We investigate the impact of pubertal development, age, and its interaction on female substance use behaviour. An extended latent transition model with two latent variables is used to reflect the dependency of adolescent substance use on pubertal development and age. A sample of females in grades 7-12 is analysed using maximum-likelihood estimation. Analyses indicate that experiencing puberty is related to increased substance use for all age groups. Among females aged 12-15, those who have experienced puberty are more likely to advance in substance use compared to their late-maturing counterparts. Particularly, among 12-year old non-substance users, those who have experienced puberty are approximately three times more likely to advance towards substance use than those who have not experienced puberty. In addition, among older females, those whose puberty is in progress are more prone to advance in substance use compared to those whose puberty has not occurred.

It is well known that most commonly used discrete distributions fail to belong to the domain of maximal attraction for any extreme value distribution. Despite this negative finding, C. W. Anderson showed that for a class of discrete distributions including the negative binomial class, it is possible to asymptotically bound the distribution of the maximum. In this paper we extend Anderson's result to discrete-valued processes satisfying the usual mixing conditions for extreme value results for dependent stationary processes. We apply our result to obtain bounds for the distribution of the maximum based on negative binomial autoregressive processes introduced by E. McKenzie and Al-Osh and Alzaid. A simulation study illustrates the bounds for small sample sizes.

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It is well known that most commonly used discrete distributions fail to belong to the domain of maximal attraction for any extreme value distribution. Despite this negative finding, C. W. Anderson showed that for a class of discrete distributions including the negative binomial class, it is possible to asymptotically bound the distribution of the maximum. In this paper we extend Anderson's result to discrete-valued processes satisfying the usual mixing conditions for extreme value results for dependent stationary processes. We apply our result to obtain bounds for the distribution of the maximum based on negative binomial autoregressive processes introduced by E. McKenzie and Al-Osh and Alzaid. A simulation study illustrates the bounds for small sample sizes.

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In this paper we consider the problem of forecasting binomial time series, modelled by the binomial autoregressive model. This paper considers proposed by McKenzie (1985) and is extended to a higher order by Weiß (2009). Since the binomial autoregressive model is a Markov chain, we can apply the earlier work of Bu and McCabe (2008) for integer valued autoregressive(INAR) model to the binomial autoregressive model. We will discuss how to compute the h-step-ahead forecast of the conditional probabilities of X T +h when T periods are used in fitting. Then we obtain the maximum likelihood estimator of binomial autoregressive model and use it to derive the maximum likelihood estimator of the h-step-ahead forecast of the conditional probabilities of X T +h . The methodology is illustrated by applying it to a data set previously analyzed by Weiß (2009).