Showing papers on "Poisson regression published in 1974"

The intervals between miniature end‐plate potentials in the frog are unlikely to be independently or exponentially distributed

Abstract: 1. It has been suggested that spontaneous quantal release of transmitter at the neuromuscular junction is a Poisson process. One logical argument against accepting the Poisson hypothesis is that so far relatively few intervals between miniature end-plate potentials (min.e.p.p.s) have been studied in any single experiment. Release is known to occur from many sites on the nerve terminal, so many intervals must be studied before drawing any conclusions about the timing of release from the individual sites. Moreover, the statistical methods that have been used are relatively insensitive to deviations from Poisson predictions.2. The Poisson hypothesis is evaluated with respect to three major criteria:(a) The fit to the exponential distribution is analysed by five goodness of fit tests which were applied to eleven sets of data, showing that it is unlikely that the data sets were generated by an exponential distribution.(b) The independence of intervals is assessed in two ways. First, the autocorrelogram of intervals is constructed. This shows an excess of significant positive correlations beyond the 5% limits of the Poisson expectation. Secondly, the unsmoothed power spectrum is calculated, and compared to the Poisson prediction by means of the modified mean test. Again, most sets deviate significantly from the Poisson expectation. It is unlikely that the intervals are independent.(c) The possibility of simultaneous occurrences is evaluated by construction of the amplitude histogram of min.e.p.p.s. In all sets the Poisson prediction for the frequency of multiples of the unit height was exceeded by the empirical data sets. The over-all conclusion is that the process which generates spontaneous releases is unlikely to be Poisson.

Probabilistic Models for Texas Gulf Coast Hurricane Occurrences

Abstract: Various statistical methods are used to analyze the occurrence of Texas Gulf Coast hurricanes. Simple Poisson, periodic Poisson, and Markov chain models are fitted to the occurrence data for an offshore site near Corpus Christi, Texas. The goodness of the fit of the models is studied, using interarrival time, hazard function, and comparative maximum likelihood tests. Also considered are the autocorrelation function for the data and the effects of varying record lengths. The periodic Poisson model provides the best fit to the data and permits a relatively simple description of cyclical occurence phenomena. (AUTHOR)

On the small sample distribution and power of the log likelihood ratio and variance tests for the poisson

Abstract: The variance test and log likelihood ratio test are both well known in examining a series of n discrete observations for agreement with an assumed common Poisson distribution. This paper compares the tests in small samples with the corresponding x 2 significance levels, and also the small sample power under several Poisson-type alternatives.

A maximum likelihood approach to prediction with applications to binomial and Poisson populations

Abstract: approved: Redacted for privacy (G. David Faulkenberry) Given a sample from a population whose distribution belongs to a parametric family we would like to make predictions on the outcome of a statistic (generally the sample sum) of a future sample from the same population. These predictions can be in the form of intervals with some associated level of confidence or in the form of predictive distributions. A "Maximum Likelihood Predictive Distribution" is introduced which is easily accessible in most regular cases and under conditions similar to those for the consistency of the maximum likelihood estimator converges almost surely to the true distribution of the predicted variable when the observed sample size becomes large. The new approach is compared to frequentist and Bayesian approaches and to another likelihood approach introduced by R. A. Fisher. The comparisons are conducted for simple random sampling from Poisson populations and from binomial populations. The various approaches yield quite similar results for all sample sizes and tend to be equivalent to the method using normal approximations when both the observed and future sample sizes tend to infinity such that their ratio remains constant. It is shown that the Maximum Likelihood Predictive Distribution is almost identical to the Bayesian predictive distribution under prior VTin the Poisson case and prior V p) in the binomial case. These approaches are also considered for Poisson and binomial stratified random sampling and the results compared. A Maximum Likelihood Approach to Prediction With Applications to Binomial and Poisson Populations by Michel Georges Lejeune A THESIS submitted to Oregon State University in partial fulfillment of the requirements for the degree of Doctor of Philosophy Completed July 1974 Commencement June 1975 APPROVED: Redacted for privacy Associate Professor of Statistics in charge of major Redacted for privacy Chairman of Department of Statistics Redacted for privacy Dean of Graduate School Date thesis is presented July 1, 1974 Typed by Robin Przybilla for Michel Georges Lejeune

A risk and comparative analysis of aircraft accident data

Abstract: Aircraft accident data was analyzed to investigate the differences in risk of Naval aircraft and to develop some overall risk measure. To analyze risk, a flight was divided into four risk areas; takeoff, inflight, transistion, and landing. Accidents were assumed to occur according to a Poisson process and tests were carried out to prove the va- lidity of the Poisson assumption. The Poisson model yielded two factors , the exposure to the risk areas and the perform- ance in them, which were used to construct a risk measure and to explain the differences in the present accident rates. A procedure to predict risk was developed. A statistic, im- provement index, was developed to allow a direct comparison between different types of aircraft with respect to safety performance with differences in risk taken into account. Another statistic, weighted improvement index, is proposed to provide insight into where the primary positive and nega- tive contributions to Naval aviation safety are made in any given year. The aircraft studied were the major Naval oper- ational and training aircraft, and the period of primary interest was fiscal year 1969 through fiscal year 1973.