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# Topic: Normal distribution

 1.3.6.6.1. Normal Distribution is the probability density function of the standard normal distribution. The location and scale parameters of the normal distribution can be estimated with the sample mean and sample standard deviation, respectively. The sampling distribution of the mean becomes approximately normal regardless of the distribution of the original variable. www.itl.nist.gov /div898/handbook/eda/section3/eda3661.htm   (458 words)

 Normal distribution - Wikipedia, the free encyclopedia The fundamental importance of the normal distribution as a model of quantitative phenomena in the natural and behavioral sciences is due to the central limit theorem (the proof of which requires rather advanced undergraduate mathematics). The derivation of the maximum-likelihood estimator of the covariance matrix of a multivariate normal distribution is subtle. In that case, the assumption of normality is not justified, and it is the logarithm of the variable of interest that is normally distributed. en.wikipedia.org /wiki/Normal_distribution   (3838 words)

 Multivariate normal distribution - Wikipedia, the free encyclopedia In probability theory and statistics, a multivariate normal distribution, also sometimes called a multivariate Gaussian distribution, is a specific probability distribution, which can be thought of as a generalization to higher dimensions of the one-dimensional normal distribution (also called a Gaussian distribution). The cumulative distribution function (cdf) F(x) is defined as the probability that all values in a random vector X are less than or equal to the corresponding values in vector x. Two random variables that are normally distributed may fail to be jointly normally distributed, i.e., the vector whose components they are may fail to have a multivariate normal distribution. en.wikipedia.org /wiki/Multivariate_normal_distribution   (993 words)

 Normal distribution Summary The normal distribution also arises in many areas of statistics: for example, the sampling distribution of the mean is approximately normal, even if the distribution of the population the sample is taken from is not normal. The derivation of the maximum-likelihood estimator of the covariance matrix of a multivariate normal distribution is subtle. In that case, the assumption of normality is not justified, and it is the logarithm of the variable of interest that is normally distributed. www.bookrags.com /Normal_distribution   (4551 words)

 The Normal Distribution The distribution of noise levels for all jets during takeoff over this neighborhood has a normal distribution. Since the area under a normal curve on each side of the mean is.5, the proportion of jets with a decibel level less than 95 is.5000 -.4306 =.0694. The normal distributions below have the desired probability (area under the curve) shaded, and the important values appropriately marked. www.nku.edu /~statistics/Normal_Distribution.htm   (573 words)

 The Individualist: Normal Distribution The standard normal distribution is the normal distribution with a mean of zero and a standard deviation of one (the green curves in the plots to the right). The normal distribution also arises in many areas of statistics: for example, the sampling distribution of the mean is approximately normal, even if the distribution of the population the sample is taken from is not normal. The normal distribution was first introduced by Abraham de Moivre in an article in 1734 (reprinted in the second edition of his The Doctrine of Chances, 1738) in the context of approximating certain binomial distributions for large n. www.dadamo.com /wiki/wiki.pl/Normal_Distribution   (697 words)

 I   (Site not responding. Last check: ) Notice that a normal distribution may come with very different dimensions (tall and skinny, short and wide), but the characteristics mentioned above hold in all cases (the high point, i.e., the most frequent value, is always in the centre, and the two sides of the curve are perfectly symmetrical). The normal curve or the normal distribution is an extremely important statistical concept, as important in many areas of enquiry as the right-angle triangle is in Euclidean geometry, and for the remainder of our short study of statistics we shall be dealing only with this frequency distribution. Normal distributions are particularly important for a number of reasons (as we shall see), not the least of which is that many of the important characteristics we wish to study (including all inherited characteristics) are normally distributed. www.mala.bc.ca /~johnstoi/maybe/maybe5.htm   (4967 words)

 PlanetMath: normal random variable The normal distribution is probably the most frequently used distribution. Its importance in probability theory and statistics is made clear by Lindeberg's central limit theorem. This is version 11 of normal random variable, born on 2001-10-26, modified 2004-10-08. planetmath.org /encyclopedia/NormalRandomVariable.html   (153 words)

 Lecture Notes 6 Among the continuous probability distribution, the uniform distribution is the simplest one of all. Normal distribution is probably one of the most important and widely used continuous distribution. The Z distribution is a normal distribution with a mean of 0 and a standard deviation of 1. business.clayton.edu /arjomand/business/l6.html   (2002 words)

 Probability and the Normal Distribution   (Site not responding. Last check: ) The normal distribution is symmetric (you can fold it in half and the two halves will match) and unimodal (single peaked). Some statistical techniques demand that individual data items follow a normal distribution, that is, that the population histogram from which the sample is drawn have a normal shape. When normality of the individual observations is essential, transformations such as logarithms can sometimes be used to produce a set of transformed data that is better described by a normal distribution that the original data. www.tufts.edu /~gdallal/normal.htm   (489 words)

 Normal Distribution The standard (or canonical) normal distribution is a special member of the normal family that has a mean of 0 and a standard deviation of 1. Exercise #2 requires you to compute probabilities and quantiles for the distribution of annual rainfall, assumed to be normally distributed, in a region. Exercise #3 requires you to compute probabilities and quantiles for the distribution of daily absences per 100 employees before and after a health improvement program, assumed to be normally distributed, at a large corporation. www.stat.wvu.edu /SRS/Modules/Normal/normal.html   (833 words)

 Normal distribution The normal distribution is an approximation to the distribution of values of a characteristic. The distribution is useful as a model for the length of certain animals, the distribution of IQ scores, and so on. The exact shape of the normal distribution depends on the mean and the standard deviation of the distribution. www.berrie.dds.nl /normal.html   (186 words)

 Normal Distribution Mapping The surface normal direction and shading for a patch of surface are represented by a statistical distribution of normal directions. Unfortunately, this distribution is quite difficult to combine and filter, and the approximation we get when we combine a mixture of two distributions into a single one is not a good one. These distributions are formed by starting with a distribution in Euclidean 3-space, and using the conditional probability of the distribution when restricted to the surface of the sphere. www.cs.unc.edu /~olano/papers/ndm   (4368 words)

 The Bell-shaped, Normal, Gaussian Distribution For a normally distributed data set, the empirical rule states that 68% of the data elements are within one standard deviation of the mean, 95% are within two standard deviations, and 99.7% are within three standard deviations. Normal in statistics generally refers to the gaussian distribution or the "normal" way we would expect errors to be distributed. Normal can refer to the fact that the area has been made equal to one (to normalize) so that area and probability are equivalent. www.andrews.edu /~calkins/math/webtexts/stat06.htm   (1287 words)

 Normal Distribution The shape of the normal distribution resembles that of a bell, so it sometimes is referred to as the "bell curve", an example of which follows: This extended applicability is possible because of the central limit theorem, which states that regardless of the distribution of the population, the distribution of the means of random samples approaches a normal distribution for a large sample size. The normal distribution often is used to describe random variables, especially those having symmetrical, unimodal distributions. www.netmba.com /statistics/distribution/normal   (463 words)

 Normal Distribution   (Site not responding. Last check: ) Normal distributions are a family of distributions that have the shape shown below. Normal distributions are symmetric with scores more concentrated in the middle than in the tails. Most of these tests work well even if the distribution is only approximately normal and in many cases as long as it does not deviate greatly from normality. davidmlane.com /hyperstat/A6929.html   (99 words)

 standard normal distribution table, curve, z value table, excel table Column B in the standard normal distribution table is the area under the standard normal distribution curve from a negative infinity to the sigma value (Z). Column D in the standard normal distribution table is the area under the standard normal distribution curve from –Z to +Z. This is the area around zero from plus or minus the SD stated. Column E in the standard normal distribution table is the area under the standard normal distribution curve outside of -Z to +Z. This is 1.0 minus the values for Column D. For outside plus or minus 1.5 SD the value is 0.1336. www.adamssixsigma.com /Newsletters/standard_normal_table.htm   (1110 words)

 Cumulative Normal Distribution: Probability Calculator Although every normal distribution has a bell-shaped curve, some normal distributions have a curve that is tall and narrow; while others have a curve that is short and wide. The normal random variable of a standard normal distribution is called a standard score or a z-score. In connection with the normal distribution, a cumulative probability refers to the probability that a randomly selected score will be less than or equal to a specified value, referred to as the normal random variable. stattrek.com /Tables/normal.aspx   (1002 words)

 The Normal Distribution Understanding the normal distribution is vital to understanding all sorts of statistics, to understanding signal detection theory, and in a host of other applications. Normal distributions are symetrical about the mean and they are bell shaped. Mathematicians have studied the normal distribution so much that there is even an equation that exactly describes it (although you don't need to know that equation). www.uark.edu /misc/lampinen/tutorials/normal.htm   (1793 words)

 Normal distribution   (Site not responding. Last check: ) A useful continuous distribution is the normal distribution with mean equal to 0 and variance (hence standard deviation) equal to 1. The CRC tables have tabulated the area under the standard normal curve to the left of a specified z-value (the letter z generally refers to standard normal distribution (mean=0, variance=1); caveat: other tables record the area between 0 and the specified cutoff). we find in a table of the normal distribution associated with the z-value 1 the area.8413 (which corresponds to the blue and cyan regions in the figure), and we find in the table associated with the z-value -.5 the area.3085 (which corresponds to the cyan area in the figure). www.cs.uni.edu /~campbell/stat/normal.html   (521 words)

 Normal Distribution In a normal distribution the variable stays close to its mean most of the time. Thus a normal distribution is completely characterized by two parameters, its mean m and its standard deviation σ. Therefore, a random variable with a normal distribution, and standard deviation s, is within x of its mean with probability erf(x/(sqrt(2)s)). www.mathreference.com /pr,normal.html   (911 words)

 The Normal Distribution The normal distribution holds an honored role in probability and statistics, mostly because of the central limit theorem, one of the fundamental theorems that forms a bridge between the two subjects. The important properties of the normal distribution are most easily obtained using the moment generating function. The key result is that the sum is still normal; the expressions for the mean and variance are standard results that hold for the sum of independent variables generally. www.ds.unifi.it /VL/VL_EN/special/special2.html   (877 words)

 Normal Distribution What we're doing is creating a correspondence between the graphical representation of the normal distribution which has two inflection points and an arithmetic formula in which we add to or subtract the value of sigma from mu. The normal distribution is completely specified by mu and sigma; once you know mu and sigma, you know everything there is to know about a normal distribution. If a distribution is normal, it is usually noted by a capital N, and then, in parentheses, the values of mu and sigma. www.psych.utah.edu /stat/introstats/web-text/Normal_Distribution   (6761 words)

 Standard Normal Distribution A standard normal distribution is a normal distribution with mean 0 and standard deviation 1. However, all other normal distributions are equivalent to this distribution when the unit of measurement is changed to measure standard deviations from the mean. The 80th percentile of the standard normal distribution is 0.84. www.oswego.edu /~srp/stats/z.htm   (1122 words)

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