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Topic: Logarithmic distribution

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discrete logarithms

common logarithm

logarithmic spiral

Logarithmic timeline

logarithmic scale

logarithmic integral

List of integrals of logarithmic functions

discrete logarithm problem

Logarithmic derivative

Logarithmic timeline of current events

List of logarithm topics

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	Probability distribution - Wikipedia, the free encyclopedia
		A probability distribution is a special case of the more general notion of a probability measure, which is a function that assigns probabilities satisfying the Kolmogorov axioms to the measurable sets of a measurable space.
		The rectangular distribution is a uniform distribution on [-1/2,1/2].
		The triangular distribution on [ a, b ], a special case of which is the distribution of the sum of two uniformly distributed random variables (the convolution of two uniform distributions).
	en.wikipedia.org /wiki/Probability_distribution (1330 words)

	Logarithmic distribution - Wikipedia, the free encyclopedia
		In probability and statistics, the logarithmic distribution (also known as the logarithmic series distribution) is a discrete probability distribution.
		The logarithmic distribution is derived from the Maclaurin series expansion of ln(1 â’ p), which is
		In this way, the negative binomial distribution is seen to be a compound Poisson distribution.
	en.wikipedia.org /wiki/Logarithmic_distribution (161 words)

	Grain Size Distribution
		The curves are cumulative percent frequency distribution curves, that represent the cumulative weight percent by particle size of the sample.
		The purpose of this procedure is to determine the distribution of grain sizes in an unconsolidated sediment sample.
		The distribution of kurtosis values in natural sediments is itself strongly skewed, since most sediments are around.85 to 1.4, yet some values as high as 3 or 4 are not uncommon.
	www.cs.pdx.edu /~ian/geology2.5.html (3398 words)

	PIEZOTRANSDUCERS CREATING NARROW WEAKLY DIVERGING ULTRASONIC BEAM
		If the "logarithmic" surface of the lens is attached to piezoelement, then its front surface is flat; and in such a case the probe can be used as both an immersion and a contact transducer.
		It was determined that piston transmitter with an oscillating pressure distribution on its surface forms acoustic field with a narrow main lobe and small side lobes in the directivity pattern.
		Parameters of pressure distribution on the surface of transducer, which forms a narrow weakly diverging axi-symmetric "needle-like" ultrasonic beam in the near zone, were optimized and computed.
	www.ndt.net /article/v07n06/karpelson/karpelson.htm (4615 words)

	UNODC - Bulletin on Narcotics - 1977 Issue 1 - 002
		The first issue deals with the distribution of the individuals who use drugs and concerns the explanatory power and scientific basis for the assumption that an effective identification of the abuser as distinct from the user can be made.
		A log-normal distribution curve describes a population in which many persons use few drugs, where fewer are moderate users, and the fewest yet consume a great deal of drugs.
		The data were analysed with respect to the shape of the distribution and the correlation between the use of licit and illicit drugs.
	www.unodc.org /unodc/bulletin/bulletin_1977-01-01_1_page003.html (2600 words)

	BioMed Central \| Full text \| Structural characterization of genomes by large scale sequence-structure threading: ...
		Figures 1a and 1b feature the survival distributions of CATH topologies and homologous superfamilies among all the studied genomes in combined (these experimental (observed) data curves are marked in red).
		Apparently, that the Weibull distributions established by the double logarithmic representations (4) (marked on Figure 1 'Weibull by plotting') are very close to those calculated by the ML method ('Weibull analytical').
		The developed approach may be applied to quantification of the distribution of different properties of genomes and can be particularly useful for assessing and comparing fold distributions between different organisms and possible impact of the "reliability" of organisms due to a higher redundancy in their fold composition.
	www.biomedcentral.com /1471-2105/5/101 (4199 words)

	A Further Look at Transformations
		The logarithmic, square root, and inverse transformations were computed for this variable.
		The computation for the logarithmic transform issued error messages because some countries had zero aids cases, and the logarithm of zero is not defined mathematically.
		The test of normality indicates that the log transformation, and not the inverse transformation, is effective in achieving a normal distribution.
	www.utexas.edu /courses/schwab/sw388r7/Tutorials/A_Further_Look_at_Transformations_doc_html/010_A_Distribution_Corrected_with_a_Logarithmic_Transformation.html (186 words)

	How to utilize posterization in contrast editing with Power Retouche
		At first we were tempted to do a linear distribution of the gaps, when the range was expanded, and a logarithmic, when the range was preserved.
		Also notice the logarithmic nature of the distribution of the gaps continues in the logarithmic increase of values at the extremes.
		As you can see the overall impression is the same and the distribution at the extremes is the same, but there are no missing values in either levels and level 3 has a more even distribution of values.
	www.powerretouche.com /Posterization.htm (1192 words)

	Environmental Protection Agency > Basic Concepts in Environmental Sciences > Module 3: Size Distribution
		The skewed distribution shown in Figure 2 is typically encountered in the field of air pollution control.
		When the particle diameters in Figure 2 are plotted on a logarithmic scale against the frequency of occurrence, a bell-shaped curve is generated.
		The geometric standard deviation of a lognormal distribution is determined by dividing the mass median particle diameter by the particle size at the 15.78 percent probability or by dividing the particle size at the 84.13 percent probability by the mass median particle diameter.
	www.epa.gov /eogapti1/module3/distribu/distribu.htm (885 words)

	Resume Distribution in TutorGig Encyclopedia
		The hypoexponential distribution is a generalization of Erlang distribution in the sense that the n exponential distributions may have different rates.
		A simple bimodal distribution, in this case the sum of two normal distribution s In statistics, a bimodal distribution is a distribution with two different peaks &mdash..
		In telecommunication, a fading distribution is the probability distribution of the value of signal fading relative to a specified reference level.
	www.tutorgig.com /es/Resume+Distribution (815 words)

	Distribution of Points (Site not responding. Last check: 2007-10-07)
		A distribution of points is linear when the absolute value of the difference between any contiguous values is constant throughout the range.
		A distribution of points is logarithmic when the absolute value of the ratio between any contiguous values is constant throughout the range.
		Inversion Engine is active instead, the distribution of points for the frequency/wavelength attribute is exactly the one determined by the measured spectrum or the combination of both measured spectra.
	www.scatterer.com /distribution%20of%20Points.htm (345 words)

	Kinetic Diversity of Single-Channel Burst Openings Underlying Persistent Na+ Current in Entorhinal Cortex Neurons -- ...
		Data were binned logarithmically (11.4 bins/decade), and the natural logarithm of the numbers of observations per ms, i.e., ln( n /ms), was plotted as a function of time in a logarithmic ( insets) or linear ( main panels) scale.
		distribution, indicating that the open-time variability along this burst is consistent with a random occurrence of open times.
		Data were binned logarithmically as explained in Methods, and in the main subpanels are shown in a log-linear plot.
	www.biophysj.org /cgi/content/full/85/5/3019 (7639 words)

	On the form of the forgetting function: The effects of arithmetic and logarithmic distributions of delays. (Site not responding. Last check: 2007-10-07)
		On the form of the forgetting function: The effects of arithmetic and logarithmic distributions of delays.
		Sargisson, R. and White, K. On the form of the forgetting function: The effects of arithmetic and logarithmic distributions of delays.
		In further conditions with a fixed set of five delays, discriminability was higher with a logarithmic distribution of delays than with an arithmetic distribution.
	seab.envmed.rochester.edu /abstracts/JeabAbstracts/80/_80-295.htm (172 words)

	approximate logarithmic spiral generated by distribution of primes (Site not responding. Last check: 2007-10-07)
		The fact that the primes are in this way 'logarithmically distributed' can be exploited in order to construct an approximate logarithmic spiral from the primes themselves.
		The primes thin out, asymptotically, at a particular rate (this much people can generally understand), but the rate is governed by a logarithm, and the public at large has no real understanding of what a logarithm is. The most familiar manifestation of the logarithm is the logarithmic spiral, visible in snailshells, seashells, etc.
		I feel that they provide a very pleasing illustration of my favoured explanation, and may perhaps provide those people unable (or unwilling) to grasp the concept of a logarithm an opportunity to witness directly the beauty of the prime number theorem.
	www.maths.ex.ac.uk /~mwatkins/zeta/crudespiral.htm (721 words)

	Logarithmic identities Information (Site not responding. Last check: 2007-10-07)
		All of these are valid for all positive real numbers a, b and c — except that the base of a logarithm may never be 1.
		These three identities lead to the use of logarithm tables and slide rules ; knowing the logarithm of two numbers allows you to multiply and divide them quickly, as well as compute powers and roots.
		This identity is needed to evaluate logarithms on calculators.
	www.articleshead.com /show_article/logarithmic-identities (432 words)

	Statistical Distribution of Childhood IQ Scores
		In a log-normal distribution of IQ scores, the logarithm of the IQ scores would be normally distributed.
		If the log-normal distribution is valid, the latter may have some interesting effects on our concept of IQ and mental development in general.
		The distribution may produce accurate results under normal circumstances, but factors such as chromosomal abnormalities in the general population severely affect the left half of the curve.
	sweb.uky.edu /~jcscov0/ratioiq.htm (815 words)

	PlanetMath: Shannon's entropy
		The logarithm is usually taken to the base 2, in which case the entropy is measured in ``bits,'' or to the base e, in which case
		The Shannon entropy was first introduced by Shannon in 1948 in his landmark paper ``A Mathematical Theory of Communication.'' The entropy is a functional of the probability distribution function
		Entropy is maximized when the probability distribution is uniform.
	planetmath.org /encyclopedia/Entropy.html (475 words)

	Measuring Size Distribution in Highly Heterogeneous Systems with Fluorescence Correlation Spectroscopy -- Sengupta et ...
		yields a distribution with a peak at 0.109 ms and a FWHM
		of the MEMFCS distribution and the uncertainty in
		10 yields a distribution that is smooth throughout
	www.biophysj.org /cgi/content/full/84/3/1977 (3748 words)

	The Logarithmic Poisson Gamma Distribution: A Model for Leadtime Demand - Storming Media
		The common assumption is that this distribution is normal.
		Assuming a logarithmic compounding distribution and a gamma distribution of leadtime we derive the exact distribution of total demand in a leadtime.
		An approximation is derived which is equivalent to a scaled version of the negative binomial distribution.
	www.stormingmedia.us /04/0454/A045421.html (227 words)

	GNU Scientific Library -- Reference Manual - Random Number Distributions (Site not responding. Last check: 2007-10-07)
		In the simplest cases a non-uniform distribution can be obtained analytically from the uniform distribution of a random number generator by applying an appropriate transformation.
		The cumulative distribution functions and their inverses are computed separately for the upper and lower tails of the distribution, allowing full accuracy to be retained for small results.
		Continuous random number distributions are defined by a probability density function, p(x), such that the probability of x occurring in the infinitesimal range x to x+dx is p dx.
	www.gnu.org /software/gsl/manual/gsl-ref_19.html (3817 words)

	Ivars Peterson's MathTrek - Prime Listening
		He observed that the pages of heavily used books of logarithms were grimier at the beginning than at the end, suggesting that fellow scientists tended to look up smaller numbers more often than larger ones.
		Using this idea, Hill came up with a new statistical form of the significant-digit law: If distributions are selected at random and random samples are taken from each of these distributions, the significant-digit frequencies of the combined sample will converge to Benford's distribution, even though the individual distributions selected may not closely follow the law.
		However, when the percentages obtained from these data sets are averaged, the resulting digital frequencies fit a logarithmic distribution much more closely.
	www.maa.org /mathland/mathtrek_6_29_98.html (969 words)

	Linking Cache performance to user behaviour (Site not responding. Last check: 2007-10-07)
		If it could be shown that user behaviours form a distribution with a well-defined mean (many human metrics, such as PSTN calling patterns, follow Poisson distributions [BOU88]) it would be possible to build simple models based on a typical user.
		The logarithmic distribution of request rates (figure 2) is approximately Poisson with a mean of 101 requests (where the mean is defined as the inverse log of the mean of the logarithmic distribution in fig.
		It is possible that analysis of a large number of traces would show that user properties have a probability distribution with a maximum likelihood and consequently, there is a meaningful definition of a typical user of the WWW.
	wwwcache.ja.net /events/workshop/11/cacheusr_c.htm (3668 words)

	Tag Cloud Font Distribution Algorithm \| Echo Chamber Project
		One way to even out the fontsize distribution in the tag cloud would be to use a logarithmic thresholding algorithm instead of a linear one.
		The differences between linear and logarithmic thresholding may be too subtle to bother with, but I thought I would also publish the following 4 tag clouds for comparison.
		The first and third use the logarithmic distribution, and the second and fourth use the linear distribution.
	www.echochamberproject.com /node/247 (1138 words)

	Citebase - Unitarization of Gluon Distribution in the Doubly Logarithmic Regime at High Density (Site not responding. Last check: 2007-10-07)
		Citation coverage and analysis is incomplete and hit coverage and analysis is both incomplete and noisy.
		We argue that the distribution functions for quarks and gluons are computable at small x for sufficiently large nuclei, perhaps larger than can be physically realized.
		I demonstrate that the leading logarithms for high-energy scattering can be obtained as a result of evolution of the nonlocal operators - straight-line ordered gauge factors - with respect to the slope of the straight line.
	citebase.eprints.org /cgi-bin/citations?id=oai:arXiv.org:hep-ph/9807462 (1245 words)

	Neal’s Blog » Linked - by Albert Laszlo Barabasi - Captured (Site not responding. Last check: 2007-10-07)
		Barabasi, a physicist, discovered that networks use logarithmic distribution, highly-linked nodes grow faster, and networks undergo phase transitions.
		Logarithmic Distribution : Instead of random distribution or bell curve distributions, the distribution of links in a network is determined by logarithmic power laws.
		This works with practically everything on websites: a few pages of a website get most of the visits, most of the searches are based on a few keywords, and so on.
	www.nealsblog.net /item/47 (740 words)

	Derivation of the negative binomial distribution from the compound Poisson process (aka ``apparent contagion'')
		In [ 2 ] Cliff and Ord explain the basic Poisson process, and then go on to describe the classical contagions, true (generalising) and apparent (compound), which are departures from the simple Poisson process (which produces Complete Spatial Randomness, or CSR).
		It is possible for true and apparent contagion models to model the same distribution, however.
		In this case, the clusters are distributed as Poisson, with the number of individuals in a cluster determined by the logarithmic distribution.
	zappa.nku.edu /~longa/geomed/modules/ss1/lec/details/details.html (275 words)

	Stat 328 Previous Class Projects
		For small or moderate sample sizes, the tests can be compared with respect to their simulated power of detecting some alternative hypotheses against a null hypothesis of generalized logarithmic series distribution.
		In this project, network data were simulated under 4 different distributional assumptions-three sociomatrices were simulated under the uniform distribution, conditional on the total number of ties, and one sociomatrix was generated under the uniform distribution, conditional on the number of outdegrees for each actor.
		It is the intention of this paper to explore the outcome distributions for a given number of trials in an evening as well as the probability that an individual will leave with a profit.
	www.stat.uiuc.edu /~babailey/stat328/projlistold.html (1049 words)

	Thermodynamics of Copper and Lead in Alumina Saturated Flash Smelting Slag (Site not responding. Last check: 2007-10-07)
		Abstract : The distribution of copper and lead between copper rich alloy and alumina saturated flash smelting slag produced from Polish copper concentrates was investigated at 1673 and 1553 K under controlled oxygen partial pressures in the range from 8.6·10
		The slope of the linear relationship between the logarithmic distribution ratio and oxygen partial pressure shows that the predominant species dissolved in the slag are CuO
		The results were used to explain the thermodynamic reasons behind potential problems in the decopperizing of the flash smelting slag.
	pubs.nrc-cnrc.gc.ca /cmq/41743-3.html (384 words)

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