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Topic: Moment about the mean

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	NationMaster - Encyclopedia: Kurtosis (Site not responding. Last check: 2007-11-06)
		In probability theory and statistics, the kth standardized moment of a probability distribution is and#956;k/and#963;k, where and#956;k is the kth moment about the mean and and#963; is the standard deviation.
		In probability theory and statistics, the kth moment about the mean (or kth central moment) of a real-valued random variable X is the quantity E[(X and#8722; E[X])k], where E is the expectation operator.
		In terms of shape, a platykurtic distribution has a smaller "peak" around the mean (that is, a lower probability than a normally distributed variable of values near the mean) and "thin tails" (that is, a lower probability than a normally distributed variable of extreme values).
	www.nationmaster.com /encyclopedia/Kurtosis (3240 words)

	Moment about the mean - Definition, explanation
		Some random variables have no mean, in which case the moment about the mean is not defined.
		The second moment about the mean is called the variance, and is usually denoted σ
		The third and fourth moments about the mean are used to define the standardized moments which are in turn used to define skewness and kurtosis, respectively.
	www.calsky.com /lexikon/en/txt/m/mo/moment_about_the_mean.php (267 words)

	Reference.com/Encyclopedia/Kurtosis
		The fourth standardized moment is defined as μ
		is the fourth moment about the mean and σ is the standard deviation.
		The most platykurtic distribution of all is the Bernoulli distribution with p = ½ (for example the number of times one obtains "heads" when flipping a coin once), for which the kurtosis is -2.
	www.reference.com /browse/wiki/Kurtosis (1276 words)

	StatPlus Help - Descriptive Statistics (Site not responding. Last check: 2007-11-06)
		Mean - The mean is a particularly informative measure of the "central tendency" of the variable if it is reported along with its confidence intervals.
		Usually we are interested in statistics (such as the mean) from our sample only to the extent to which they are informative about the population.
		The standard error of the mean (first used by Yule, 1897) is the theoretical standard deviation of all sample means of size n drawn from a population and depends on both the population variance (sigma) and the sample size (n) as indicated below:
	www.statplus.net.ua /eng/help_full/source/a_descr_stat.htm (720 words)

	moment. The American Heritage® Dictionary of the English Language: Fourth Edition. 2000.
		The first moment is the mean of the distribution.
		A moment is an indeterminately short but significant period: I'll be with you in a moment.
		Jiffy and flash usually combine with in a; in a jiffy means in a short space of time, while in a flash suggests the almost imperceptible duration of a flash of light: “He was on his stool in a jiffy, driving away with his pen” (Charles Dickens).
	www.bartleby.com /61/80/M0378000.html (324 words)

	Moment about the mean
		Some random variables have no mean, in which case the moment about the mean is not defined.
		The second moment about the mean is called the variance, and is usually denoted σ
		The third and fourth moments about the mean are used to define the standardized moments which are in turn used to define skewness and kurtosis, respectively.
	www.xasa.com /wiki/en/wikipedia/m/mo/moment_about_the_mean.html (173 words)

	Portfolio Definitions - MKW 2001
		Coefficient of Determination: "The primary meaning of the coefficient of correlation lies in the amount of variation in one variable that is accounted for by the variable it is correlated with.
		Mean: The mean is the sum of all the scores divided by the number of scores.
		Null Hypothesis: A hypothesis about a population parameter.
	www.west.asu.edu /mwilliam/quantitative/definitions.htm (630 words)

	Normalization
		The greater is the difference between the mean and the median, the greater is the skew.
		The first moment above the mean is always equal to zero, as the standard scores are defined as scores with a mean of zero and standard deviation equal to one.
		The value of the fourth moment about the mean depends in part on the shape of the scrutinized distribution.
	www.public.asu.edu /~jwang2/portfolio/statistics/chapt6/chapt6.htm (781 words)

	Buddhist Meditation \| Background \| Being "in the moment"
		Being in the moment is just another way of saying that we are aware of what is going on in our experience, that we are not just being angry (or whatever) but are aware that we are angry and are aware that we can choose to be otherwise.
		Or we may be fantasizing about a future in which we have won the lottery and are living out our lives in some imagined paradise, or daydreaming about being with the perfect partner.
		When we are thinking about the past or future while being in the moment, we are conscious that we are reflecting and we're not lost in thought.
	www.wildmind.org /meditation/background/moment.htm (738 words)

	Being In The Moment
		Being in the moment is just another way of saying that we are aware of what is going on in our experience, that we are not just being angry (or whatever) but are aware that we are angry and are aware that we can choose to be otherwise.
		Or we may be fantasizing about a future in which we have won the lottery and are living out our lives in some imagined paradise, or daydreaming about being with the perfect partner.
		When we are thinking about the past or future while being in the moment, we are conscious that we are reflecting and we're not lost in thought.
	steppingstones.to /light/enlightening/mind/m002.html (745 words)

	Kurtosis - Psychology Wiki - a Wikia wiki (Site not responding. Last check: 2007-11-06)
		is the fourth moment about the mean and σ is the standard deviation.
		In terms of shape, a leptokurtic distribution has a more acute "peak" around the mean (that is, a higher probability than a normally distributed variable of values near the mean) and "fat tails" (that is, a higher probability than a normally distributed variable of extreme values).
		In terms of shape, a platykurtic distribution has a smaller "peak" around the mean (that is, a lower probability than a normally distributed variable of values near the mean) and "thin tails" (that is, a lower probability than a normally distributed variable of extreme values).
	psychology.wikia.com /wiki/Kurtosis (655 words)

	Math Forum - Ask Dr. Math (Site not responding. Last check: 2007-11-06)
		Mean, median, and mode are all types of averages, although the mean is the most common type of average and usually refers to the _arithmetic mean_ (There are other kinds of means that are more difficult).
		But sometimes the arithmetic mean doesn't give you all the information you want, and here is where your first and third questions come in.
		Now, mean, median and mode are all good types of averages, and each works best in different types of situations.
	mathforum.org /library/drmath/view/57603.html (896 words)

	PSCH 343 Study_Guide (Site not responding. Last check: 2007-11-06)
		Take that in the broadest sense; you may be asked about things that relate to these items, not just these items directly.
		There are questions you have to think about, and some that you should be able to answer off the top of your head.
		Remember that “to within rounding errors” means the answer could differ by a neighboring digit in the last place offered.
	www.uic.edu /classes/psych/psych343/P343sgT.htm (591 words)

	Classes
		There is a slightly different equation needed to calculate this probability of the means being significantly different depending on whether the variances of the two data sets are the same or not.
		Moment initializes an array (pointer to a float) data, and integer nset.
		Mean() returns the average of the set of numbers in the array.
	www.ps.uci.edu /~youngs/Phy231C/Classes.html (1343 words)

	☞Risk Management Glossary - Finance, Energy, Technology & Statistics. Model Risk. Monte Carlo, Mean reversion, ...
		Mean - is often considered as the simple arithmetic average of the sum of the observed values divided by the number of observations.
		Mean Reversion - a tendency for a stochastic process to remain near, or return over time to a long-run average.
		The fourth moment is the Kurtosis which indicates the degree of central "peakedness" or, equivalently, the "fatness of the outer tails.
	www.zynex.com /glossary-m.htm (451 words)

	Computation - Operations Research Models and Methods
		The most common is the mean, the first moment about the origin, and the variance, the second moment about the mean.
		The mean is a measure of the centrality of the distribution and the variance is a measure of the spread of the distribution about the mean.
		The formula for this measure subtracts 3 from the ratio of the fourth moment about the mean and the square of the variance.
	www.me.utexas.edu /~jensen/ORMM/computation/unit/rvadd/discrete_dist/distributions.html (803 words)

	Descriptors
		The n-th moment about the mean, denoted as
		In a sense, the sequence of moments is analogous to the components of a Fourier sequence--the first few terms give the general shape, and the later terms fill in finer detail.
		Moments have been shown to be a very useful set of descriptors for matching.
	rivit.cs.byu.edu /morse/550-F95/node29.html (1586 words)

	Central Limit Theorem (fine print)
		Statistical Moments are analogous to moments in physics, where we consider a force multiplied by its distance from the centroid or fulcrum.
		The variance is the second statistical moment, and is the sum of the squared distances from the mean, times the probability of being at that distance.
		If the population mean doesn't exist, then the CLT doesn't apply and the characteristics of the sample mean, Xbar, are not predictable.
	www.statisticalengineering.com /central_limit_theorem_fineprint.htm (574 words)

	BE MINDFUL OF THE MOMENT (Site not responding. Last check: 2007-11-06)
		Are you someone who is rushing from moments to moment, regretting what you did and wishing for things that you do not have.
		Live in the moment, and accept the moment as it is. After all, you do not have a choice.
		Be convinced that the moment is perfect as is. It may not always be pleasant, but every moment is a seed encapsulating infinite potentiality.
	www.profound-happiness.org /be_mindful_of_the_moment.htm (645 words)

	Parameter Estimation Techniques (Site not responding. Last check: 2007-11-06)
		Moment estimation is based on the concept of matching the moments of the sample data with the moments defined by the distribution of interest and its parameters.
		The second moment about the mean is equal to the distribution variance.
		The number of moments needed is determined by the number of parameters being estimated.
	www.engineeredsoftware.com /nasa/pe_techniques.htm (600 words)

	About Daylight Saving Time
		See The World Clock for current times and places observing DST at the moment.
		Read more about Daylight Saving Time in United States Canada in 2007.
		Click on a city in The World Clock and you can see information about that city, including if it practices daylight saving this year, and when it starts and when it ends.
	www.timeanddate.com /time/aboutdst.html (818 words)

	Fractalic Awakening - New metaphysics, fractals, consciousness, awareness, spirituality, enlightenment
		This means you are completely Aware of your body, all sensations of the body, your surroundings, your emotional state, and your mental state, all without doing any "thinking" or "feeling" about it at all.
		This means that you are not engaged in the exercise of distinguishing one "part" of Experience from another.
		As I contemplated the nature of Moment and moments, I was struck by a nagging familiarity; something about this way of understanding reminded me of something else I would never have connected Moment and moments to before.
	www.fractalicawakening.com /moment.htm (1971 words)

	The Length of the Lunar Cycle (Site not responding. Last check: 2007-11-06)
		Mean Solar Time at the Prime Meridian, running at the same rate as TT but intermittently adjusted to match the observationally determined Earth rotation rate by insertion of leap second(s).
		Average lunar conjunction moment, assuming that Moon's orbit is a circle with Earth at its center, and that Earth's orbit is a circle with Sun at its center.
		In the present era the median length of the lunar cycle is about 29d 12h 30m, the average (MSM) is slightly more than 29d 12h 44m, the shortest lunations are about 29d 6h 30m, and the longest are about 29d 20h.
	individual.utoronto.ca /kalendis/lunar/index.htm (4304 words)

	Linear Algebra (1.3) ~ 3DSoftware.com
		The moment is measured from the hinge to the line of action of the force.
		Calculating the moment that way involves multiplying two scalars together, after finding the magnitude (scalar length) of the moment arm, and specifying the maximum force as the other scalar quantity.
		One way to do that is to specify the moment arm as a vector (distance displacement from the hinge to the point on the force line of action that is closest to the hinge), and specify the other vector as the force (coordinate displacement of the force magnitude and direction).
	www.3dsoftware.com /Math/Programming/LinAlg01/03 (1254 words)

	Mean and Variance
		The mean, or first moment, of a distribution is a measure of the average.
		We calculated its mean as 6 and its variance as 9.6.
		Then calculate the mean and variance of V using the values and their probabilities.
	arnoldkling.com /apstats/meanvar.html (534 words)

	Portfolio Reflections of Learning - MKW 2001
		The comparison of the true meaning of variance, which rests in squaring the deviation scores to obtain their corresponding areas, appearing to be implausible, although it is geometrically correct (as expressed through the words of Professor Keating in Dead Poets Society) and the application of the
		The text explains that "the term moment is used in mechanics as a measure of the force of rotation.
		To form a z ratio, calculate the difference between a random sample mean and the mean of the population over the standard error of the mean.
	www.west.asu.edu /mwilliam/quantitative/reflections.htm (1864 words)

	ECMWF
		Mean wave period from 1st moment of wind waves
		Mean wave period from 2nd moment of wind waves
		Mean wave period from 1st moment of swell
	www.ecmwf.int /research/ifsdocs/CY28r1/Waves/Waves-7-7.html (467 words)

	A note on separation in mean-lower-partial-moment portfolio optimization with fixed and moving targets - Publication - ... (Site not responding. Last check: 2007-11-06)
		As measures of portfolio risk, Lower Partial Moments (LPMs) have several advantages over variance, the traditional measure of risk.
		A separation theorem can be proven in the context of mean-LPM portfolio optimization, when the target is equal to the risk-free interest rate.
		Among moving targets, we show that linear separation holds if the target is set equal to the mean return of the portfolio under consideration.
	www.rti.org /abstract.cfm?pubid=5916 (199 words)

	MOMENT
		The MOMENT function computes the mean, variance, skewness, and kurtosis of a sample population contained in an n-element vector X.
		If the vector contains n identical elements, MOMENT computes the mean and variance, and returns the IEEE value NaN for the skewness and kurtosis, which are not defined.
		Set this keyword to a named variable that will contain the mean absolute deviation of X.
	star.pst.qub.ac.uk /idl/MOMENT.html (235 words)

	Hypertext Style: Cool URIs don't change.
		Some seem to think that because there is research about namespaces which will be more persistent, that they can be as lax about dangling links as they like as "URNs will fix all that".
		Enough people complain all the time about dangling links that I hope the damage is obvious.
		Often, this is because they are using tools whose task is seen as to present the best site in the moment, and no one has evaluated what will happen to the links when things change.
	www.w3.org /Provider/Style/URI (2713 words)

	Moment Saving - Website Development by Lauren Barden (Site not responding. Last check: 2007-11-06)
		Moment Saving - Website Development by Lauren Barden
		It means we have a brand new website and as Ben is a professional developer who specialises in PHP systems, we can offer you even more great services while continuing the level of support, experience and reasonable prices that you have come to expect from Moment Saving.
		Please click to view our new website at injader.com.
	www.momentsaving.com (74 words)

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