Comparison of estimation methods for the Weibull distribution

Weibull distributions have received wide ranging applications in many areas including reliability, hydrology and communication systems. Many estimation methods have been proposed for Weibull distributions. But there has not been a comprehensive comparison of these estimation methods. Most studies have focused on comparing the maximum likelihood estimation (MLE) with one of the other approaches. In this paper, we first propose an L-moment estimator for the Weibull distribution. Then, a comprehensive comparison is made of the following methods: the method of maximum likelihood estimation (MLE), the method of logarithmic moments, the percentile method, the method of moments and the method of L-moments.     

Peer and Selection Effects on Youth Smoking in California

Previous research has found that youth smoking choices are strongly influenced by peer smoking. However, these studies often fail to account for simultaneity and nonrandom peer selection. This article describes an equilibrium model of peer effects that incorporates both of these features, and estimates its parameters using data on California teenagers. Identification is aided by using the influence of observable variables on group selection as a proxy for the influence of unobservables. I find that the effect of peer smoking on the decision to smoke is much weaker than found in previous studies.     

Tables of the cumulative non-central cm-square distribution-part 4

The cumulative non-central chi-square .distribution is tabulated for all combinations of values of λ = 0 (0.1) 1.0 (0.2) 3.0 (0.5) 5.0 (1.0) 34.0, y=l (I) 30 (2) 50 (5) 100 and y = 0.01 (0.01) 0.1 (0.1) 1.0 (0.2) 3.0 (0.5) 10.0 (1.0 30,0 (2.0) 50,0 (5.0) 165.0. The computations have been correctly rounded to five decimal places. Also, there is a discussion about the error involved in the computations. Furthermore, there is a discussion about possible interpolation in the table using the Lagrange's method     

Confidence regions for parameters in linear models with additional information

Using given significant additional information it is possible to improve different confidence regions for the regression parameters in a linear model. Thereby, the given informations may concern the expectation and (or) the variance of the observations, and an improvement is possible in the sense of the decrease of the confidence regions' size. In particular it is possible to improve the so called confidence ellipsoids which are often used to estimate the considered parameters.     

Log-linear models for correlated marginal totals of a contingency table

The marginal totals of a contingency table can be rearranged to form a new table. If at least twoof these totals include the same cell of the original table, the new table cannot be treated as anordinary contingency table. An iterative method is proposed to calculate maximum likelihood estimators for the expected cell frequencies of the original table under the assumption that some marginal totals (or more generally, some linear functions) of these expected frequencies satisfy a log-linear model.In some cases, a table of correlated marginal totals is treated as if it was an ordinary contingency table. The effects of ignoring the special structure of the marginal table on thedistributionof the goodness-of-fit test statistics are discussed and illustrated, with special reference to stationary Markov chains.     

More powerful modifications of unit root tests allowing structural change

It is well known that more powerful variants of Dickey–Fuller unit root tests are available. We apply two of these modifications, on the basis of simple maximum statistics and weighted symmetric estimation, to Perron tests allowing for structural change in trend of the additive outlier type. Local alternative asymptotic distributions of the modified test statistics are derived, and it is shown that their implementation can lead to appreciable finite sample and asymptotic gains in power over the standard tests. Also, these gains are largely comparable with those from GLS-based modifications to Perron tests, though some interesting differences do arise. This is the case for both exogenously and endogenously chosen break dates. For the latter choice, the new tests are applied to the Nelson–Plosser data.     

Bayesian sample size determination for estimating binomial parameters from data subject to misclassification

We investigate the sample size problem when a binomial parameter is to be estimated, but some degree of misclassification is possible. The problem is especially challenging when the degree to which misclassification occurs is not exactly known. Motivated by a Canadian survey of the prevalence of toxoplasmosis infection in pregnant women, we examine the situation where it is desired that a marginal posterior credible interval for the prevalence of width w has coverage 1−α, using a Bayesian sample size criterion. The degree to which the misclassification probabilities are known a priori can have a very large effect on sample size requirements, and in some cases achieving a coverage of 1−α is impossible, even with an infinite sample size. Therefore, investigators must carefully evaluate the degree to which misclassification can occur when estimating sample size requirements.     

Simulation-Based Density Estimation for Time Series Using Covariate Data

This article proposes a simulation-based density estimation technique for time series that exploits information found in covariate data. The method can be paired with a large range of parametric models used in time series estimation. We derive asymptotic properties of the estimator and illustrate attractive finite sample properties for a range of well-known econometric and financial applications.     

Space-time Multi Type Log Gaussian Cox Processes with a View to Modelling Weeds

Log Gaussian Cox processes as introduced in Moller et al. (1998) are extended to space-time models called log Gaussian Cox birth processes. These processes allow modelling of spatial and temporal heterogeneity in time series of increasing point processes consisting of different types of points. The models are shown to be easy to analyse yet flexible enough for a detailed statistical analysis of a particular agricultural experiment concerning the development of two weed species on an organic barley field. Particularly, the aspects of estimation, model validation and intensity surface prediction are discussed.     

Nonlinear voxel-based modelling of the haemodynamic response in fMRI

A common assumption for data analysis in functional magnetic resonance imaging is that the response signal can be modelled as the convolution of a haemodynamic response (HDR) kernel with a stimulus reference function. Early approaches modelled spatially constant HDR kernels, but more recently spatially varying models have been proposed. However, convolution limits the flexibility of these models and their ability to capture spatial variation. Here, a range of (nonlinear) parametric curves are fitted by least squares minimisation directly to individual voxel HDRs (i.e., without using convolution). A ‘constrained gamma curve’ is proposed as an efficient form for fitting the HDR at each individual voxel. This curve allows for spatial variation in the delay of the HDR, but places a global constraint on the temporal spread. The approach of directly fitting individual parameters of HDR shape is demonstrated to lead to an improved fit of response estimates.