength model, Shanon and Rényi entropies, order statistics and probability weighted moments. The model parameters of the new family is estimated by using the method of maximum likelihood and the observed information matrix is also obtained. We introduce two real applications to show the importance of the new family.

scholarly journals Complementary Kumaraswamy Weibull Power Series Distribution: Some Properties and Application

2020 ◽  
pp. 361-398
Author(s):  
Innocent Boyle Eraikhuemen ◽  
Julian Ibezimako Mbegbu ◽  
Friday Ewere
Keyword(s):  
Power Series ◽  
Likelihood Estimation ◽  
Real Data ◽  
Model Parameters ◽  
Data Set ◽  
Power Series Distribution ◽  
Mathematical Properties ◽  
Method Of Maximum Likelihood ◽  
The Family ◽  
Distance Problem

In this paper, we propose Complementary Kumaraswamy Weibull Power Series (CKWPS) Distributions. The method is obtained by compounding the Kumaraswamy-G distribution and Power Series distribution on a latent complementary distance problem base. The mathematical properties of the proposed class of distribution are studied. The method of Maximum Likelihood Estimation is used for obtaining the estimates of the model parameters. A member of the family is investigated in detail. Finally an application of the proposed class is illustrated using a real data set.

scholarly journals The Hamza Distribution with Statistical Properties and Applications

2020 ◽  
pp. 28-42
Author(s):  
Ahmad Aijaz ◽  
Muzamil Jallal ◽  
S. Qurat Ul Ain ◽  
Rajnee Tripathi
Keyword(s):  
Cumulative Distribution Function ◽  
Likelihood Estimation ◽  
Moment Generating Function ◽  
Rate Function ◽  
Cumulative Distribution ◽  
Parameter Distribution ◽  
Residual Function ◽  
Lorenz Curves ◽  
Method Of Maximum Likelihood ◽  
Two Parameter

This paper suggested a new two parameter distribution named as Hamza distribution. A detailed description about the properties of a suggested distribution including moments, moment generating function, deviations about mean and median, stochastic orderings, Bonferroni and Lorenz curves, Renyi entropy, order statistics, hazard rate function and mean residual function has been discussed. The behavior of a probability density function (p.d.f) and cumulative distribution function (c.d.f) have been depicted through graphs. The parameters of the distribution are estimated by the known method of maximum likelihood estimation. The performance of the established distribution have been illustrated through applications, by which we conclude that the established distribution provide better fit.

scholarly journals A New Generalized Cauchy Distribution with an Application to Annual One Day Maximum Rainfall Data

2021 ◽  
Vol 9 (1) ◽  
pp. 123-136
Author(s):  
Cory Ball ◽  
Binod Rimal ◽  
Sher Chhetri
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Simulation Study ◽  
Likelihood Estimation ◽  
Cauchy Distribution ◽  
Maximum Rainfall ◽  
Mathematical Properties ◽  
Proposed Model ◽  
Method Of Maximum Likelihood ◽  
Map Approach

In this article, we introduce a new three-parameter transmuted Cauchy distribution using the quadratic rank transmutation map approach. Some mathematical properties of the proposed model are discussed. A simulation study is conducted using the method of maximum likelihood estimation to estimate the parameters of the proposed model. We used two real datasets and compare various statistics to show the fitting and versatility of the model.

scholarly journals Samade Probability Distribution: Its Properties and Application to Real Lifetime Data

2021 ◽  
pp. 1-11
Author(s):  
Samuel Aderoju
Keyword(s):  
Survival Function ◽  
Real Life ◽  
Likelihood Estimation ◽  
Reliability Function ◽  
Entropy Measure ◽  
Lifetime Distributions ◽  
Mathematical Properties ◽  
Real Life Data ◽  
Proposed Model ◽  
First Four Moments

A new two-parameter lifetime distribution has been proposed in this study. The distribution is called Samade distribution. The model is motivated by the wide use of the lifetime models derived from the mixture of gamma and exponential distributions. Its mathematical properties which include the first four moments, variance as well as coefficient of variation, reliability function, hazard function, survival function, Renyi entropy measure and distribution of order statistics have been successfully derived. The maximum likelihood estimation of its parameters and application to real life data have been discussed. Application of this model to three real datasets shown that the proposed model yields a satisfactorily better fit than other existing lifetime distributions. The comparism of goodness-of-fits were established using -2Loglikelihood, AIC and BIC. 

scholarly journals A master exceptional field theory

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Guillaume Bossard ◽  
Axel Kleinschmidt ◽  
Ergin Sezgin
Keyword(s):  
Field Theory ◽  
Gauge Invariance ◽  
Sigma Model ◽  
Linear Equations ◽  
Field Theories ◽  
Gauge Invariant ◽  
Non Linear ◽  
Non Linear Equations

Abstract We construct a pseudo-Lagrangian that is invariant under rigid E11 and transforms as a density under E11 generalised diffeomorphisms. The gauge-invariance requires the use of a section condition studied in previous work on E11 exceptional field theory and the inclusion of constrained fields that transform in an indecomposable E11-representation together with the E11 coset fields. We show that, in combination with gauge-invariant and E11-invariant duality equations, this pseudo-Lagrangian reduces to the bosonic sector of non-linear eleven-dimensional supergravity for one choice of solution to the section condi- tion. For another choice, we reobtain the E8 exceptional field theory and conjecture that our pseudo-Lagrangian and duality equations produce all exceptional field theories with maximal supersymmetry in any dimension. We also describe how the theory entails non-linear equations for higher dual fields, including the dual graviton in eleven dimensions. Furthermore, we speculate on the relation to the E10 sigma model.

scholarly journals Framework for Reconstruction of Pseudo Quad Polarimetric Imagery from General Compact Polarimetry

2021 ◽  
Vol 13 (3) ◽  
pp. 530
Author(s):  
Junjun Yin ◽  
Jian Yang
Keyword(s):  
Linear Equations ◽  
Estimation Method ◽  
Data Sets ◽  
Reconstruction Procedure ◽  
Component Decomposition ◽  
Reconstruction Methods ◽  
Sar Imagery ◽  
Key Aspects ◽  
Non Linear Equations ◽  
Reconstruction Model

Pseudo quad polarimetric (quad-pol) image reconstruction from the hybrid dual-pol (or compact polarimetric (CP)) synthetic aperture radar (SAR) imagery is a category of important techniques for radar polarimetric applications. There are three key aspects concerned in the literature for the reconstruction methods, i.e., the scattering symmetric assumption, the reconstruction model, and the solving approach of the unknowns. Since CP measurements depend on the CP mode configurations, different reconstruction procedures were designed when the transmit wave varies, which means the reconstruction procedures were not unified. In this study, we propose a unified reconstruction framework for the general CP mode, which is applicable to the mode with an arbitrary transmitted ellipse wave. The unified reconstruction procedure is based on the formalized CP descriptors. The general CP symmetric scattering model-based three-component decomposition method is also employed to fit the reconstruction model parameter. Finally, a least squares (LS) estimation method, which was proposed for the linear π/4 CP data, is extended for the arbitrary CP mode to estimate the solution of the system of non-linear equations. Validation is carried out based on polarimetric data sets from both RADARSAT-2 (C-band) and ALOS-2/PALSAR (L-band), to compare the performances of reconstruction models, methods, and CP modes.

scholarly journals Striated Tire Yaw Marks—Modeling and Validation

Energies ◽  
2021 ◽  
Vol 14 (14) ◽  
pp. 4309
Author(s):  
Wojciech Wach ◽  
Jakub Zębala
Keyword(s):  
Vehicle Dynamics ◽  
Linear Equations ◽  
Tire Model ◽  
Vehicle Accidents ◽  
The Road ◽  
Variable Curvature ◽  
Macro Scale ◽  
On The Road ◽  
Multi Body ◽  
Non Linear Equations

Tire yaw marks deposited on the road surface carry a lot of information of paramount importance for the analysis of vehicle accidents. They can be used: (a) in a macro-scale for establishing the vehicle’s positions and orientation as well as an estimation of the vehicle’s speed at the start of yawing; (b) in a micro-scale for inferring among others things the braking or acceleration status of the wheels from the topology of the striations forming the mark. A mathematical model of how the striations will appear has been developed. The model is universal, i.e., it applies to a tire moving along any trajectory with variable curvature, and it takes into account the forces and torques which are calculated by solving a system of non-linear equations of vehicle dynamics. It was validated in the program developed by the author, in which the vehicle is represented by a 36 degree of freedom multi-body system with the TMeasy tire model. The mark-creating model shows good compliance with experimental data. It gives a deep view of the nature of striated yaw marks’ formation and can be applied in any program for the simulation of vehicle dynamics with any level of simplification.

scholarly journals Compartmental Learning versus Joint Learning in Engineering Education

Mathematics ◽  
2021 ◽  
Vol 9 (6) ◽  
pp. 662
Author(s):  
María Jesús Santos ◽  
Alejandro Medina ◽  
José Miguel Mateos Roco ◽  
Araceli Queiruga-Dios
Keyword(s):  
Engineering Students ◽  
Chemical Engineering ◽  
Linear Equations ◽  
Mathematical Software ◽  
Mathematical Concepts ◽  
Joint Learning ◽  
The University ◽  
Academic Year ◽  
Non Linear Equations ◽  
Mathematics And Physics

Sophomore students from the Chemical Engineering undergraduate Degree at the University of Salamanca are involved in a Mathematics course during the third semester and in an Engineering Thermodynamics course during the fourth one. When they participate in the latter they are already familiar with mathematical software and mathematical concepts about numerical methods, including non-linear equations, interpolation or differential equations. We have focused this study on the way engineering students learn Mathematics and Engineering Thermodynamics. As students use to learn each matter separately and do not associate Mathematics and Physics, they separate each matter into different and independent compartments. We have proposed an experience to increase the interrelationship between different subjects, to promote transversal skills, and to make the subjects closer to real work. The satisfactory results of the experience are exposed in this work. Moreover, we have analyzed the results obtained in both courses during the academic year 2018–2019. We found that there is a relation between both courses and student’s final marks do not depend on the course.

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