Markov Chains and De-initializing Processes

We define a notion of de-initializing Markov chains. We prove that to analyse convergence of Markov chains to stationarity, it suffices to analyse convergence of a de-initializing chain. Applications are given to Markov chain Monte Carlo algorithms and to convergence diagnostics.     

Alternative Factors for Control Chart Construction

Conflicting decision signals resulting from Shewhart Mean and Variability Control Charts produce undesirable consequences. Therefore, we construct “six-sigma” control charts by alternative methods to avoid problems associated with Control Charts yielding different signals. By adjusting methods for control chart construction for dispersion charts, we produce new reference tables. The new tables provide consistent signals and appear similar and familiar to users of historical tables.     

On the use of curve fitting to model the error of the Cornish-Fisher expansion of the pearson type-VI distribution

The Cornish-Fisher expansion of the Pearson type VI distribution is known to be reasonably accurate when both degrees of freedom are relatively large (say greater than or equal to 5). However, when either or both degrees of freedom are less than 5, the accuracy of the computed percentage point begins to suffer; in some cases severely. To correct for this, the error surface in the degrees of freedom plane is modeled by least squares curve fitting for selected levels of tail probability (.025, .05, and .10) which can be used to adjust the percentage point obtained from the usual Cornish-Fisher expansion. This adjustment procedure produces a computing algorithm that computes percentage points of the Pearson type VI distribution at the above probability levels, accurate to at least + 1 in 3 digits in approximately 11 milliseconds per subroutine call on an IBM 370/145. This adjusted routine is valid for both degrees of freedom greater than or equal to 1.     

Interdistributional Income Inequality

Incomplete moments are used to characterize income inequality and provide the basis for interdistributional Lorenz curves. Four measures of interdistributional inequality are considered and seen to be related to an interdistributional welfare interpretation. Based upon these measures, there has been a significant secular decline in interdistributional inequality between blacks and whites over the past 30 years.     

Estimating the Structure of Agricultural Investment: A Stochastic- Coefficients Approach

Two approaches, a flexibie-accelerator model and a stochastic-coefficients alternative, are used to estimate the structure of aggregate agricultural investment. Structural estimates of the adjustment rates for each model differ. The stochastic-coefficients model, however, performs better in out-of-sample forecasting.