scholarly journals An Analytical EM Algorithm for Sub-Gaussian Vectors

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 945
Author(s):  
Audrius Kabašinskas ◽  
Leonidas Sakalauskas ◽  
Ingrida Vaičiulytė
Keyword(s):  
Em Algorithm ◽  
Likelihood Ratio ◽  
Goodness Of Fit ◽  
Stable Distribution ◽  
Likelihood Estimation ◽  
Estimation Methods ◽  
Normal Vector ◽  
Ratio Test ◽  
Estimation Of Parameters ◽  
Goodness Of Fit Test

The area in which a multivariate α-stable distribution could be applied is vast; however, a lack of parameter estimation methods and theoretical limitations diminish its potential. Traditionally, the maximum likelihood estimation of parameters has been considered using a representation of the multivariate stable vector through a multivariate normal vector and an α-stable subordinator. This paper introduces an analytical expectation maximization (EM) algorithm for the estimation of parameters of symmetric multivariate α-stable random variables. Our numerical results show that the convergence of the proposed algorithm is much faster than that of existing algorithms. Moreover, the likelihood ratio (goodness-of-fit) test for a multivariate α-stable distribution was implemented. Empirical examples with simulated and real world (stocks, AIS and cryptocurrencies) data showed that the likelihood ratio test can be useful for assessing goodness-of-fit.

scholarly journals Identification of Factors Determining Winning in Men’s and Women’s Beach Volleyball: a Logistical Regression Approach

2021 ◽  
Vol 21 (1) ◽  
pp. 26-35
Author(s):  
Gopal Kumar ◽  
Anshuman Shukla ◽  
Amit Chhoker ◽  
Rohit Kumar Thapa
Keyword(s):  
Odds Ratio ◽  
Goodness Of Fit ◽  
Binary Logistic Regression ◽  
Ratio Test ◽  
Goodness Of Fit Test ◽  
Men And Women ◽  
Regression Approach ◽  
Lemeshow Test ◽  
Calculated Model ◽  
Women's Competition

The purpose of this study was to find the factors responsible for winning in the men’s and women’s beach volleyball championship. Materials and methods. The study sample consisted of a total of 212 matches for men and 214 matches for women of the 2017 & 2019 FIVB Men and Women Beach Volleyball World Championships held at Vienna & Hamburg from 28 July to 6 Aug 2017 and 28 June to 7 July 2019. The matches were played by 192 teams (both men and women combined) consisting of 384 numbers (both men and women combined) of players from different nations. The data were analyzed using Binary Logistic Regression (Forward: LR Method) with the result of the game as the dependent variable and predictor variables as covariates. β, standard error β, Wald’s χ2, odds ratio with 95% confidence interval were calculated. Model evaluation was conducted using the likelihood ratio test, Cox & Snell (R2), and Nagelkerke (R2) tests. The goodness of fit test for the models was conducted using the Hosmer & Lemeshow test. Results. The analysis revealed seven factors related to winning in men’s and women’s competition. While in league rounds, six factors in men’s and seven factors in women’s competition were related to winning. Besides, in knockout rounds, four factors in men’s and six factors in women’s competition were related to winning. Conclusion. The study shows that there is a significant association of important factors with respect to winning a match in an elite beach volleyball championship. The coaches and players can take note of the important factors responsible for winning in the elite beach volleyball championship, with different factors playing an important role in men’s and women’s competition during league and knockout rounds as well.

scholarly journals Modelling the number of olive groves in Spanish municipalities

2016 ◽  
Vol 14 (1) ◽  
pp. e0201
Author(s):  
Maria-Dolores Huete ◽  
Juan A. Marmolejo
Keyword(s):  
Goodness Of Fit ◽  
Likelihood Estimation ◽  
External Factors ◽  
Discrete Distributions ◽  
Future Research ◽  
Total Output ◽  
Goodness Of Fit Test ◽  
Chi Square ◽  
Total Variability ◽  
Olive Groves

<p>The univariate generalized Waring distribution (UGWD) is presented as a new model to describe the goodness of fit, applicable in the context of agriculture. In this paper, it was used to model the number of olive groves recorded in Spain in the 8,091 municipalities recorded in the 2009 Agricultural Census, according to which the production of oil olives accounted for 94% of total output, while that of table olives represented 6% (with an average of 44.84 and 4.06 holdings per Spanish municipality, respectively). UGWD is suitable for fitting this type of discrete data, with strong left-sided asymmetry. This novel use of UGWD can provide the foundation for future research in agriculture, with the advantage over other discrete distributions that enables the analyst to split the variance. After defining the distribution, we analysed various methods for fitting the parameters associated with it, namely estimation by maximum likelihood, estimation by the method of moments and a variant of the latter, estimation by the method of frequencies and moments. For oil olives, the chi-square goodness of fit test gives <em>p</em>-values of 0.9992, 0.9967 and 0.9977, respectively. However, a poor fit was obtained for the table olive distribution. Finally, the variance was split, following Irwin, into three components related to random factors, external factors and internal differences. For the distribution of the number of olive grove holdings, this splitting showed that random and external factors only account about 0.22% and 0.05%. Therefore, internal differences within municipalities play an important role in determining total variability.</p>

scholarly journals A comparison of three parameter estimation methods of the gamma distribution of annual maximum low flow duration and deficit in the Upper Vistula catchment (Poland)

2018 ◽  
Vol 23 ◽  
pp. 00001
Author(s):  
Katarzyna Baran-Gurgul
Keyword(s):  
Gamma Distribution ◽  
Goodness Of Fit ◽  
Probability Distributions ◽  
Low Flow ◽  
Estimation Methods ◽  
Goodness Of Fit Test ◽  
Flow Duration ◽  
Distribution Parameters ◽  
Anderson Darling ◽  
Parameter Estimation Methods

Based on 30-year 24-hour flow sequences at 69 water gauging stations in the Upper Vistula catchment, it was determined that the probability distributions of the low flow duration and its maximum annual deficit can be described by the gamma distribution with the estimated parameters by the methods: MOM, the method of moments, LMOM, the method of linear moments, and MLE, the method of maximum likelihood. The stationarity of the time series was tested by the Mann-Kendall correlation using the Hamed and Rao variance correction. The low flows were defined by the SPA method, with the limit flow Q70%. The quality of the match was tested by the Anderson-Darling goodness of fit test. This test allowed accepting the gamma distribution in all analysed cases, regardless of the method used to estimate the distribution parameters, since the pv (p-values) values were greater than 5% (over 18% for Tmax and 7.5% for Vmax). The highest pv values for individual water gauging stations, as well as the highest 90% Tmax and Vmax quantiles were noted using LMOM to estimate the gamma distribution parameters. The highest 90% Tmax and Vmax quantiles were observed in the uppermost part of the studied area.

Calibration of microscopic traffic-flow models using multiple data sources

2010 ◽  
Vol 368 (1928) ◽  
pp. 4497-4517 ◽  
Author(s):  
Serge Hoogendoorn ◽  
Raymond Hoogendoorn
Keyword(s):  
Driving Simulator ◽  
Likelihood Estimation ◽  
Joint Estimation ◽  
Data Sources ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Ratio Test ◽  
Estimation Of Parameters ◽  
Flow Models ◽  
Car Following

Parameter identification of microscopic driving models is a difficult task. This is caused by the fact that parameters—such as reaction time, sensitivity to stimuli, etc.—are generally not directly observable from common traffic data, but also due to the lack of reliable statistical estimation techniques. This contribution puts forward a new approach to identifying parameters of car-following models. One of the main contributions of this article is that the proposed approach allows for joint estimation of parameters using different data sources, including prior information on parameter values (or the valid range of values). This is achieved by generalizing the maximum-likelihood estimation approach proposed by the authors in previous work. The approach allows for statistical analysis of the parameter estimates, including the standard error of the parameter estimates and the correlation of the estimates. Using the likelihood-ratio test, models of different complexity (defined by the number of model parameters) can be cross-compared. A nice property of this test is that it takes into account the number of parameters of a model as well as the performance. To illustrate the workings, the approach is applied to two car-following models using vehicle trajectories of a Dutch freeway collected from a helicopter, in combination with data collected with a driving simulator.

Determination of Yearly Wind Energy Potential and Extraction of Wind Energy Using Wind Turbine for Coastal Cities of Baluchistan, Pakistan

2019 ◽  
Vol 10 (3) ◽  
pp. 56-63
Author(s):  
Muhammad Shoaib ◽  
Imran Siddiqui ◽  
Saif Ur Rehman
Keyword(s):  
Wind Energy ◽  
Goodness Of Fit ◽  
Estimation Methods ◽  
Energy Potential ◽  
Goodness Of Fit Test ◽  
Wind Speeds ◽  
Energy Assessment ◽  
Weibull Pdf ◽  
Parameter Estimation Methods ◽  
Two Parameters

04 March, 2019 Accepted: 24 April, 2019Abstract: Wind energy assessment of Ormara, Gwadar and Lasbela wind sites which are located in provinceBaluchistan is presented. The daily averaged wind speed data for the three sites is recorded for a period of four yearsfrom 2010-2013 at mast heights 7 m, 9.6 m and 23 m. Measured wind data are extrapolated to heights 60 m (Ormara),80 m (Gwadar) and 60 m (Lasbela). Yearly averaged wind speeds are modeled using a two parameters Weibullfunction whose shape (k) and scale (c) parameters are computed using seven well known numerical iterative methods.Reliability of the fitting process is assessed by employing three goodness-of-fit test statistics, namely, RMSE, R2 and χ2tests. Tests indicate that MLE, MLM and EPFM outperformed other Weibull parameter estimation methods for a betterfit behavior. Yearly Weibull pdf and cdf are obtained and Weibull wind characteristics are determined. Wind turbinesEcotecnia 60/1.67 MW and Nordex S77 1500 kW are used to extract wind energy on yearly basis. Estimated yearlyWeibull power densities are in the range 623.00 - 700.13 W/m2, 276.04 – 307.55 W/m2 and 66.85 – 75.93 W/m2 forOrmara, Gwadar and Lasbela respectively. Extracted wind energy values for Ormara and Gwadar using wind turbinesare reported as ca. 8623 kWh and ca. 4622 kWh, respectively.

scholarly journals Binary Logistic Model to Identify the Factors Associated with Households with Bank Accounts in Nepal

2020 ◽  
Vol 2 (2) ◽  
pp. 323-336
Author(s):  
Santosh Kumar Shah
Keyword(s):  
Logistic Regression ◽  
Financial Institutions ◽  
Goodness Of Fit ◽  
Receiver Operating Curve ◽  
P Value ◽  
Ratio Test ◽  
Multiple Logistic Regression ◽  
Goodness Of Fit Test ◽  
Factors Associated ◽  
Bank Accounts

Introduction: Banks play an important role in ensuringthe economicand social stability, and the sustainablegrowth of the economy. The savings and other accounts in financial institutions, including banks, finances, microfinances and cooperatives, enable people to execute important financial functions. Thus, households that have accounts in any of financial institutions can have access to various banking services. Objective: The objective of the study is to identify the factors associated with households having bank accounts in Nepal. Methods: The analysis is based on household data extracted from the dataset of Nepal Demographic and Health Survey, 2016. The dependent variable is dichotomous, as the households with bank accounts and without bank accounts in any formal financial channels. In order to identify the factors associated with households receiving financial services in Nepal, multiple logistic regression models were developed by examining the model adequacy test. Results: The study finds that a total of 66.9% of the households had bank accounts. Several variables were found to be 1% of significance level. The predictive power of the model is found to be 31.2% and multicollinearity among the independent variables was absent. The Hosmer-Lemoshow goodness of fit test revealed that the data were poorly (p-value=0.056) fitted by the model. However, Osius-Rojek goodness of fit test (z=0.11; p-value=0.911), Stukel test (Z=0.683, p-value=0.494), likelihood ratio test (χ2=2770; p-value<0.0001) and area under receiver operating curve (79.8%) revealed that fitted model was good. Conclusion: Multiple logistic regression model revealed that in mountainous and hilly regions, women-headed households have less chances of not having bank accounts compared to the Terai region and men-headed households. The chances of having a bank account in province-2 is even worse than in Karnali and other provinces. The odds of not having bank accounts gradually decreased with the increase in size of agricultural land, wealth index, increase in family size and the number of family members who have completed secondary education.

scholarly journals A New Generalized t Distribution Based on a Distribution Construction Method

Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2413
Author(s):  
Ruijie Guan ◽  
Xu Zhao ◽  
Weihu Cheng ◽  
Yaohua Rong
Keyword(s):  
Maximum Likelihood ◽  
Em Algorithm ◽  
Iterative Algorithm ◽  
Likelihood Estimation ◽  
Estimation Methods ◽  
Modified Method ◽  
The Em Algorithm ◽  
Likelihood Approach ◽  
T Distribution ◽  
Better Than

In this paper, a new generalized t (new Gt) distribution based on a distribution construction approach is proposed and proved to be suitable for fitting both the data with high kurtosis and heavy tail. The main innovation of this article consists of four parts. First of all, the main characteristics and properties of this new distribution are outined. Secondly, we derive the explicit expression for the moments of order statistics as well as its corresponding variance–covariance matrix. Thirdly, we focus on the parameter estimation of this new Gt distribution and introduce several estimation methods, such as a modified method of moments (MMOM), a maximum likelihood estimation (MLE) using the EM algorithm, a novel iterative algorithm to acquire MLE, and improved probability weighted moments (IPWM). Through simulation studies, it can be concluded that the IPWM estimation performs better than the MLE using the EM algorithm and the MMOM in general. The newly-proposed iterative algorithm has better performance than the EM algorithm when the sample kurtosis is greater than 2.7. For four parameters of the new Gt distribution, a profile maximum likelihood approach using the EM algorithm is developed to deal with the estimation problem and obtain acceptable.

scholarly journals A Modified Chi-square Type Test Statistic for the Double Burr X Model with Applications to Right Censored Medical and Reliability Data

2021 ◽  
pp. 615-623
Author(s):  
Khaoula Aidi ◽  
Nadeem Shafique Butt ◽  
Mir Masoom Ali ◽  
Mohamed Ibrahim ◽  
Haitham M. Yousof ◽  
...  
Keyword(s):  
Censored Data ◽  
Goodness Of Fit ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Data Sets ◽  
Test Statistic ◽  
Goodness Of Fit Test ◽  
Chi Square ◽  
Right Censored Data ◽  
The Right

A new modified version of the Bagdonavičius-Nikulin goodness-of-fit test statistic is presented for validity for the right censor case under the double Burr type X distribution. The maximum likelihood estimation method in censored data case is used and applied. Simulations via the algorithm of Barzilai-Borwein is performed for assessing the right censored estimation method. Another simulation study is presented for testing the null hypothesis under the modified version of the Bagdonavičius and Nikulin goodness-of-fit statistical test. Four right censored data sets are analyzed under the new modified test statistic for checking the distributional validation.

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