The power of the Poisson index of dispersion

Darwin, J. H.

doi:10.1093/biomet/44.1-2.286

Cited by 19 publications

(8 citation statements)

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“…Since the mean and variance of a discrete Poisson distribution are equal, the sample variance-to-mean ratio, S*/K provides a useful measure of spatial randomness. This ratio has been termed either the "index of dispersion" (Darwin, 1957;Selby, 1968;Stitler and Patil, 1969;Ripley, 198 l), or "coefficient of dispersion" (Sokal and Rohlf, 1981). For a Poisson distribution the coefficient of dispersion (CD) will be close to 1.…”

Section: Resultsmentioning

confidence: 99%

Clustered distribution and variability in kinetics of transient K channels in molluscan neuron cell bodies

1989

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The spatial distribution of transient K current, IA, was studied using a combination of patch-clamp and whole-cell voltage-clamp techniques. The average IA current density in somatic patches is 0.64 times the current density in the entire axotomized cell body, a finding which suggests that the axon hillock or initial segment of the axon has a higher concentration of IA channels than much of soma. The highest density of active channels during the peak IA is 1/micron2 at a membrane voltage of -20 mV. There is no evidence for a gradient in the distribution of IA channels in the cell body, but the channels are not evenly distributed. The variability in the number of channels per patch for multiple patches on the same neuron is much higher than expected for a random distribution. Statistical analysis of the data yields a coefficient of dispersion of 8.1, a value indicating a high degree of clustering. The utility of this statistic for evaluating channel distributions is discussed. Several lines of evidence suggest that the upper limit for the area of IA channel clusters is approximately 250 micron2. Single-channel currents attributed to IA were recorded in the cell-attached configuration. The voltage dependence of channel opening and inactivation are the same as measured in whole-cell voltage-clamp experiments. The single-channel conductance is about 9 pS in normal saline. Patches 9-30 micron2 in areas that contain IA channels are often devoid of other K channel types, suggesting that IA channels can occur in isochannel clusters. IA inactivation follows an exponential time course in all of the neurons examined, but the time constant of inactivation ranges from 25 to 560 msec in different cells. The voltage dependence of activation and inactivation and the reversal potential of the current are approximately the same in all cells. When multiple patches on the same neuron are studied, it is found that IA inactivates exponentially with approximately the same time constant in each patch, regardless of patch area. The data suggest that each neuron expresses predominantly, and perhaps exclusively, a single type of IA channel with distinct kinetic properties. The wide range of IA inactivation time constants observed in different cell suggests that a large number of channel types are available for expression. Possible mechanisms for generating diversity in channel types are discussed.

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Section: Resultsmentioning

confidence: 99%

Clustered distribution and variability in kinetics of transient K channels in molluscan neuron cell bodies

1989

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“…The test is known to have good power under an alternative hypothesis of over-dispersion, provided that the intensity of the population and the sample size are not too small (Darwin, 1957). In order to fully investigate the properties of the index of dispersion test, information is needed r~~garding the sampling distribution of the index of dispersion statistic.…”

Section: Anderson and Siddiquimentioning

confidence: 99%

“…In addition to these methods, an equation due to Darwin (1957) is also considered and is given by Downloaded by [New York University] at 09:56 08 February 2015 ANDERSON AND SIDDIQUI…”

Section: The Sampling Distributionmentioning

confidence: 99%

The sampling distribution of the index of dispersion

Anderson

Siddiqui

1994

Communications in Statistics - Theory and Methods

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“…For Case A asymptotic properties of the test based on SA against various alternative distributions are considered by Bateman (1950), Darwin (1957), and Selby (1965), among others. Moran (1973) showed that the test based on S, is a C(a) test [see Neyman 1959or Moran 1970 for a discussion of C(a) tests] against a wide class of compound-Poisson alternative distributions, and that it is asymptotically equivalent to the test based on likelihood ratio methods for the same class of alternatives.…”

Section: Introductionmentioning

confidence: 99%