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A class of bivariate continuous-discrete distributions is proposed to fit Poisson dynamic models in a single unified framework via bivariate mixture transition distributions (BMTDs). Potential advantages of this class over the current models include its ability to capture stretches, bursts and nonlinear patterns characterized by Internet network traffic, high-frequency financial data and many others. It models the inter-arrival times and the number of arrivals (marks) in a single unified model which benefits from the dependence structure of the data. The continuous marginal distributions of this class include as special cases the exponential, gamma, Weibull and Rayleigh distributions (for the inter-arrival times), whereas the discrete marginal distributions are geometric and negative binomial. The conditional distributions are Poisson and Erlang. Maximum-likelihood estimation is discussed and parameter estimates are obtained using an expectation–maximization algorithm, while the standard errors are estimated using the missing information principle. It is shown via real data examples that the proposed BMTD models appear to capture data features better than other competing models. [ABSTRACT FROM PUBLISHER]

In this study, an incident pulse signal of several harmonics (i.e., multiples of the fundamental frequency) was used as a source in the time domain reflectometry (TDR) probing technique. Reflected signals were captured by an oscilloscope and their characteristics were determined via eigendecomposition. Autoregressive modeling and singular value decomposition were used to calculate the eigenvalues and the most significant ones were identified based on power spectrum. A multivariate statistical analysis was performed for the two most dominant eigenvalues, which are dependent on water content and salt concentrations, and regression equations were obtained. To determine the water content and salt concentrations in terms of the first and second eigenvalues, a modified Powell hybrid algorithm was used to solve the obtained system of nonlinear equations. Actual and predicted results are in agreement indicating that the developed method is very successful in predicting water content and salt concentrations. Furthermore, on comparing the eigendecomposition method with Fourier spectral analysis, one can observe that the former is superior in predicting water content and salt concentrations. [ABSTRACT FROM AUTHOR]

Explores the problem of constructing confidence intervals to estimate the mean in a two-stage nested model. Approximate intervals based on linear and nonlinear estimators; Use of the bootstrap method to correct the bias in the usual variance of nonlinear estimators; Failure of nonlinear estimator-based intervals to achieve a nominal confidence coefficients; Performance in terms of coverage and length.

Investigates two 'non-exact' t-type tests of the individual coefficients of a linear regression model, based on two ordinary ridge estimators. Theoretical motivation of the ridge-based t-type tests; Description of the simulation study.