In this paper, the problem of goodness of fit test for the inverse Rayleigh distribution based on progressively Type-II censored samples is studied. We develop two test statistics via entropy and propose one new non-entropy test statistic via a pivotal method. We also study the properties of these test statistics. Critical values are obtained by simulations. Then, we do power analysis of these test statistics against various alternatives under different censoring schemes. We conclude that the tests we proposed perform well against various alternatives, especially for non-monotone hazard alternatives. Finally, one real data set is analyzed.

Relational event models are becoming increasingly popular in modeling temporal dynamics of social networks. Due to their nature of combining survival analysis with network model terms, standard methods of assessing model fit are not suitable to determine if the models are specified sufficiently to prevent biased estimates. This paper tackles this problem by presenting a simple procedure for model-based simulations of relational events. Predictions are made based on survival probabilities and can be used to simulate new event sequences. Comparing these simulated event sequences to the original event sequence allows for in depth model comparisons (including parameter as well as model specifications) and testing of whether the model can replicate network characteristics sufficiently to allow for unbiased estimates.

In the classical collective model over a fixed time period of two insurance portfolios, we are interested, in this contribution, in the models that relate to the joint distribution F of the largest claim amounts observed in both insurance portfolios. Specifically, we consider the tractable model where the claim counting random variable N follows a discrete-stable distribution with parameters (α,λ). We investigate the dependence property of F with respect to both parameters α and λ. Furthermore, we present several applications of the new model to concrete insurance data sets and assess the fit of our new model with respect to other models already considered in some recent contributions. We can see that our model performs well with respect to most data sets.

Insurance and annuity products covering several lives require the modelling of the joint distribution of future lifetimes. In the interest of simplifying calculations, it is common in practice to assume that the future lifetimes among a group of people are independent. However, extensive research over the past decades suggests otherwise. In this paper, a copula approach is used to model the dependence between lifetimes within a married couple using data from a large Canadian insurance company. As a novelty, the age difference and the gender of the elder partner are introduced as an argument of the dependence parameter. Maximum likelihood techniques are thus implemented for the parameter estimation. Not only do the results make clear that the correlation decreases with age difference, but also the dependence between the lifetimes is higher when husband is older than wife. A goodness-of-fit procedure is applied in order to assess the validity of the model. Finally, considering several annuity products available on the life insurance market, the paper concludes with practical illustrations.

The distributional behavior of futures price spreads is examined for four commodities: corn, live cattle, gold and T-bonds. Remarkably different results are found over commodities, time period, and sample size. Actual spread changes for the smaller sample size of gold and T-bonds and for corn produce more normal distributions for weekly than for daily differencing intervals, while all live cattle spreads for actual changes are normally distributed. However, the larger sample size of both gold and T-bonds and the relative spread changes for corn and live cattle do not become more normally distributed under temporal aggregation of the data.

State-of-the-art item response theory (IRT) models use logistic functions exclusively as their item response functions (IRFs). Logistic functions meet the requirements that their range is the unit interval and that they are monotonically increasing, but they impose a parameter space whose dimensions can only be assigned a metaphorical interpretation in the context of testing. Applications of IRT models require obtaining the set of values for logistic function parameters that best fit an empirical data set. However, success in obtaining such set of values does not guarantee that the constructs they represent actually exist, for the adequacy of a model is not sustained by the possibility of estimating parameters. This article illustrates how mechanical adoption of off-the-shelf logistic functions as IRFs for IRT models can result in off-the-shelf parameter estimates and fits to data. The results of a simulation study are presented, which show that logistic IRT models can fit a set of data generated by IRFs other than logistic functions just as well as they fit logistic data, even though the response processes and parameter spaces involved in each case are substantially different. An explanation of why logistic functions work as they do is offered, the theoretical and practical consequences of their behavior are discussed, and a testable alternative to logistic IRFs is commented upon.

The principal aim of this paper is to exhibit applications of techniques of time series analysis for establishing limit distribution theorems of statistical relevance on a subcritical Galton–Watson process X with immigration. In this approach the results obtained by Heyde and Seneta, Quine, and Klimko and Nelson are re-established in a more concise form on adopting new methods of proof, which seek to unify these results. In addition, Quenouille-type limit theorems on X are proved leading to the construction of Quenouille-type goodness-of-fit tests for X. It appears that Billingsley's central limit theorem for martingales is appropriate for proving the basic result, Theorem 1.1. This is done on converting the entire problem as a martingale problem through a use of Lemma 2 of Venkataraman (1968).

In a paper of the same title, Ewens has considered the problem of inferring whether the genotypic frequencies observed in a small sample are consistent with a particular population model, in which all types are selectively neutral. The present paper gives the general theory of such sampling schemes, when the sampling is from either a deterministic, or a stochastically varying, population.

The theory is illustrated on a population model which was introduced by Karlin and McGregor. Various results are proved for both the population, and its sample. It is shown that Ewens' sampling theory applies to this population model, and conjectures as to why different population models may have the same sampling theory are made.