Does the Moment-Generating Function Characterize a Distribution?

It is shown that two visibly distinct distributions can have almost identical moment-generating functions.     

Estimation of Covariate Distribution with Capture–Recapture Data

The main purpose of this article is to estimate the underlying covariate distribution with a biased capture–recapture sample. Two procedures are proposed, and the derived estimates are found to be consistent and asymptotically normal. The proposed methods are compared and are shown to perform well in most circumstances via simulation study, and are applied to a real example.     

How Long Is a Spell of Unemployment? Illusions and Biases in the Use of CPS Data

Most data used to study the durations of unemployment spells come from the Current Population Survey (CPS), which is a point-in-time survey and gives an incomplete picture of the underlying duration distribution. We introduce a new sample of completed unemployment spells obtained from panel data and apply CPS sampling and reporting techniques to replicate the type of data used by other researchers. Predicted duration distributions derived from this CPS-like data are then compared to the actual distribution. We conclude that the best inferences that can be made about unemployment durations by using CPS-like data are seriously biased.     

Asymptotically Efficient Estimation of a Bivariate Gaussian–Weibull Distribution and an Introduction to the Associated Pseudo-truncated Weibull

Two important wood properties are stiffness (modulus of elasticity or MOE) and bending strength (modulus of rupture or MOR). In the past, MOE has often been modeled as a Gaussian and MOR as a lognormal or a two or three parameter Weibull. It is well known that MOE and MOR are positively correlated. To model the simultaneous behavior of MOE and MOR for the purposes of wood system reliability calculations, we introduce a bivariate Gaussian–Weibull distribution and the associated pseudo-truncated Weibull. We use asymptotically efficient likelihood methods to obtain an estimator of the parameter vector of the bivariate Gaussian–Weibull, and then obtain the asymptotic distribution of this estimator.     

A Note on Estimation of a Distribution Function in a Nonparametric Set-up Using Stein’s Shrinkage Estimation Technique

Based on Stein’s famous shrinkage estimation of a multivariate normal distribution, we propose a new type of estimators of the distribution function of a random variable in a nonparametric setup. The proposed estimators are then compared with the empirical distribution function, which is the best equivariant estimator under a well-known loss function. Our extensive simulation study shows that our proposed estimators can perform better for moderate to large sample sizes.     

Is Early Smoking a Causal Risk Factor for Later Cognitive Impairment? A 20-year Prospective Study with Time-varying Propensity Score Matching Based on Random Intercept and Slope

Although epidemiological studies support an association between smoking and cognitive impairment, existing data do not answer the question of whether this association is causal or arises from covariates. In this paper, we investigate smoking status, assessed from adolescence to adulthood, and subsequent cognitive problems in a large representative sample of youths. To analyze this data, we propose a method for causal effects using full matching based on the subject-specific random intercept and slope of the propensity scores. The findings suggest that earlier smoking is not a causal factor for later cognitive problem (odds ratio = 1.64, 95% CI: 0.97–2.80, p = 0.06).