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Journal articles on the topic 'Student-t Distribution'

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Published: 4 June 2021

Last updated: 13 February 2022

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Moreno-Arenas, Germán, Guillermo Martínez-Flórez, and Heleno Bolfarine. "Power Birnbaum-Saunders Student t distribution." Revista Integración 35, no. 1 (2017): 51–70. http://dx.doi.org/10.18273/revint.v35n1-2017004.

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Chen, William W. S. "On Finding Geodesic Equation of Student T Distribution." Journal of Mathematics Research 9, no. 2 (2017): 32. http://dx.doi.org/10.5539/jmr.v9n2p32.

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Student t distribution has been widely applied in the course of statistics. In this paper, we focus on finding a geodesic equation of the two parameter student t distributions. To find this equation, we applied both the well-known Darboux Theorem and a triply of partial differential equations taken from Struik D.J. (Struik, D.J., 1961) or Grey A (Grey A., 1993), As expected, the two different approaches reach the same type of results. The solution proposed in this paper could be used as a general solution of the geodesic equation for the student t distribution.

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Nugroho, Didit Budi, Agus Priyono, and Bambang Susanto. "SKEW NORMAL AND SKEW STUDENT-T DISTRIBUTIONS ON GARCH(1,1) MODEL." MEDIA STATISTIKA 14, no. 1 (2021): 21–32. http://dx.doi.org/10.14710/medstat.14.1.21-32.

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The Generalized AutoRegressive Conditional Heteroskedasticity (GARCH) type models have become important tools in financial application since their ability to estimate the volatility of financial time series data. In the empirical financial literature, the presence of skewness and heavy-tails have impacts on how well the GARCH-type models able to capture the financial market volatility sufficiently. This study estimates the volatility of financial asset returns based on the GARCH(1,1) model assuming Skew Normal and Skew Student-t distributions for the returns errors. The models are applied to daily returns of FTSE100 and IBEX35 stock indices from January 2000 to December 2017. The model parameters are estimated by using the Generalized Reduced Gradient Non-Linear method in Excel’s Solver and also the Adaptive Random Walk Metropolis method implemented in Matlab. The estimation results from fitting the models to real data demonstrate that Excel’s Solver is a promising way for estimating the parameters of the GARCH(1,1) models with non-Normal distribution, indicated by the accuracy of the estimation of Excel’s Solver. The fitting performance of models is evaluated by using log-likelihood ratio test and it indicates that the GARCH(1,1) model with Skew Student-t distribution provides the best fitting, followed by Student-t, Skew-Normal, and Normal distributions.

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Chen, Zexun, Bo Wang, and Alexander N. Gorban. "Multivariate Gaussian and Student-t process regression for multi-output prediction." Neural Computing and Applications 32, no. 8 (2019): 3005–28. http://dx.doi.org/10.1007/s00521-019-04687-8.

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AbstractGaussian process model for vector-valued function has been shown to be useful for multi-output prediction. The existing method for this model is to reformulate the matrix-variate Gaussian distribution as a multivariate normal distribution. Although it is effective in many cases, reformulation is not always workable and is difficult to apply to other distributions because not all matrix-variate distributions can be transformed to respective multivariate distributions, such as the case for matrix-variate Student-t distribution. In this paper, we propose a unified framework which is used not only to introduce a novel multivariate Student-t process regression model (MV-TPR) for multi-output prediction, but also to reformulate the multivariate Gaussian process regression (MV-GPR) that overcomes some limitations of the existing methods. Both MV-GPR and MV-TPR have closed-form expressions for the marginal likelihoods and predictive distributions under this unified framework and thus can adopt the same optimization approaches as used in the conventional GPR. The usefulness of the proposed methods is illustrated through several simulated and real-data examples. In particular, we verify empirically that MV-TPR has superiority for the datasets considered, including air quality prediction and bike rent prediction. At last, the proposed methods are shown to produce profitable investment strategies in the stock markets.

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Ceretta, Paulo Sérgio, Fernanda Galvão De Barba, Kelmara Mendes Vieira, and Fernando Casarin. "Previsão da volatilidade intradiária: análise das distribuições alternativas." Brazilian Review of Finance 9, no. 2 (2011): 209. http://dx.doi.org/10.12660/rbfin.v9n2.2011.2586.

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Volatility forecasting has been of great interest both in academic and professional fields all over the world. However, there is no agreement about the best model to estimate volatility. New models include measures of skewness, changes of regimes and different distributions; few studies, though, have considered different distributions. This paper aims to investigate how the specification of a distribution influences the performance of volatility forecasting on Ibovespa intraday data, using the APARCH model. The forecasts were carried out assuming six distinct distributions: normal, skewed normal, t-student, skewed t-student, generalized and skewed generalized. The results evidence that the model considering the skewed t-student distribution offered the best fit to the data inside the sample, on the other hand, the model assuming a normal distribution provided a better out-of-the-sample performance forecast.

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Safiul Haq, M., and Shahjahan Khan. "Prediction distribution for a linear regression model with multivariate student-t error distribution." Communications in Statistics - Theory and Methods 19, no. 12 (1990): 4705–12. http://dx.doi.org/10.1080/03610929008830469.

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da Silva Braga, Altemir, Gauss M. Cordeiro, Edwin M. M. Ortega, and Giovana O. Silva. "The Odd Log-Logistic Student t Distribution: Theory and Applications." Journal of Agricultural, Biological and Environmental Statistics 22, no. 4 (2017): 615–39. http://dx.doi.org/10.1007/s13253-017-0301-x.

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Sales, Francisco Das Chagas Vieira, José Antonio Aleixo da Silva, Rinaldo Luiz Caraciolo Ferreira, and Fernando Henrique de Lima Gadelha. "AJUSTES DE MODELOS VOLUMÉTRICOS PARA O CLONE Eucalyptus grandis x E. urophylla CULTIVADOS NO AGRESTE DE PERNAMBUCO." FLORESTA 45, no. 4 (2015): 663. http://dx.doi.org/10.5380/rf.v45i4.37594.

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O presente trabalho teve como objetivo avaliar o ajuste de modelos volumétricos para um clone de Eucalyptus usando distribuição normal e t-Student, utilizando dados de um experimento implantado no Instituto Agronômico de Pernambuco (IPA) em São Bento do Una, PE. Para o ajuste dos modelos volumétricos de Silva e Bailey modificado, Chapman e Richard modificado, Schumacher e Hall e, Brody modificado, foram utilizados dados de 62 árvores cubadas rigorosamente pelo método de Smalian. Os critérios usados nas comparações das equações foi o valor ponderado (VP) entre o Índice de Ajuste corrigido (IAc) e o erro percentual absoluto médio (EPAM). De acordo com os resultados o modelo que mostrou melhores ajustes nas duas distribuições foi o de Schumacher e Hall, com melhores ajuste quando da distribuição t-Student. A distribuição t-Student promoveu melhorias nos ajustes das equações em relação à distribuição Normal, quando comparando as duas distribuições em cada equação.AbstractAdjustment of volumetric models for clone of Eucalyptus grandis x E. Urophylla grown on agreste, Pernambuco. This research aimed to evaluate the volumetric models fitting for Eucalyptus clone using normal and t-Student distributions, based on data from an experiment implanted at the Agronomic Institute of Pernambuco (IPA) in São Bento do Una, PE. In order to set the modified volumetric models of Silva and Bailey, modified Chapman and Richard, Schumacher and Hall, and modified Brody, we used data from 62 trees rigorously scaled by Smalian method. The criteria for equation comparing were the weighted value (PV) between the corrected index adjustment (IAc) and absolute mean error percentage (EPAM). According to the results, the model that best fits for the two distributions is Schumacher and Hall, with better adjustment related to the Student-t distribution. The t-Student distribution promoted improvements of equations regarding the Normal distribution, compared to the two distributions per equation.Keywords: Forest management; symmetric distributions; volume equations.

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Singh, Surbhi, Harsh Vikram Singh, and Anand Mohan. "Secure and Robust Watermarking Using Wavelet Transform and Student t-distribution." Procedia Computer Science 70 (2015): 442–47. http://dx.doi.org/10.1016/j.procs.2015.10.071.

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Wang, Zongyuan, and Weidong Zhou. "Robust Linear Filter with Parameter Estimation Under Student-t Measurement Distribution." Circuits, Systems, and Signal Processing 38, no. 6 (2018): 2445–70. http://dx.doi.org/10.1007/s00034-018-0972-8.

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Xu, Su. "A VaR assuming Student t distribution not significantly different from a VaR assuming normal distribution." Risk Management 19, no. 3 (2017): 189–201. http://dx.doi.org/10.1057/s41283-017-0017-9.

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Christoph, Gerd, and Vladimir V. Ulyanov. "Chebyshev–Edgeworth-Type Approximations for Statistics Based on Samples with Random Sizes." Mathematics 9, no. 7 (2021): 775. http://dx.doi.org/10.3390/math9070775.

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Second-order Chebyshev–Edgeworth expansions are derived for various statistics from samples with random sample sizes, where the asymptotic laws are scale mixtures of the standard normal or chi-square distributions with scale mixing gamma or inverse exponential distributions. A formal construction of asymptotic expansions is developed. Therefore, the results can be applied to a whole family of asymptotically normal or chi-square statistics. The random mean, the normalized Student t-distribution and the Student t-statistic under non-normality with the normal limit law are considered. With the chi-square limit distribution, Hotelling’s generalized T02 statistics and scale mixture of chi-square distributions are used. We present the first Chebyshev–Edgeworth expansions for asymptotically chi-square statistics based on samples with random sample sizes. The statistics allow non-random, random, and mixed normalization factors. Depending on the type of normalization, we can find three different limit distributions for each of the statistics considered. Limit laws are Student t-, standard normal, inverse Pareto, generalized gamma, Laplace and generalized Laplace as well as weighted sums of generalized gamma distributions. The paper continues the authors’ studies on the approximation of statistics for randomly sized samples.

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Finlay, Richard, and Eugene Seneta. "Stationary-increment Student and variance-gamma processes." Journal of Applied Probability 43, no. 02 (2006): 441–53. http://dx.doi.org/10.1017/s0021900200001741.

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A continuous-time model with stationary increments for asset price {P t } is an extension of the symmetric subordinator model of Heyde (1999), and allows for skewness of returns. In the setting of independent variance-gamma-distributed returns the model resembles closely that of Madan, Carr, and Chang (1998). A simple choice of parameters renders {e−rt P t } a familiar martingale. We then specify the activity time process, {T t }, for which {T t − t} is asymptotically self-similar and {τ t }, with τ t = T t − T t−1, is gamma distributed. This results in a skew variance-gamma distribution for each log price increment (return) X t and a model for {X t } which incorporates long-range dependence in squared returns. Our approach mirrors that for the (symmetric) Student process model of Heyde and Leonenko (2005), to which the present work is intended as a complement and a sequel. One intention is to compare, partly on the basis of fitting to data, versions of the general model wherein the returns have either (symmetric) t-distributions or variance-gamma distributions.

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Zimmerman, Donald W., and Bruno D. Zumbo. "Effect of Outliers on the Relative Power of Parametric and Nonparametric Statistical Tests." Perceptual and Motor Skills 71, no. 1 (1990): 339–49. http://dx.doi.org/10.2466/pms.1990.71.1.339.

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It is known that parametric statistical tests, such as t and F, are more powerful than their nonparametric counterparts, such as the Wilcoxon-Mann-Whitney test or the Kruskal-Wallis test, when the assumption of a normal population distribution is satisfied. However, it has been found that, for quite a few nonnormal distributions, the Wilcoxon-Mann-Whitney test ( W) is more powerful than the Student t-test ( t) both in the asymptotic limit and for small samples. The present computer-simulation study examined the role of outliers in determining the relative power of W and t. In a series of five steps, a standard normal distribution, as well as a uniform distribution, was altered so that extreme scores occurred with increasingly higher probability. It was found that the initial power advantage of t gradually diminished in favor of W. In contrast, in a series of five steps, exponential and Cauchy distributions were truncated at less and less extreme values, so that the influence of outliers was reduced, and the initial power advantage of W gradually diminished in favor of t. For all distributions, the ordinary Student t-test performed on the ranks of measures instead of the measures was affected by addition or elimination of outliers in the same way as W and yielded the same probabilities of Type I and Type II errors as W.

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Lachos, Víctor H., Edgar J. López Moreno, Kun Chen, and Celso Rômulo Barbosa Cabral. "Finite mixture modeling of censored data using the multivariate Student-t distribution." Journal of Multivariate Analysis 159 (July 2017): 151–67. http://dx.doi.org/10.1016/j.jmva.2017.05.005.

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Matos, Larissa A., Luis M. Castro, Celso R. B. Cabral, and Víctor H. Lachos. "Multivariate measurement error models based on Student-t distribution under censored responses." Statistics 52, no. 6 (2018): 1395–416. http://dx.doi.org/10.1080/02331888.2018.1527841.

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Deschamps, Philippe J. "A flexible prior distribution for Markov switching autoregressions with Student-t errors." Journal of Econometrics 133, no. 1 (2006): 153–90. http://dx.doi.org/10.1016/j.jeconom.2005.03.012.

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Dear, Roger, and Zvi Drezner. "On the significance level of the multirelation coefficient." Journal of Applied Mathematics and Decision Sciences 1, no. 2 (1997): 119–30. http://dx.doi.org/10.1155/s1173912697000114.

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The concept of the multirelation coefficient is defined to describe the closeness of a set of variables to a linear relation. This concept extends the linear correlation between two variables to two or more variables. Parameters of a beta distribution are determined that are utilized to approximate significance levels of the multirelation coefficient for any given number of observations and variables. A generalized Student t distribution is defined. This distribution, which is termed the multirelated t distribution, reduces to the Student t distribution for two variables. It is useful in the determination of the significance level of the multirelation coefficient.

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Nugroho, Didit Budi, Bintoro Ady Pamungkas, and Hanna Arini Parhusip. "Volatility Fitting Performance of QGARCH(1,1) Model with Student-t, GED, and SGED Distributions." ComTech: Computer, Mathematics and Engineering Applications 11, no. 2 (2020): 97–104. http://dx.doi.org/10.21512/comtech.v11i2.6391.

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The research had two objectives. First, it compared the performance of the Generalized Autoregressive Conditional Heteroscedasticity (1,1) (GARCH) and Quadratic GARCH (1,1) (QGARCH)) models based on the fitting to real data sets. The model assumed that return error follows four different distributions: Normal (Gaussian), Student-t, General Error Distribution (GED), and Skew GED (SGED). Maximum likelihood estimation was usually employed in estimating the GARCH model, but it might not be easily applied to more complicated ones. Second, it provided two ways to evaluate the considered models. The models were estimated using the Generalized Reduced Gradient (GRG) Non-Linear method in Excel’s Solver and the Adaptive Random Walk Metropolis (ARWM) in the Scilab program. The real data in the empirical study were Financial Times Stock Exchange Milano Italia Borsa (FTSEMIB) and Stoxx Europe 600 indices over the daily period from January 2000 to December 2017 to test the conditional variance process and see whether the estimation methods could adapt to the complicated models. The analysis shows that GRG Non-Linear in Excel’s Solver and ARWM methods have close results. It indicates a good estimation ability. Based on the Akaike Information Criterion (AIC), the QGARCH(1,1) model provides a better fitting than the GARCH(1,1) model on each distribution specification. Overall, the QGARCH(1,1) with SGED distribution best fits both data.

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Fonseca, Thais C. O., Vinicius S. Cerqueira, Helio S. Migon, and Christian A. C. Torres. "Evaluating the performance of degrees of freedom estimation in asymmetric GARCH models with t-student innovations." Brazilian Review of Econometrics 40, no. 2 (2021): 347–73. http://dx.doi.org/10.12660/bre.v40n22020.80292.

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This work investigates the effects of using the independent Jeffreys prior for the degrees of freedom parameter of a t-student model in the asymmetric generalised autoregressive conditional heteroskedasticity (GARCH) model. To capture asymmetry in the reaction to past shocks, smooth transition models are assumed for the variance. We adopt the fully Bayesian approach for inference, prediction and model selection We discuss problems related to the estimation of degrees of freedom in the Student-t model and propose a solution based on independent Jeffreys priors which correct problems in the likelihood function. A simulated study is presented to investigate how the estimation of model parameters in the t-student GARCH model are affected by small sample sizes, prior distributions and misspecification regarding the sampling distribution. An application to the Dow Jones stock market data illustrates the usefulness of the asymmetric GARCH model with t-student errors.

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Chan, Jennifer S. K., S. T. Boris Choy, and Udi E. Makov. "Robust Bayesian Analysis of Loss Reserves Data Using the Generalized-t Distribution." ASTIN Bulletin 38, no. 01 (2008): 207–30. http://dx.doi.org/10.2143/ast.38.1.2030411.

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This paper presents a Bayesian approach using Markov chain Monte Carlo methods and the generalized-t (GT) distribution to predict loss reserves for the insurance companies. Existing models and methods cannot cope with irregular and extreme claims and hence do not offer an accurate prediction of loss reserves. To develop a more robust model for irregular claims, this paper extends the conventional normal error distribution to the GT distribution which nests several heavy-tailed distributions including the Student-t and exponential power distributions. It is shown that the GT distribution can be expressed as a scale mixture of uniforms (SMU) distribution which facilitates model implementation and detection of outliers by using mixing parameters. Different models for the mean function, including the log-ANOVA, log-ANCOVA, state space and threshold models, are adopted to analyze real loss reserves data. Finally, the best model is selected according to the deviance information criterion (DIC).

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Chan, Jennifer S. K., S. T. Boris Choy, and Udi E. Makov. "Robust Bayesian Analysis of Loss Reserves Data Using the Generalized-t Distribution." ASTIN Bulletin 38, no. 1 (2008): 207–30. http://dx.doi.org/10.1017/s0515036100015142.

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As’ad, Muhammad, Ely Anita, and Yulianto Yulianto. "PENGARUH KEPEMIMPINAN KEPALA SEKOLAH DAN KOMPETENSI PEDAGOGIK GURU TERHADAP HASIL BELAJAR SISWA SMK PGRI 11 CILEDUG PADA KOTA TANGERANG BANTEN." Transparansi Jurnal Ilmiah Ilmu Administrasi 1, no. 2 (2019): 149–57. http://dx.doi.org/10.31334/trans.v1i2.310.

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For the Effect of Principal Leadership and Teacher Pedagogical Competence on the learning outcomes of SMK PGRI 11 Ciledug students in Tangerang City, Banten, the method used was quantitative and questionnaire distribution using saturated samples. By using a statistical formula in which Variable X1 is the number of scores from respondents' questions about Principal Leadership and Variable X2 is the number of scores from respondents' questions about teacher pedagogical competencies and Y variable is the number of scores from respondents' questions about student learning outcomes. From the results of the comparison of t count (-8,202) and t table (1,995) then t count> t table means a negative significant effect between the principal's leadership on student learning outcomes. From the results of the comparison of t arithmetic 16.972 and t table 1.995, t count> from t table means a positive significant effect between teacher pedagogical competencies and student learning outcomes. From the results of the comparison of F count 2.116 F, table 0.309 then F count> F there is a significant influence between the leadership of the principal and the competent teachers of teachers on student learning outcomes..

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Agboola, Samson. "A Study of Literature on Robust Skew Student T Distribution for Parameter Estimation." International Journal of Wireless Communications and Mobile Computing 5, no. 3 (2017): 15. http://dx.doi.org/10.11648/j.wcmc.20170503.11.

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Zhu, Hao, Henry Leung, and Zhongshi He. "A variational Bayesian approach to robust sensor fusion based on Student-t distribution." Information Sciences 221 (February 2013): 201–14. http://dx.doi.org/10.1016/j.ins.2012.09.017.

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Wang, Xin, Zhongze Piao, Biye Wang, Runqing Yang, and Zhixiang Luo. "Robust Bayesian mapping of quantitative trait loci using Student-t distribution for residual." Theoretical and Applied Genetics 118, no. 3 (2008): 609–17. http://dx.doi.org/10.1007/s00122-008-0924-y.

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Gong, Yang, and Chen Cui. "A Robust SMC-PHD Filter for Multi-Target Tracking with Unknown Heavy-Tailed Measurement Noise." Sensors 21, no. 11 (2021): 3611. http://dx.doi.org/10.3390/s21113611.

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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.

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Motsnyi, F. V. "Chi-square, Student and Fisher-Snedecor Statistical Distributions and Their Application." Statistics of Ukraine 80, no. 1 (2018): 16–23. http://dx.doi.org/10.31767/su.1(80).2018.01.02.

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The Chi-square distribution is the distribution of the sum of squared standard normal deviates. The degree of freedom of the distribution is equal to the number of standard normal deviates being summed. For the first time this distribution was studied by astronomer F. Helmert in connection with Gaussian low of errors in 1876. Later K. Pearson named this function by Chi-square. Therefore Chi –square distribution bears a name of Pearson’s distribution. The Student's t-distribution is any member of a family of continuous probability distributions that arises when estimating the mean of a normally distributed population in situations where the sample size is small and population standard deviation is unknown. It was developed by W. Gosset in 1908. The Fisher–Snedecor distribution or F-distribution is the ratio of two-chi-squared variates. The F-distribution provides a basis for comparing the ratios of subsetsof these variances associated with different factors. The Fisher-distribution in the analysis of variance is connected with the name of R.Fisher (1924), although Fisher himself used quantity for the dispersion proportion. The Chi-square, Student and Fisher – Snedecor statistical distributions are connected enough tight with normal one. Therefore these distributions are used very extensively in mathematical statistics for interpretation of empirical data. The paper continues ideas of the author’s works [15, 16] devoted to advanced based tools of mathematical statistics. The aim of the work is to generalize the well known theoretical and experimental results of statistical distributions of random values. The Chi-square, Student and Fisher – Snedecor distributions are analyzed from the only point of view. The application peculiarities are determined at the examination of the agree criteria of the empirical sample one with theoretical predictions of general population. The numerical characteristics of these distributions are considered. The theoretical and experimental results are generalized. It is emphasized for the corrected amplification of the Chi-square, Student and Fisher – Snedecor distributions it is necessary to have the reliable empirical and testing data with the normal distribution.

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RAHMAN, MOHAMMAD MASUDUR, LAILA ARJUMAN ARA, and ZHENLONG ZHENG. "JUMP, NON-NORMAL ERROR DISTRIBUTION AND STOCK PRICE VOLATILITY — A NONPARAMETRIC SPECIFICATION TEST." Singapore Economic Review 54, no. 01 (2009): 101–21. http://dx.doi.org/10.1142/s0217590809003203.

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This paper examines a wide variety of popular volatility models for stock index return, including Random Walk model, Autoregressive model, Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model, and extensive GARCH model, GARCH-jump model with Normal, and Student t-distribution assumption as well as nonparametric specification test of these models. We fit these models to Dhaka stock return index from 20 November 1999 to 9 October 2004. There has been empirical evidence of volatility clustering, alike to findings in previous studies. Each market contains different GARCH models, which fit well. From the estimation, we find that the volatility of the return and the jump probability were significantly higher after 27 November 2001. The model introducing GARCH jump effect with normal and Student t-distribution assumption can better fit the volatility characteristics. We find that RW-GARCH-t, RW-AGARCH-t RW-IGARCH-t and RW-GARCH-M-t can pass the nonparametric specification test at 5% significance level. It is suggested that these four models can capture the main characteristics of Dhaka stock return index.

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Galea, Manuel, Heleno Bolfarine, and Filidor Vilcalabra. "Influence diagnostics for the structural errors-in-variables model under the Student-t distribution." Journal of Applied Statistics 29, no. 8 (2002): 1191–204. http://dx.doi.org/10.1080/0266476022000011265.

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Xu, Dingjie, Chen Shen, and Feng Shen. "A Robust Particle Filtering Algorithm With Non-Gaussian Measurement Noise Using Student-t Distribution." IEEE Signal Processing Letters 21, no. 1 (2014): 30–34. http://dx.doi.org/10.1109/lsp.2013.2289975.

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Adcock, C. J. "Asset pricing and portfolio selection based on the multivariate extended skew-Student-t distribution." Annals of Operations Research 176, no. 1 (2009): 221–34. http://dx.doi.org/10.1007/s10479-009-0586-4.

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Castro, Luis Mauricio, Denise Reis Costa, Marcos Oliveira Prates, and Victor Hugo Lachos. "Likelihood-based inference for Tobit confirmatory factor analysis using the multivariate Student-t distribution." Statistics and Computing 25, no. 6 (2014): 1163–83. http://dx.doi.org/10.1007/s11222-014-9502-0.

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Abid, Salah, Uday Quaez, and Javier Contreras-Reyes. "An Information-Theoretic Approach for Multivariate Skew-t Distributions and Applications." Mathematics 9, no. 2 (2021): 146. http://dx.doi.org/10.3390/math9020146.

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Shannon and Rényi entropies are two important measures of uncertainty for data analysis. These entropies have been studied for multivariate Student-t and skew-normal distributions. In this paper, we extend the Rényi entropy to multivariate skew-t and finite mixture of multivariate skew-t (FMST) distributions. This class of flexible distributions allows handling asymmetry and tail weight behavior simultaneously. We find upper and lower bounds of Rényi entropy for these families. Numerical simulations illustrate the results for several scenarios: symmetry/asymmetry and light/heavy-tails. Finally, we present applications of our findings to a swordfish length-weight dataset to illustrate the behavior of entropies of the FMST distribution. Comparisons with the counterparts—the finite mixture of multivariate skew-normal and normal distributions—are also presented.

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Beckman, Richard J., and Mark E. Johnson. "Fitting the Student-t Distribution to Grouped Data, with Application to a Particle Scattering Experiment." Technometrics 29, no. 1 (1987): 17. http://dx.doi.org/10.2307/1269879.

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Nugroho, Didit Budi, Tundjung Mahatma, and Yulius Pratomo. "Modeling of Stochastic Volatility to Validate IDR Anchor Currency." Gadjah Mada International Journal of Business 20, no. 2 (2018): 165. http://dx.doi.org/10.22146/gamaijb.26006.

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This study aims to assess the performance of stochastic volatility models for their estimation of foreign exchange rate returns' volatility using daily data from Bank Indonesia (BI). The model is then applied to validate the anchor currency of Indonesian rupiah (IDR). Two stylized facts are incorporated into the models: A correlation between the previous returns and their conditional variance, and return errors following four different error distributions namely Normal, Student-t, non-central Student-t, and generalized hyperbolic skew Student-t. The analysis is based on the application of daily returns data from nine foreign currency selling rates to IDR from 2010 to 2015, including the AUD, CHF, CNY, EUR, GBP, JPY, MYR, SGD, and USD. The main results are: (1) Mixed evidence of positive and negative relationships between the return and its variance were found, especially significant correlations being found for the IDR/AUD, IDR/CHF, IDR/JPY, IDR/SGD, and IDR/USD returns series; (2) the model with the generalized hyperbolic skew Student's t-distribution specification for the returns error provides the best performance; and (3) anchoring the IDR to established hard currencies is more appropriate than anchoring it to other currencies.

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Finlay, Richard, and Eugene Seneta. "Stationary-increment Student and variance-gamma processes." Journal of Applied Probability 43, no. 2 (2006): 441–53. http://dx.doi.org/10.1239/jap/1152413733.

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A continuous-time model with stationary increments for asset price {Pt} is an extension of the symmetric subordinator model of Heyde (1999), and allows for skewness of returns. In the setting of independent variance-gamma-distributed returns the model resembles closely that of Madan, Carr, and Chang (1998). A simple choice of parameters renders {e−rtPt} a familiar martingale. We then specify the activity time process, {Tt}, for which {Tt−t} is asymptotically self-similar and {τt}, with τt=Tt−Tt−1, is gamma distributed. This results in a skew variance-gamma distribution for each log price increment (return)Xtand a model for {Xt} which incorporates long-range dependence in squared returns. Our approach mirrors that for the (symmetric) Student process model of Heyde and Leonenko (2005), to which the present work is intended as a complement and a sequel. One intention is to compare, partly on the basis of fitting to data, versions of the general model wherein the returns have either (symmetric)t-distributions or variance-gamma distributions.

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Anjaningrum, Widiya Dewi. "PENERAPAN METODE STABLE TAIL ADJUSTED RETURN RATIO (STARR) DALAM PENGUKURAN KINERJA INVESTASI." Jurnal Ilmiah Bisnis dan Ekonomi Asia 10, no. 2 (2018): 91–97. http://dx.doi.org/10.32812/jibeka.v10i2.78.

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The purpose of this study was to determine the appropriate approach and method for measuring the performance of the investment, if the return data provided just a little or the data don’t follow the normal distribution. Then, apply it in a real case, that is, investment portfolio performance measurement of a pension fund managed by a private university in Malang town. Data processing was aided by MS Excel which the steps are calculating the average return (mean), standard deviation, VaR and CVaR, deviation VaR and CVaR, BI rate and STARR both in the case of a Gaussian distribution and T-Student. The result of the analysis showed that the T-Student distribution approach and STARR method are better to use for measuring pension fund investment performance than the Gaussian distribution approach and traditional Sharpe method. Two investment instruments that have the best performance are a Direct Placement and Property.

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Wu, Shengjun, Danmin Miao, Xia Zhu, et al. "THE PERSONALITY TYPES OF CHINESE DENTAL POSTGRADUATE STUDENTS." Social Behavior and Personality: an international journal 35, no. 8 (2007): 1077–86. http://dx.doi.org/10.2224/sbp.2007.35.8.1077.

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The objective of this study was to find the personality types of Chinese dental postgraduate students using the Chinese version of the Myers-Briggs Type Indicator (MBTI-Form G; Myers, 1987). The subjects were 372 dental postgraduate students and 336 postgraduates from other professions as a control group. The dental students were at Fourth Military Medical University and Xi'an Medical University. The control group attended Xi'an Jiaotong University. The three dominant personality types among the dental postgraduates were ISTJ (15.3%), ESTJ (13.7%) and ISFP (11.8%). The distribution of Extroversion (E) over Introversion (I) and Thinking (T) over Feeling (F) was different from other professions. Male and female dental postgraduates had similar types of mental attitude (E-I; judging-perceiving J-P) and mental function (sensing-intuition, S-N; T-F). Statistically significant differences were found between males and females in the distribution of J-P types. It was found that Chinese dental postgraduates have personality types that differ from the other comparative Chinese professional student groups.

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Korolev, V. Yu. "On the relationship between the generalized student t-distribution and the variance gamma distribution in statistical analysis of random-size samples." Doklady Mathematics 86, no. 1 (2012): 566–70. http://dx.doi.org/10.1134/s1064562412040424.

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Khumairah, Rantika, Agus Sundaryono, and Dewi Handayani. "PENGARUH MODEL PEMBELAJARAN FLIPPED CLASSROOM TERHADAP HASIL BELAJAR KIMIA SISWA PADA MATERI LARUTAN PENYANGGA DI SMAN 5 KOTA BENGKULU." Alotrop 4, no. 2 (2020): 92–97. http://dx.doi.org/10.33369/atp.v4i2.13832.

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The purposes of this study is to know student learning outcomes of chemistry using flipped classroom learning model and know influence of flipped classroom learning model to on buffer solution. The study was conducted in February-March of 2019 in SMAN 5 Bengkulu City This study is pre-experimental design with one-grup pretes-posttest design. Population of this study is all of XI MIPA’s student which a total of 216 students with sample of this study is XI MIPA 5’s student which a total of 36 students. Technique of sampling in this study is used with purposive sampling technique. Instrument of this study used test of learning outcomes with 20 items pretest and posttest. Analysis of the data used are mean values, normality test, homogeneity test, and t-test to the student learning outcomes. Based on normality test and homogeneity test obtained that pretest and posttest have normal distribution and distributed to homogeneous. Average value of pretest and posttest are 60,1 and 80,0. The result of hypotheses using t-test showed that value of significance is 0.000 < 0.05, so flipped classroom model influenced of significance to student learning outcomes. The result of this study showed that flipped classroom learning model can positive influence to learning outcomes and increased student learning outcomes on buffer solution in XI MIPA 5 SMA N 5 Bengkulu city on academic year of 2018/2019.

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Agboola, S., H. G. Dikko, and O. E. Asiribo. "On Exponentiated Skewed Student t Error Distribution on Some Heteroscedastic Models: Evidence of Nigeria Stock Exchang." Journal of Statistics Applications & Probability 7, no. 1 (2018): 205–16. http://dx.doi.org/10.18576/jsap/070118.

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Chan, C. M., and S. K. Tang. "On analysis of exponentially decaying pulse signals using stochastic volatility model. Part II: Student-t distribution." Journal of the Acoustical Society of America 120, no. 4 (2006): 1783–86. http://dx.doi.org/10.1121/1.2266455.

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Syaputra, Ahmad Danu, Fitria Fitria, and Dheo Rimbano. "Perbandingan Model Pembelajaran Mata Kuliah Metodologi Penelitian Dalam Meningkatkan Kompetensi Mahasiswa." FOKUS Jurnal Kajian Keislaman dan Kemasyarakatan 4, no. 2 (2019): 149. http://dx.doi.org/10.29240/jf.v4i2.1092.

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The lack of analytical, critical and creative attitudes occurs because of the mindset of students or their teaching staff. This explanation is the basis for why researchers try to study with the aim of making a Comparative Study Model for Research Methodology Courses in Improving Student Competencies to Arrange Final Projects in PTS (Private Universities) in Lubuklinggau City and Musi Rawas Districts. The research population of 5,604 students spread across well-known private Universities in Lubuklinggau City and Musi Rawas District, researchers took a sample of 1%, with a uniform distribution. The researcher uses the frequency crosstab analysis (cross percentage), for the comparative type the researcher uses the technique of One Sample T Test, Independent Sample T Test, and One Way Anova. Research results (1) There are differences in each PTS in the application of learning models in general; (2) There is no difference in each PTS in the application of specific learning models, both the parametric approach model and the micromorph approach model; (3) There are differences in student competencies in each in terms of physical competence; and (4) There are no differences in student competencies in each in terms of intellectual competence; personal; social; and spiritual.

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Canton, Letícia E. D., Luciana P. C. Guedes, Miguel A. Uribe-Opazo, Rosangela A. B. Assumpção, and Tamara C. Maltauro. "Sampling redesign of soil penetration resistance in spatial t-Student models." Spanish Journal of Agricultural Research 19, no. 1 (2021): 0202. http://dx.doi.org/10.5424/sjar/2021191-16949.

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Aim of study: To reduce the sample size in an agricultural area of 167.35 hectares, cultivated with soybean, to analyze the spatial dependence of soil penetration resistance (SPR) with outliers. Area of study: Cascavel, Brazil Material and methods: The reduction of sample size was made by the univariate effective sample size ( ) methodology, assuming that the t-Student model represents the probability distribution of SPR. Main results: The radius and the intensity of spatial dependence have an inverse relationship with the estimated value of the . For the depths of SPR with spatial dependence, the highest estimated value of the reduced the sample size by 40%. From the new sample size, the sampling redesign was performed. The accuracy indexes showed differences between the thematic maps with the original and reduced sampling designs. However, the lowest values of the standard error in the parameters of the spatial dependence structure evidenced that the new sampling design was appropriate. Besides, models of semivariance function were efficiently estimated, which allowed identifying the existence of spatial dependence in all depth of SPR.Research highlights: The sample size was reduced by 40%, allowing for lesser financial investments with data collection and laboratory analysis of soil samples in the next mappings in the agricultural area. The spatial t-Student model was able to reduce the influence of outliers in the spatial dependence structure.

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Sismulyanto, Sismulyanto, and Made Mahaguna Putra. "Effectiveness Learning Model Mind Mapping, Discussion, and Role Playing in Learning Outcomes Nursing Student in Community Nursing." INDONESIAN NURSING JOURNAL OF EDUCATION AND CLINIC (INJEC) 3, no. 1 (2018): 9. http://dx.doi.org/10.24990/injec.v3i1.178.

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Introduction: Low graduation rates UKNI (Indonesian nurses Competency Test) encourages nursing students for their innovative teaching model. MDR learning methods (Mind mapping, discussion and role play) is a new teaching method and innovative that can improve student understanding. The purpose of this study was to determine the effect of learning the MDR model towards the understanding of the students in the subject of community nursing. Methods: This study uses a pre-experiment approach pre-post test. Sample of this study was 50 7th-semester student. All students who followed the MDR learning model were given practice questions then followed this learning model and measured again using practice questions. Results: Analysis of data using statistical test paired t-test. Distribution of respondents by sex is 15 people (30 %) men and 35 (70%) of women. Average male student GPA was 3.1, average female student GPA was 3.3. Conclusions: The results show that there are differences in the pre and post (mean = 35.46). Learning MDR Model improves critical thinking, motivation and makes learning fun.Keywords : Mind Mapping, Nursing, Education, Discussion, Role Playing

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Yugianti, Astiti, Sigid Edy Purwanto, and Mimin Ninawati. "The Influence of Brain Based Learning Model to Mathematical Creative Thinking Skills of Student." Jurnal Inovasi Pendidikan Dasar 3, no. 2 (2018): 53–58. http://dx.doi.org/10.22236/jipd.v3i2.45.

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The purpose of the research was to find out the influence of using Brain Based Learning model to mathematical creative thinking skills of student. The research method was quasi experiment with Posttest-Only Control Design. Population of this research are 60 students consist of 30 from experiment class and 30 from control class. The technique sampling was saturation sampling. The data analysis using T test. Prior to hypothesis testing, there were two prerequisite tests that consist of the normality test and homogeneity test. The result of prerequisite tests showed that both classes had the normal distribution and the same variance. Based on the t-test, it can be seen that there was an influence of Brain Based Learning model mathematical creative thinking.

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Wang, Pengyuan, Mikhail Traskin, and Dylan S. Small. "Robust Inferences from a Before-and-After Study with Multiple Unaffected Control Groups." Journal of Causal Inference 1, no. 2 (2013): 209–34. http://dx.doi.org/10.1515/jci-2012-0010.

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AbstractThe before-and-after study with multiple unaffected control groups is widely applied to study treatment effects. The current methods usually assume that the control groups’ differences between the before and after periods, i.e. the group time effects, follow a normal distribution. However, there is usually no strong a priori evidence for the normality assumption, and there are not enough control groups to check the assumption. We propose to use a flexible skew-t distribution family to model group time effects, and consider a range of plausible skew-t distributions. Based on the skew-t distribution assumption, we propose a robust-t method to guarantee nominal significance level under a wide range of skew-t distributions, and hence make the inference robust to misspecification of the distribution of group time effects. We also propose a two-stage approach, which has lower power compared to the robust-t method, but provides an opportunity to conduct sensitivity analysis. Hence, the overall method of analysis is to use the robust-t method to test for the overall hypothesized range of shapes of group variation; if the test fails to reject, use the two-stage method to conduct a sensitivity analysis to see if there is a subset of group variation parameters for which we can be confident that there is a treatment effect. We apply the proposed methods to two datasets. One dataset is from the Current Population Survey (CPS) to study the impact of the Mariel Boatlift on Miami unemployment rates between 1979 and 1982.The other dataset contains the student enrollment and grade repeating data in West Germany in the 1960s with which we study the impact of the short school year in 1966–1967 on grade repeating rates.

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Bohdalová, Mária, and Michal Greguš. "ESTIMATING THE HEDGE RATIOS." CBU International Conference Proceedings 4 (September 17, 2016): 229–34. http://dx.doi.org/10.12955/cbup.v4.874.

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This paper examines the problem of hedging portfolio returns. Many practitioners and academicians endeavor to solve the problem of how to calculate the optimal hedge ratio accurately. In this paper we compare estimates of the hedge ratio from a classical approach of a linear quantile regression, based on selected quantiles as medians, with that of a non-linear quantile regression. To estimate the hedge ratios, we have used a calibrated Student t distribution for the marginal densities and a Student t copula of the portfolio returns using a maximum likelihood estimation. We created two portfolios of the assets, one for equal weight and another for optimal weight in respect of minimal risk. Our findings show that an assumption of Student t marginal leads to a better estimation of the hedge ratio.

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