Frender and Doubilet suggest that Bousfield’s ratio of repetitions (RR) is the best measure of clustering in free recall presently available. Conditioning only on the number of words recalled, they determine the mean of RR in the absence of clustering. In this note the null variance of RR is presented. This permits development of conservative significance tests based on the Cramér inequality.

Inference is considered for the marginal distribution of X, when (X, Y) has a truncated bivariate normal distribution. The Y variable is truncated, but only the X values are observed. The relationship of this distribution to Azzalini's “skew-normal” distribution is obtained. Method of moments and maximum likelihood estimation are compared for the three-parameter Azzalini distribution. Samples that are uniformative about the skewness of this distribution may occur, even for large n. Profile likelihood methods are employed to describe the uncertainty involved in parameter estimation. A sample of 87 Otis test scores is shown to be well-described by this model.

The distribution of visits to a particular gene frequency in a finite population of size N with non-overlapping generations is derived. It is shown, by using well-known results from the theory of finite Markov chains, that all such distributions are geometric, with parameters dependent only on the set of bij's, where bij is the mean number of visits to frequency j/2N, given initial frequency i/2N. The variance of such a distribution does not agree with the value suggested by the diffusion method. An improved approximation is derived.

The purpose of the present experiments was to evaluate the contribution of the glutamate-glutamine cycle in retinal glial (Müller) cells to photoreceptor cell synaptic transmission. Dark-adapted isolated rat retinas were superfused with oxygenated bicarbonate-buffered media. Recordings were made of the b-wave of the electroretinogram as a measure of light-induced photoreceptor to ON-bipolar neuron transmission. L-methionine sulfoximine (1–10 mM) was added to superfusion media to inhibit glutamine synthetase, a Müller cell specific enzyme, by more than 99% within 5–10 min, thereby disrupting the conversion of glutamate to glutamine in the Müller cells. Threo-hydroxyaspartic acid and D-aspartate were used to block glutamate transporters. The amplitude of the b-wave was well maintained for 1–2 h provided 0.25 mM glutamate or 0.25 mM glutamine was included in the media. Without exogenous glutamate or glutamine the amplitude of the b-wave declined by about 70% within 1 h. Inhibition of glutamate transporters led to a rapid (2–5 min) reversible loss of the b-wave in the presence and absence of the amino acids. In contrast, inhibition of glutamine synthetase did not alter significantly either the amplitude of the b-wave in the presence of glutamate or glutamine or the rate of decline of the b-wave found in the absence of these amino acids. Excellent recovery of the b-wave was found when 0.25 mM glutamate was resupplied to L-methionine sulfoximine–treated retinas. The results suggest that in the isolated rat retina uptake of released glutamate into photoreceptors plays a more important role in transmitter recycling than does uptake of glutamate into Müller cells and its subsequent conversion to glutamine.

Using a simple characterization of the Linnik distribution, discrete-time processes having a stationary Linnik distribution are constructed. The processes are structurally related to exponential processes introduced by Arnold (1989), Lawrance and Lewis (1981) and Gaver and Lewis (1980). Multivariate versions of the processes are also described. These Linnik models appear to be viable alternatives to stable processes as models for temporal changes in stock prices.

A stochastic model is presented which yields a stationary Markov process whose invariant distribution is logistic. The model is autoregressive in character and is closely related to the autoregressive Pareto processes introduced earlier by Yeh et al. (1988). The model may be constructed to have absolutely continuous joint distributions. Analogous higher-order autoregressive and moving average processes may be constructed.

An autoregressive process ARP(1) with Pareto-distributed inputs, analogous to those of Lawrance and Lewis (1977), (1980), is defined and its properties developed. It is shown that the stationary distributions are Pareto. Further, the maximum and minimum processes are asymptotically Weibull, and the ARP(1) process is shown to be closed under maximization or minimization when the number of terms is geometrically distributed. The ARP(1) process leads naturally to an extremal process in the sense of Lamperti (1964). Statistical inference for the ARP(1) process is developed. An absolutely continuous variant of the Pareto process is described.

Characterizations of strong ergodicity for Markov chains using mean visit times have been found by several authors (Huang and Isaacson (1977), Isaacson and Arnold (1978)). In this paper a characterization of uniform strong ergodicity for a continuous-time non-homogeneous Markov chain is given. This extends the characterization, using mean visit times, that was given by Isaacson and Arnold.

Excess life distributions for discrete renewal processes may be computed by using elementary discrete Markov chain concepts involving absorption probabilities. Excess life distributions in general may then be obtained by approximating the renewal process under study by a suitably chosen sequence of discrete renewal processes. The technique is illustrated in the cases of renewal processes with interarrival distributions which are a linear combination of two exponentials and uniform [0, 1]. A related algorithm is described for computer generated approximations of excess life distributions corresponding to continuous interarrival time distributions with an increasing c.d.f. Conditions for convergence of this algorithm are examined.

Let X1, X2, …, Xn be independent identically distributed positive integer-valued random variables with order statistics X1:n, X2:n, …, Xn:n. If the Xi's have a geometric distribution then the conditional distribution of Xk+1:n – Xk:n given Xk+1:n – Xk:n > 0 is the same as the distribution of X1:n–k. Also the random variable X2:n – X1:n is independent of the event [X1:n = 1]. Under mild conditions each of these two properties characterizes the geometric distribution.

The concept of strong ergodicity for discrete-time homogeneous Markov chains has been characterized in several ways (Dobrushin (1956), Lin (1975), Isaacson and Tweedie (1978)). In this paper the characterization using mean visit times (Huang and Isaacson (1977)) is extended to continuous-time Markov chains. From this it follows that for a certain subclass of continuous-time Markov chains, X(t), is strongly ergodic if and only if the associated embedded chain is Cesaro strongly ergodic.

A class of multivariate exponential distributions is suggested which includes those presented by Marshall and Olkin, Downton, and Hawkes. It is based on a concept of hierarchical successive damage. Recursive expressions for the Laplace transforms and for first and second moments are derived in the bivariate case. Related multivariate geometric distributions are described.

Balls are drawn with replacement from an urn containing m distinguishable balls until a match is noted. The distribution of the number of drawings required is considered in the case where only the last k balls drawn are remembered. The asymptotic behavior of this distribution, as m and k become large, is investigated. Two further variants of the problem are suggested.

Let {X(n): n = 0, 1, 2, …} be a Markov chain with state space {0, 1, 2, …, N} and transition probability matrix P = (pij).