Multivariate Normal Data: A Tool for Instruction

1992 ◽  
Vol 19 (3) ◽  
pp. 188-189 ◽  
Author(s):  
John F. Walsh
Keyword(s):  
Monte Carlo ◽  
Experimental Design ◽  
Monte Carlo Simulations ◽  
Covariance Structure ◽  
Data Sets ◽  
Multivariate Normal ◽  
International Mathematical ◽  
Statistical Library ◽  
Scale Transformations

Courses in statistics and experimental design can be enhanced through use of crafted data sets. The use of examples highlights the interface between data and statistical routine. FORTRAN programs utilizing the International Mathematical and Statistical Library subroutines permit the user to control the variance—covariance structure of multivariate normal variables and build data sets that have instructional value. Scale transformations and Monte Carlo simulations of the data can be performed as well.

scholarly journals On spherical Monte Carlo simulations for multivariate normal probabilities

2015 ◽  
Vol 47 (03) ◽  
pp. 817-836 ◽  
Author(s):  
Huei-Wen Teng ◽  
Ming-Hsuan Kang ◽  
Cheng-Der Fuh
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Variance Reduction ◽  
Multivariate Normal ◽  
Integration Rule ◽  
Radial Integral ◽  
Normal Probability ◽  
Antithetic Variates ◽  
Number Problem ◽  
Spherical Transformation

The calculation of multivariate normal probabilities is of great importance in many statistical and economic applications. In this paper we propose a spherical Monte Carlo method with both theoretical analysis and numerical simulation. We start by writing the multivariate normal probability via an inner radial integral and an outer spherical integral using the spherical transformation. For the outer spherical integral, we apply an integration rule by randomly rotating a predetermined set of well-located points. To find the desired set, we derive an upper bound for the variance of the Monte Carlo estimator and propose a set which is related to the kissing number problem in sphere packings. For the inner radial integral, we employ the idea of antithetic variates and identify certain conditions so that variance reduction is guaranteed. Extensive Monte Carlo simulations on some probabilities confirm these claims.

State-Dependent Demand Estimation with Initial Conditions Correction

2020 ◽  
Vol 57 (5) ◽  
pp. 789-809
Author(s):  
Andrey Simonov ◽  
Jean-Pierre Dubé ◽  
Günter Hitsch ◽  
Peter Rossi
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Initial Conditions ◽  
Brand Choice ◽  
State Dependence ◽  
The State ◽  
Data Sets ◽  
True Parameter ◽  
State Dependent ◽  
Initial Conditions Problem

The authors analyze the initial conditions bias in the estimation of brand choice models with structural state dependence. Using a combination of Monte Carlo simulations and empirical case studies of shopping panels, they show that popular, simple solutions that misspecify the initial conditions are likely to lead to bias even in relatively long panel data sets. The magnitude of the bias in the state dependence parameter can be as large as a factor of 2–2.5. The authors propose a solution to the initial conditions problem that samples the initial states as auxiliary variables in a Markov chain Monte Carlo procedure. The approach assumes that the joint distribution of prices and consumer choices is in equilibrium, which is plausible for the mature consumer packaged goods products commonly used in empirical applications. In Monte Carlo simulations, the approach recovers the true parameter values even in relatively short panels. Finally, the authors propose a diagnostic tool that uses common, biased approaches to bound the values of the state dependence and construct a computationally light test for state dependence.

scholarly journals Selection Bias in Comparative Research: The Case of Incomplete Data Sets

2003 ◽  
Vol 11 (3) ◽  
pp. 255-274 ◽  
Author(s):  
Simon Hug
Keyword(s):  
Monte Carlo ◽  
Political Parties ◽  
Monte Carlo Simulations ◽  
Recent Work ◽  
Selection Bias ◽  
Incomplete Data ◽  
Comparative Research ◽  
Data Sets ◽  
Comparative Case Studies ◽  
Cross National

Selection bias is an important but often neglected problem in comparative research. While comparative case studies pay some attention to this problem, this is less the case in broader cross-national studies, where this problem may appear through the way the data used are generated. The article discusses three examples: studies of the success of newly formed political parties, research on protest events, and recent work on ethnic conflict. In all cases the data at hand are likely to be afflicted by selection bias. Failing to take into consideration this problem leads to serious biases in the estimation of simple relationships. Empirical examples illustrate a possible solution (a variation of a Tobit model) to the problems in these cases. The article also discusses results of Monte Carlo simulations, illustrating under what conditions the proposed estimation procedures lead to improved results.

scholarly journals The Generalized Transmuted Poisson-G Family of Distributions: Theory, Characterizations and Applications

2018 ◽  
pp. 759-779 ◽  
Author(s):  
Haitham Yousof ◽  
Ahmed Z Afify ◽  
Morad Alizadeh ◽  
G. G. Hamedani ◽  
S. Jahanshahi ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Order Statistics ◽  
Real Data ◽  
Model Parameters ◽  
Data Sets ◽  
Continuous Distributions ◽  
New Class ◽  
Mathematical Properties ◽  
Family Of Distributions

In this work, we introduce a new class of continuous distributions called the generalized poissonfamily which extends the quadratic rank transmutation map. We provide some special models for thenew family. Some of its mathematical properties including Rényi and q-entropies, order statistics andcharacterizations are derived. The estimations of the model parameters is performed by maximumlikelihood method. The Monte Carlo simulations is used for assessing the performance of the maximumlikelihood estimators. The ‡exibility of the proposed family is illustrated by means of two applicationsto real data sets.

scholarly journals Data sets of migration barriers for atomistic Kinetic Monte Carlo simulations of Fe self-diffusion

Data in Brief ◽  
2018 ◽  
Vol 19 ◽  
pp. 564-569
Author(s):  
Ekaterina Baibuz ◽  
Simon Vigonski ◽  
Jyri Lahtinen ◽  
Junlei Zhao ◽  
Ville Jansson ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Kinetic Monte Carlo ◽  
Data Sets ◽  
Self Diffusion ◽  
Migration Barriers ◽  
Kinetic Monte Carlo Simulations

scholarly journals On spherical Monte Carlo simulations for multivariate normal probabilities

2015 ◽  
Vol 47 (3) ◽  
pp. 817-836 ◽  
Author(s):  
Huei-Wen Teng ◽  
Ming-Hsuan Kang ◽  
Cheng-Der Fuh
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Variance Reduction ◽  
Multivariate Normal ◽  
Integration Rule ◽  
Radial Integral ◽  
Normal Probability ◽  
Antithetic Variates ◽  
Number Problem ◽  
Spherical Transformation

The calculation of multivariate normal probabilities is of great importance in many statistical and economic applications. In this paper we propose a spherical Monte Carlo method with both theoretical analysis and numerical simulation. We start by writing the multivariate normal probability via an inner radial integral and an outer spherical integral using the spherical transformation. For the outer spherical integral, we apply an integration rule by randomly rotating a predetermined set of well-located points. To find the desired set, we derive an upper bound for the variance of the Monte Carlo estimator and propose a set which is related to the kissing number problem in sphere packings. For the inner radial integral, we employ the idea of antithetic variates and identify certain conditions so that variance reduction is guaranteed. Extensive Monte Carlo simulations on some probabilities confirm these claims.

The Performance of Modified Least Trimmed Squares-Based Methods for Large Data Sets Based on Monte Carlo Simulations

2016 ◽  
Vol 22 (12) ◽  
pp. 4359-4363
Author(s):  
Nur Azimah Rahim Abdul ◽  
Norazan Mohamed Ramli ◽  
Nor Azura Md Ghani
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Large Data ◽  
Large Data Sets ◽  
Data Sets ◽  
Least Trimmed Squares
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