A fortran implementation of univariate fourier series density estimation

A set of Fortran-77 subroutines is described which compute a nonparametric density estimator expressed as a Fourier series. In addition, a subroutine is given for the estimation of a cumulative distribution. Performance measures are given based on samples from a Weibull distribution. Due to small size and modest space demands, these subroutines are easily implemented on most small computers.     

The collected works of john w. tukey

We describe novel, analytical, data-analysis, and Monte-Carlo-simulation studies of strongly heteroscedastic data of both small and wide range.Many different types of heteroscedasticity and fixed or variable weighting are incorporated through error-variance models.Attention is given to parameter bias determinations, evaluations of their significances, and to new ways to correct for bias.The error-variance models allow for both additive and independent power-law errors, and the power exponent is shown to be able to be well determined for typical physicalsciences data by the rapidly-converging, general-purpose, extended-least-squares program we use.The fitting and error-variance models are applied to both low-and high-heteroscedasticity situations, including single-response data from radioactive decay.Monte-Carlo simulations of data with similar parameters are used to evaluate the analytical models developed and the various minimization methods em-ployed, such as extended and generalized least squares.Logarithmic and inversion transformations are investigated in detail, and it is shown analytically and by simulations that exponential data with constant percentage errors can be logarithmically transformed to allow a simple parameter-bias-removal procedure.A more-general bias-reduction approach combining direct and inversion fitting is also developed.Distributions of fitting-model and error-variance-model parameters are shown to be typically non-normal, thus invalidating the usual estimates of parameter bias and precision.Errors in conventional confidence-interval estimates are quantified by comparison with accurate simulation results.     

An algorithm to compute the cdf of the product of two normal random variables

This paper provides a fortran algorithm that can be used to compute the cdf of the product of two normal distribution random variables. We also give references that provide mathematical properties, tables, and applications of this distribution     

A stepwise discrete variable selection procedure

A stepwise variable selection procedure for multinomial discrimination is presented and discussed. Based upon the work of Kullback and Hills, stopping rules are proposed and illustrated for a set of data on communication buyer behavior.     

How non-normality affects the quadratic discriminant function

The quadratic discriminant function is commonly used for the two group classification problem when the covariance matrices in the two populations are substantially unequal. This procedure is optimal when both populations are multivariate normal with known means and covariance matrices. This study examined the robustness of the QDF to non-normality. Sampling experiments were conducted to estimate expected actual error rates for the QDF when sampling from a variety of non-normal distributions. Results indicated that the QDF was robust to non-normality except when the distributions were highly skewed, in which case relatively large deviations from optimal were observed. In all cases studied the average probabilities of misclassification were relatively stable while the individual population error rates exhibited considerable variability.     

Time Series Modeling of Degradation Due to Outdoor Weathering

Environmental variables have an important effect on the reliability of many products such as coatings and polymeric composites. Long-term prediction of the performance or service life of such products must take into account the probabilistic/stochastic nature of the outdoor weather. In this article, we propose a time series modeling procedure to model the time series data of daily accumulated degradation. Daily accumulated degradation is the total amount of degradation accrued within one day and can be obtained by using a degradation rate model for the product and the weather data. The fitted model of the time series can then be used to estimate the future distribution of cumulative degradation over a period of time, and to compute reliability measures such as the probability of failure. The modeling technique and estimation method are illustrated using the degradation of a solar reflector material. We also provide a method to construct approximate confidence intervals for the probability of failure.