Simulation of the p-generalized Gaussian distribution

In this paper, we introduce the p-generalized polar methods for the simulation of the p-generalized Gaussian distribution. On the basis of geometric measure representations, the well-known Box–Muller method and the Marsaglia–Bray rejecting polar method for the simulation of the Gaussian distribution are generalized to simulate the p-generalized Gaussian distribution, which fits much more flexibly to data than the Gaussian distribution and has already been applied in various fields of modern sciences. To prove the correctness of the p-generalized polar methods, we give stochastic representations, and to demonstrate their adequacy, we perform a comparison of six simulation techniques w.r.t. the goodness of fit and the complexity. The competing methods include adapted general methods and another special method. Furthermore, we prove stochastic representations for all the adapted methods.     

A consistent method of estimation for the parameters of the three-parameter inverse Gaussian distribution

In this paper, we propose a consistent method of estimation for the parameters of the three-parameter inverse Gaussian distribution. We then discuss some properties of these estimators and show by means of a Monte Carlo simulation study that the proposed estimators perform better than some other prominent estimators in terms of bias and root mean squared error. Finally, we present two real-life examples to illustrate the method of inference developed here.     

Accent on Teaching Materials

A linear combination test for combining several tests of the correlation coefficient in the bivariate normal distribution is proposed. The linear combination test is compared with the well-known Fisher method of combining tests. It is shown by a Monte Carlo study that the linear combination test has a larger power.     

On the Alias Method for Generating Random Variables from a Discrete Distribution

The alias method of Walker is a clever, new, fast method for generating random variables from an arbitrary, specified discrete distribution. A simple probabilistic proof is given, in terms of mixtures, that the method works for any discrete distribution with a finite number of outcomes. A more efficient version of the table-generating portion of the method is described. Finally, a brief discussion on efficiency of the method is given. We believe that the generality, speed, and simplicity of the method make it attractive for use in generating discrete random variables.     

An Empirical Comparison of Estimating Methods for the Ramberg–Osgood EIV Model

The standard tensile test is one of the most frequent tools performed for the evaluation of mechanical properties of metals. An empirical model proposed by Ramberg and Osgood fits the tensile test data using a nonlinear model for the strain in terms of the stress. It is an Error-In-Variables (EIV) model because of the uncertainty affecting both strain and stress measurement instruments. The SIMEX, a simulation-based method for the estimation of model parameters, is powerful in order to reduce bias due to the measurement error in EIV models. The plan of this article is the following. In Sec. 2, we introduce the Ramberg–Osgood model and another reparametrization according to different assumptions on the independent variable. In Sec. 3, there is a summary of SIMEX method for the case at hand. Section 4 is a comparison between SIMEX and others estimating methods in order to highlight the peculiarities of the different approaches. In the last section, there are some concluding remarks.     

A Practical Implementation and Bayesian Estimation in Franklin's Randomized Response Procedure

A Bayesian estimator based on Franklin's randomized response procedure is proposed for proportion estimation in surveys dealing with a sensitive character. The method is simple to implement and avoids the usual drawbacks of Franklin's estimator, i.e., the occurrence of negative estimates when the population proportion is small. A simulation study is considered in order to assess the performance of the proposed estimator as well as the corresponding credible interval.     

Evaluation of the parameters of su by rational fractions

A rational fraction approximation is given for a function of one of the parameters defining Johnson's S_UError assessment for a segment of the domain of validity shows remarkable accuracy.     

Inferences on regression coefficients in a regression model under heteroscedasticity and robustness with respect to departure from normality

In this paper we consider a simple linear regression model under heteroscedasticity and nonnormality. A statistical test for testing the regression coefficient is then derived by assuming normality for the random disturbances and by applying Welch's method. Some Monte Carlo studies are generated for assessing robustness of this test. By combining Tiku's robust procedure with the new test, a robust but more powerful test is developed.     

Tables to Facilitate Fitting Tadikamalla and Johnson's LB Distributions

This paper is concerned with estimating the parameters of Tadikamalla-Johnson's L_B distribution using the first four moments. Tables of the parameters of the L_B distribution are given for selected values of skewness (0.0(0.05) 1.0(0.1)2.0) and corresponding available values of kurtosis at intervals of 0.2. The construction and use of these tables is explained with a numerical example.     

Small sample properties of parameter estimation in the dirichlet distribution

A numerically feasible algorithm is proposed for maximum likelihood estimation of the parameters of the Dirichlet distribution. The performance of the proposed method is compared with the method of moments using bias ratio and squared errors by Monte Carlo simulation. For these criteria, it is found that even in small samples maximum likelihood estimation has advantages over the method of moments.