Does the Gamma Distribution Refer to an Underlying Mechanism in Binocular Rivalry?

Perception ◽  
1997 ◽  
Vol 26 (1_suppl) ◽  
pp. 22-22 ◽  
Author(s):  
P H C Vallen ◽  
P R Snoeren ◽  
Ch M M de Weert

Thirty years ago, Levelt (1967 British Journal of Psychology58 143 – 145) fitted the distribution of dominance times in binocular rivalry with the gamma distribution (the distribution function of waiting times for N random events with process speed lambda). Ever since, the gamma distribution has been used to describe the rivalry phase durations, without an explanatory underlying mechanism being given. Although Levelt suggested lambda to be proportional to the stimulus strength (eg contrast, luminance, blur, amount of contour) and N to be ‘successive neural spikes’, this suggestion has never been tested. The purpose of this study was to test whether or not N and lambda represent characteristics of the observer and the stimulus, respectively. To collect the data as accurately as possible, we performed a large number of measurements involving different designs and stimuli. In contrast to previous experiments, collected data were not pooled but were compared within each subject. We tested the hypothesis by collecting time intervals from subjects responding to numerous conditions in which disk - ring stimuli were varied in contrast, blur, or amount of contour in one eye.

Perception ◽  
1996 ◽  
Vol 25 (1_suppl) ◽  
pp. 146-146
Author(s):  
P R Snoeren

Some decades ago, it was noticed that the distribution function of waiting times in binocular rivalry looked similar to the gamma distribution function. The best fit of experimental data with a gamma distribution function was obtained with an argument very close to 4, for all stimuli and all subjects. The Poisson distribution function is conceptually related to the gamma distribution, ie the distribution function of waiting times for n random events is the gamma distribution with the integer n as argument. The fact that the best fitted parameter is an integer suggests that the process underlying binocular rivalry is a Poisson process. More precisely, it suggests that a percept under binocular rivalry alternates after four successive random events. Without passing judgment about the nature of these events, the above suggestion is currently investigated. One can think of many mechanisms that cause similar distribution functions of waiting times, but distinguishing them is only possible by using dynamic stimuli. The easiest dynamic stimulus, from both experimental and computational viewpoints, is the so-called step function. With a step function, one rivalrous static stimulus is instantaneously replaced by another. Because this operation changes the mean event rate, the time behaviour directly after the step is different from the time behaviour of both stimuli viewed in static conditions separately. When the mean event rates of the two separate static stimuli are known, statistical predictions about the time behaviour directly after the step can be tested.


1972 ◽  
Vol 9 (3) ◽  
pp. 681-683
Author(s):  
Leon Podkaminer

The probabilities of the occurrence of n events in a certain time period are calculated under the assumptions that the time intervals between the neighbouring events are mutually independent random variables, satisfying some analytic conditions.


Author(s):  
R.J. Milner ◽  
F. Reyers ◽  
J.H. Taylor ◽  
J.S. Van den Berg

A clinical trial was designed to evaluate the effects of diminazene aceturate and its stabiliser antipyrine on serum pseudocholinesterase (PChE) and red blood cell acetylcholinesterase (RBC AChE) in dogs with babesiosis. The trial was conducted on naturally occurring, uncomplicated cases of babesiosis (n = 20) that were randomly allocated to groups receiving a standard therapeutic dose of diminazene aceturate with antipyrine stabiliser (n = 10) or antipyrine alone (n = 10). Blood was drawn immediately before and every 15 minutes for 1 hour after treatment. Plasma PChE showed a 4 % decrease between 0 and 60 min within the treatment group (p < 0.05). No statistically significant differences were found between the treatment and control groups at any of the time intervals for PChE. There was an increase in RBC AChE activity at 15 min in the treatment group (p < 0.05). No significant differences were found between the treatment and control groups at any time interval for RBC AChE. In view of the difference in PChE, samples from additional, new cases (n = 10) of canine babesiosis were collected to identify the affect of the drug over 12 hours. No significant depression was identified over this time interval. The results suggests that the underlying mechanism in producing side-effects, when they do occur, is unlikely to be through cholinesterase depression.


2010 ◽  
Vol 1 (10) ◽  
pp. 88-93
Author(s):  
R. Kar ◽  
V. Maheshwari ◽  
Ashis K. Mal ◽  
A.K. Bhattacharjee

Author(s):  
Ю.В. Горгуца

При проектировании рейдовых причалов, строительство которых получило широкое развитие в настоящее время, невозможно воспользоваться методами, предлагаемыми ныне действующими Нормами технологического проектирования, так как они были выполнены для традиционных защищённых акваторий и опираются на статистический материал, полученный по существующим портам. Для разработки методов определения простоев судов при обработке судов на рейдовых причалах с учётом потока помех от метеофакторов (штормов) как потока случайных событий в данной статье описывается исследование новых моделей систем массового обслуживания. Используется метод суперпозиций – находятся решения для простых моделей, которые затем используются для получения решений по более сложным моделям. Первоначально рассматривается простейшая модель, состоящая из потоков вызовов (штормов) и прибора (порта). Поток вызовов - пуассоновский. Время обслуживания – произвольное с преобразованием Лапласа-Стилтьеса Полученные результаты используются для исследования модели с потоками помех от ветров двух различных направлений. Далее исследуется однолинейная модель с «ненадёжным» прибором. Входящий поток – пуассоновский поток подходящих к порту судов. Время обслуживания - длительность интервалов времени между освобождением места у причала для судна, ожидающих на рейде. Выход из строя прибора, как в свободном, так и в занятом обслуживанием состоянии определяется наступлением шторма – событием пуассоновского потока с интервалами между событиями – интервалами между наступлением штормов. Длительность восстановления работоспособности прибора – определяемая в первой модели длительность простоя причала из-за воздействия метеофакторов. Суда, оказавшиеся в порту при наступлении шторма «дообслуживаются» после его окончания Итоговая модель – многоканальная с параллельно работающими приборами (причалам) и экспоненциальным временем обслуживания судов. Полученные результаты сравнивались со статистическими и показали их высокую сходимость, что доказывает их достоверность. While designing offshore terminals, which are being built quite widely in recent time, it is impossible to use methods, proposed by current technological design norms, because they were created for traditional protected waters and are based on statistical data, acquired by existing ports. This article describes the research of new models of mass service systems to develop methods of defining demurrage while processing vehicles on offshore terminals, taking into account disturbance flow from weather factors (storms) as flow of random events. Method of superpositions is used - to find solutions for simple models, which are used afterwards for getting solutions for more complicated models. Initially the basic model is reviewed, consisting of flow of challenges (storms) and device (port). Challenges flow is Poisson. Service time - arbitrary with transformation of Laplace-Stiltjes. Results acquired are used for researching the model with disturbance flows from windows of various directions. Next the unilineal model with “unreliable” device is researched. Incoming flow is Poisson flow of incoming vehicles. Service time - length of time intervals between berths exemption for vehicles awaing on raid. Device failure, both in free and in maintenance mode was defined by storm incoming - the event of Poisson flow with intervals between events - intervals between storms. Duration of device efficiency recovery - is the defined in the first model duration of terminal demurrage due to weather influence. Vessels, caught up in the port during storm will be maintained after its end. Final model is multi-channel one with working devices (terminals) and exponential time of vessel service. Acquired results have been compared with statistical data, which showed they high convergence, proving their reliability.


1977 ◽  
Vol 9 (1-2) ◽  
pp. 213-218 ◽  
Author(s):  
Hilary L. Seal

It seems that there are people who are prepared to accept what the numerical analyst would regard as a shockingly poor approximation to F (x, t), the distribution function of aggregate claims in the interval of time (o, t), provided it can be quickly produced on a desk or pocket computer with the use of standard statistical tables. The so-called NP (Normal Power) approximation has acquired an undeserved reputation for accuracy among the various possibilities and we propose to show why it should be abandoned in favour of a simple gamma function approximation.Discounting encomiums on the NP method such as Bühlmann's (1974): “Everybody known to me who has worked with it has been surprised by its unexpectedly good accuracy”, we believe there are only three sources of original published material on the approximation, namely Kauppi et al (1969), Pesonen (1969) and Berger (1972). Only the last two authors calculated values of F(x, t) by the NP method and compared them with “true” four or five decimal values obtained by inverting the characteristic function of F(x, t) on an electronic computer.


1972 ◽  
Vol 9 (04) ◽  
pp. 821-831 ◽  
Author(s):  
E. K. Kyprianou

This paper demonstrates that, when in heavy traffic, the quasi-stationary distribution of the virtual waiting time process of both the M/G/1 and GI/M/1 queues as well as the quasi-stationary distribution of the waiting times {Wn } of the M/G/1 queue can be approximated by the same gamma distribution. What characterises this approximating gamma distribution are the first two moments of the service time and inter-arrival time distributions only. A similar approximating behaviour is demonstrated for the queue size process.


Sign in / Sign up

Export Citation Format

Share Document