Sufficient Reduction in Multivariate Surveillance

The relation between change points in multivariate surveillance is important but seldom considered. The sufficiency principle is here used to clarify the structure of some problems, to find efficient methods, and to determine appropriate evaluation metrics. We study processes where the changes occur simultaneously or with known time lags. The surveillance of spatial data is one example where known time lags can be of interest. A general version of a theorem for the sufficient reduction of processes that change with known time lags is given. A simulation study illustrates the benefits or the methods based on the sufficient statistics.     

Identifying Preferences for Conditional Cooperation Using Individual Beliefs

The relationship between contributions and elicited beliefs in a repeated two-person public good experiment is modeled with the help of a parsimounious random-utility function that allows for conditionally cooperative, opportunistic, and altruistic patterns of behavior. Under standard assumptions, a latent-class mixed logit specification with three sub-populations is shown to capture well heterogeneity in individual contribution levels over time, while also accomodating for different degrees of heteroscedasticity. The estimation results are consistent with the conjecture that the majority of players in public goods games are strongly conditional cooperators, with smaller fractions of the population leaning to opportunistic or altruistic behavior.     

Objective Bayesian Analysis of an Exponential Regression Model with Constrained Parameters Applied to Animal Digestibility

In animal digestibility the proportion of degraded food along the time has usually been modeled as a normal random variable with mean a function of the time and the following three parameters: the proportion of degraded food almost instantaneously, remaining proportion of food to be degraded, and velocity of degradation. The estimation of these parameters has been carried out mainly from a frequentist viewpoint by using the asymptotic distribution of the maximum likelihood estimator. This may give inadmissible estimates, such as values outside of the range of the parameters. This drawback could not appear if a Bayesian approach were adopted. In this article an objective Bayesian analysis is developed and illustrated on real and simulated data.     

Presmoothed Estimation with Left-Truncated and Right-Censored Data

We propose a new method to estimate the cumulative hazard function and the corresponding distribution function of survival times under randomly left-truncated and right-censored observations (LTRC). The new estimators are based on presmoothing ideas, the estimation of the conditional expectation m of the censoring indicator. An almost sure representation for both estimators is established, from which a strong consistency rate and asymptotic normality are derived. It is shown that the presmoothed modification leads to a gain in terms of asymptotic mean squared error. This efficiency with respect to the classical estimators is also shown in a simulation study. Finally, an application to a real data set is provided.     

The 3 F 2 with Complex Parameters as Generating Function of Discrete Distribution

A new discrete family of probability distributions that are generated by the ₃ F ₂ function with complex parameters is presented. Some of the properties of this new family are studied as well as methods of estimation for its parameters. It affords considerable flexibility of shape which turns the distribution into an appropriate candidate for modeling data that cannot be adequately fitted by classical families with fewer parameters. Finally, three examples in the fields of Agriculture and Education are included in order to show the versatility and utility of this distribution.     

A characterization based on conditional expectations

We obtain the necessary and sufficient conditions so that any real function (x) is the conditional expectation E(h(X)/X≥x) of a random variable X with continuous distribution function, where h is a given real, continuous and strictly monotonic function.     

Waiting time to exhaust lottery numbers

Questions related to lotteries are usually of interest to the public since people think there is a magic formula which will help them to win lottery draws. This note shows how to compute the expected waiting time to observe specific numbers in a sequence of lottery draws and show that surprising facts are expected to occur.     

On the minimum expected quantity for the validity of the chi-squared test in 2 2 2 tables

A 2 2 2 contingency table can often be analysed in an exact fashion by using Fisher's exact test and in an approximate fashion by using the chi-squared test with Yates' continuity correction, and it is traditionally held that the approximation is valid when the minimum expected quantity E is E S 5. Unfortunately, little research has been carried out into this belief, other than that it is necessary to establish a bound E>E*, that the condition E S 5 may not be the most appropriate (Martín Andrés et al., 1992) and that E* is not a constant, but usually increasing with the growth of the sample size (Martín Andrés & Herranz Tejedor, 1997). In this paper, the authors conduct a theoretical experimental study from which they ascertain that E* value (which is very variable and frequently quite a lot greater than 5) is strongly related to the magnitude of the skewness of the underlying hypergeometric distribution, and that bounding the skewness is equivalent to bounding E (which is the best control procedure). The study enables estimating the expression for the above-mentioned E* (which in turn depends on the number of tails in the test, the alpha error used, the total sample size, and the minimum marginal imbalance) to be estimated. Also the authors show that E* increases generally with the sample size and with the marginal imbalance, although it does reach a maximum. Some general and very conservative validity conditions are E S 35.53 (one-tailed test) and E S 7.45 (two-tailed test) for alpha nominal errors in 1% h f h 10%. The traditional condition E S 5 is only valid when the samples are small and one of the marginals is very balanced; alternatively, the condition E S 5.5 is valid for small samples or a very balanced marginal. Finally, it is proved that the chi-squared test is always valid in tables where both marginals are balanced, and that the maximum skewness permitted is related to the maximum value of the bound E*, to its value for tables with at least one balanced marginal and to the minimum value that those marginals must have (in non-balanced tables) for the chi-squared test to be valid.     

Accuracy of approximate progressively censored reliability sampling plans for exponential models

Reliability sampling plans provide an efficient method to determine the acceptability of a product based upon the lifelengths of some test units. Usually, they depend on the producer and consumer’s quality requirements and do not admit closed form solutions. Acceptance sampling plans for one- and two-parameter exponential lifetime models, derived by approximating the operating characteristic curve, are presented in this paper. The accuracy of these approximate plans, which are explicitly expressible and valid for failure and progressive censoring, is assessed. The approximation proposed in the one-parameter case is found to be practically exact. Explicit lower and upper bounds on the smallest sample size are given in the two-parameter case. Some additional advantages are also pointed out.