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Topic: Lognormal distribution

 Log-normal distribution - Wikipedia, the free encyclopedia In probability and statistics, the log-normal distribution is the probability distribution of any random variable whose logarithm is normally distributed (the base of the logarithmic function is immaterial in that log The log-normal distribution, the geometric mean, and the geometric standard deviation are related. If a sample of data is determined to come from a log-normally distributed population, the geometric mean and the geometric standard deviation may be used to estimate confidence intervals akin to the way the arithmetic mean and standard deviation are used to estimate confidence intervals for a normally distributed sample of data. en.wikipedia.org /wiki/Lognormal_distribution   (393 words)

 Mathematically Analytic Distributions Can Explain Radioanalytic Results Actual distributions of radionuclides in samples that might be truly lognormal   will appear at low levels to deviate from their actual distribution because the subtraction of blank measurements having random fluctuations produces an increased population of small and negative values at low analyte levels. Since the lognormal functions of Equations 8-10 are not defined at their lower limits of integration (as a result, e.g., of w in the denominator and non-convergence of the integrand),   the value of the integrand must avoid zero. The probability density function (pdf) for the distribution of fy/m is obtained from the integrand of Equation 8, using a notation of pw(w) for convenience of notation in MATHCAD, where w is the dummy variable representing fy/m, and pw is the specific functional form for the pdf of fy/m. www.lanl.gov /BAER-Conference/BAERCon-46p011.htm   (3261 words)

 IDEAL lognormal   (Site not responding. Last check: 2007-11-04) The question of the distribution of wealth across a population is very similar to that of the size distribution of airborne particles or aerosols. A distribution called the lognormal is sometimes fit to such a distribution, and X is said to follow a lognormal distribution if log X has a normal distribution. However, the lognormal distribution is asymmetric, and dividing the distribution at the abscissa mid-point will result in two unequal parts, a larger 'mass' to the left of the division and a smaller 'tail' to the right. www.idealectic.com /idealectic/idlog.htm   (1005 words)

 5.4.3 Fitting examples   (Site not responding. Last check: 2007-11-04) Figures 5.3, 5.4 illustrate the cumulative distribution of the actual data, their fitting into a hybrid distribution (lognormal for the body and power-law for the tail), and the fitting of the hybrid distribution into a hyper-exponential one. By changing simultaneously both the a and b parameters of a lognormal distribution, we change both the scale and shape of the distribution so as to vary the variance of the distribution and at the same type keep the mean of the distribution constant (and equal to the mean of day 57, i.e., 3629 Bytes. Figure 5.5 illustrates how the cdf of the distribution changes when we change the workload variability (the fitting technique we use resulted in three, four, or five stages for the lognormal fitting, thus a total of six, seven, or eight stages were used to fit the mixture of the lognormal and power-law distribution). www.cs.wm.edu /~riska/main/node59.html   (407 words)

 Lognormal Distribution The lognormal distribution is defined with reference to the normal distribution. The lognormal distribution for a random variable X may be specified with its mean As with the normal distribution, the cumulative distribution function (CDF) of a lognormal distribution exists, but cannot be expressed in terms of standard functions. www.riskglossary.com /articles/lognormal_distribution.htm   (425 words)

 Stata help for streg   (Site not responding. Last check: 2007-11-04) A specified distribution() is remembered from one estimation to the next when distribution() is not specified. ancillary( varlist) specifies that the ancillary parameter for the Weibull, lognormal, Gompertz, and log-logistic distributions and the first ancillary parameter (sigma) of the generalized log-gamma distribution be estimated as a linear combination of varlist. anc2( varlist) specifies that the second ancillary parameter (kappa) for the generalized log-gamma distribution be estimated as a linear combination of varlist. www.stata.com /help.cgi?streg   (947 words)

 [No title]   (Site not responding. Last check: 2007-11-04) While the new probability distribution that provides very close approximations when the underlying severity distribution is lognormal, the form of this new density function can be extended by analogy to forms that produce close approximations when the underlying severity distribution is either a weibull or a pareto distribution. The lognormal distribution was used as the basis for most of the development work in deriving the formula for the density function of the aggregate distribution because the form of this new density function is more obviously related to that of the lognormal density function. Distribution has a thicker tail than the lognormal distribution at its upper end, dramatically increasing the goodness of fit to the aggregate loss distribution. www.casualtyactuaries.com /coneduc/clrs/98clrs/handouts/sherman1.doc   (1508 words)

 Lognormal Distribution Lognormal distributions (with two parameters) have a central role in human and ecological risk assessment for at least three reasons. The lognormal distribution is used to model continuous random quantities when the distribution is believed to be skewed, such as certain income and lifetime variables. This property is one of the reasons for the fame of the lognormal distribution. www.mlahanas.de /Math/Lognormal.htm   (1466 words)

 LogNormal Distribution In the mining and extraction industries, it has been observed that where the value of an item is proportional to size, the population is probably lognormally distributed, with few valuable items and lots of uncommercial items, the biosciences may have a different perception. The lognormal distribution is often used to model the distribution of reserves in oilfields within a province. The range of random numbers generated for the LogNormal distribution is from greater than zero to positive infinity. www.brighton-webs.co.uk /distributions/lognormal.asp   (256 words)

 [No title] Kurtosis is an indicator of the peakedness of a distribution and is postive for a very peaked distribution, negative for a flat distribution and zero for a normal distribution. A test which representation of the I; distribution in t space can be used to predict the arithmetic mean (in the case of the y1/ distribution the test is irrelevant since the y1/ distribution mean is set equal to the permits a more intuitive understanding of the quality of an y1/ or L 1.11 I. The use of the lognormal distribution to predict the arithmetic mean and standard deviation of the histogram in t space yielded reasonably accurate estimates and as such provides a means of ensuring the continuity of data archives based on arithmetic means. aeronet.gsfc.nasa.gov /TXT/2000GL011581.txt   (2033 words)

 1.3.6.6.14. Power Lognormal Distribution Since the general form of probability functions can be expressed in terms of the standard distribution, all subsequent formulas in this section are given for the standard form of the function. is the cumulative distribution function of the standard normal distribution. Nelson discusses the mean, median, mode, and standard deviation of the power lognormal distribution and provides references to the appropriate tables. www.itl.nist.gov /div898/handbook/eda/section3/eda366e.htm   (491 words)

 Boost Random Number Library Distributions In addition to the random number generators, this library provides distribution functions which map one distribution (often a uniform distribution provided by some generator) to another. The distribution functions no longer satisfy the input iterator requirements (std:24.1.1 [lib.input.iterators]), because this is redundant given the Generator interface and imposes a run-time overhead on all users. Such a distribution produces random numbers x > 0 distributed with probability density function p(x) = lambda * exp(-lambda * x), where lambda is the parameter of the distribution. www.solarix.ru /for_developers/cpp/boost/random/random-distributions.shtml   (1427 words)

 Life is log-normal !   (Site not responding. Last check: 2007-11-04) The sensitivity of the individuals in a population to a chemical compound. Often, distributions are summarized by mean and standard deviation which is a poor description for skew distributions. Lognormal distributions across the sciences: keys and clues. www.inf.ethz.ch /personal/gut/lognormal/brochure.html   (533 words)

 1.4.2.9.2. Graphical Output and Interpretation If the distribution does have a shape parameter, then we are actually addressing a family of distributions rather than a single distribution. Exponential distribution - the exponential distribution is a special case of the Weibull with shape parameter equal to 1. Note that for the Weibull distribution, the Anderson-Darling test is actually testing the 2-parameter Weibull distribution (based on maximum likelihood estimates), not the 3-parameter Weibull distribution. www.itl.nist.gov /div898/handbook/eda/section4/eda4292.htm   (1211 words)

 Repetitive Genetic Inversion of Optical Extinction Data It is apparent that although the larger diameters of the inverted distributions in Fig. The inverted distributions show a large amount of variation, dramatically demonstrating the non-uniqueness inherent retrieving a bimodal size distribution from extinction measurements in the wavelength range 0.35-1.06 m. This distribution pattern of volcanic aerosol was consistent with the wind fields as well as aerosol optical depths derived from the SeaWifs satellite. www.soest.hawaii.edu /lidar/genetic_inversion_paper.htm   (3477 words)

 Distribution Form Frame   (Site not responding. Last check: 2007-11-04) The exponential distribution, also known as the waiting-time distribution, describes the amount of time or distance between the occurrence of random events (such as the time between major earthquakes or the time between no hitters pitched in major league baseball). The distribution is used in the analysis of variance and is a function of the ratio of two independent random variables each of which has a chi-square distribution and is divided by its number of degrees of freedom. The Gumbel distribution, a special case of the Fisher-Tippett Distribution, is particularly convenient for extreme value distribution purposes, and it may be used as an alternative to the normal distribution in the case of skewed empirical data. ic.net /~jnbohr/java/CdfDemoArgs.html   (1684 words)

 Functions and CALL Routines : CDF Function The CDF function for the F distribution returns the probability that an observation from an F distribution, with ndf numerator degrees of freedom, ddf denominator degrees of freedom, and non-centrality parameter nc, is less than or equal to x. The CDF function for the normal mixture distribution returns the probability that an observation from a mixture of normal distribution is less than or equal to x. The CDF function for the Pareto distribution returns the probability that an observation from a Pareto distribution, with the shape parameter a and the scale parameter k, is less than or equal to x. support.sas.com /onlinedoc/912/getDoc/lrdict.hlp/a000208980.htm   (1186 words)

 Getting to know the lognormal disrribution From the many distributions that Crystal Ball offers, many users pick one standard distribution, such as triangular, normal, or uniform, and use it repeatedly, unaware that a different distribution might be more appropriate. The lognormal distribution is a positively skewed distribution, meaning that most of the distribution is concentrated around the left end, closest to zero. Model builders use the lognormal distribution to describe values that cannot fall below zero, but that might increase without limit, such as the value of securities (financial applications) or properties (real estate applications) or the failure rate of electronic parts (engineering applications). www.decisioneering.com /support/cbtips/cb_tips27.html   (187 words)

 Probability Plotting for the Lognormal Distribution   (Site not responding. Last check: 2007-11-04) However, since the lognormal distribution models the natural logarithms of the times-to-failure, the values of the parameter estimates must be read and calculated based on a logarithmic scale, as opposed to the linear time scale as it was done with the normal distribution. The process of lognormal probability plotting is illustrated in the following example. Estimate the parameters for the lognormal distribution using probability plotting. www.weibull.com /LifeDataWeb/probability_plotting_log.htm   (319 words)

 Publications List The integral number versus peak flux distribution can be fit by a truncated lognormal distribution or by functions consisting of a single lognormal distribution with a power law tail of slope -1.5. The lognormal properties of GRBs are similar to terrestial lightning and suggest that relativistic discharges between regions of charge separation may be the emission mechanism responsible for GRBs originating in the Solar System, the galaxy or at cosmological distances. The time intervals between the microjumps in the Vela pulsar and the size of the microjumps are compatible with lognormal distributions and there is no correlation between the time interval and the size of the microjump. www.ucd.ie /ssamr/astro/papers.html   (853 words)

 Nat' Academies Press, Forensic Analysis: Weighing Bullet Lead Evidence (2004) Thus, for three reasons—the nature of the error in chemical measurements, the approximate normality of the distributions, and the more constant variance (that is, the variance is not a function of the magnitude of the measurement itself)—logarithmic transformation of the measurements is advisable. Because µx and µy are assumed to be constant, and hence have variance 0, and The distribution of measurement errors is often (not always) assumed to be normal (Gaussian). Simulation suggests that the distribution of the ratio (sx + sy)/sp has a mean of 1.334 (10%, 25%, 75%, and 90% quantiles are 1.198, 1.288, 1.403, and 1.413, respectively). www.nap.edu /books/0309090792/html/133.html   (2468 words)

 Genesis Lognormal Distribution   (Site not responding. Last check: 2007-11-04) The lognormal-factor (or the increment in case of normal distribution), defining the relation of the horizontal position of the tips of triangles in two neighbour columns. AITCHISON, J., BROWN, J.A.C., The lognormal distribution, Cambridge University Press, Cambridge, 1957. The page and specially the model were developped by Christian Gut as a Semesterarbeit at the Institute of Scientific Computing of the ETH Zürich, supervised by Prof. www.inf.ethz.ch /personal/gut/lognormal   (383 words)

 [No title] The joint probability distribution (or density function) of these two continuous random variables can be specified by providing a method for calculating the probability that x1 and x2 assume a value in any region R of two-dimensional space, where the region R is often called the range space of the random variable. The lognormal distribution is defined only for positive values of the random variable x and the probability density function is  EMBED Equation.DSMT4  The parameters of the lognormal distribution are  EMBED Equation.DSMT4 . The exponential distribution is frequently used in reliability engineering as a model for the lifetime or time to failure of a component or system. www3.interscience.wiley.com:8100 /legacy/college/montgomery/0471656313/supp_text/ch02.doc   (2565 words)

 Recovering Probabilistic Information From Option Markets In this study, the performance of the candidate distribution which seems to be most representative of the data is tested against the lognormal which serves as a convenient benchmark. Intuitively, this procedure is similar to that of recovering an implied volatility except that the dimension of the choice variable vector corresponds to the number of parameters of the candidate distribution (two for lognormal distribution and three for the Burr III distribution). Figures 1 and 2 display a sample of the distributions as implied in option prices for the November 1990 soybeans futures contract at several points in the contract life under the Burr III and lognormal parametizations, respectively. www.ace.uiuc.edu /ofor/ss0395/brucejs.html   (3797 words)

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