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# Topic: Hypergeometric distribution

###### In the News (Fri 24 May 13)

 Hypergeometric distribution - Wikipedia, the free encyclopedia In probability theory and statistics, the hypergeometric distribution is a discrete probability distribution that describes the number of successes in a sequence of n draws from a finite population without replacement. The hypergeometric distribution describes the probability that in a sample of n distinctive objects drawn from the shipment exactly k objects are defective. When the population size is large compared to the sample size (i.e., N is much larger than n) the hypergeometric distribution is approximated reasonably well by a binomial distribution with parameters n (number of trials) and p = D / N (probability of success in a single trial). en.wikipedia.org /wiki/Hypergeometric_distribution   (1071 words)

 Probability Distributions (Statistics Toolbox)   (Site not responding. Last check: 2007-09-06) The hypergeometric distribution models the total number of successes in a fixed size sample drawn without replacement from a finite population. The distribution is discrete, existing only for nonnegative integers less than the number of samples or the number of possible successes, whichever is greater. The hypergeometric distribution differs from the binomial only in that the population is finite and the sampling from the population is without replacement. www-rohan.sdsu.edu /doc/matlab/toolbox/stats/prob_d19.html   (149 words)

 Hypergeometric Distribution The hypergeometric distribution is similar to the binomial distribution. The difference is that the binomial distribution requires the probability of success to be the same for all trials, while the hypergeometric distribution does not. The binomial distribution can be used to approximate the hypergeometric distribution when the population is large with respect to the sample size. www.engineeredsoftware.com /nasa/hypergeometric.htm   (465 words)

 Distributions Binomial Distribution: The binomial distribution, also known as Bernoulli distribution, describes the random sampling processes that all outcomes are either yes or no (success/failure) without ambiguity. Hypergeometric Distribution: The hypergeometric distribution describes the random sampling processes in which once a sample has been chosen, it will NOT be placed back into the sampling pool (sampling without replacement). Normal Distribution: The normal distribution, or Gaussian distribution, is a symmetrical distribution commonly referred to as the bell curve. www.efunda.com /math/distributions/distributions.cfm   (253 words)

 PlanetMath: hypergeometric random variable This approximation simplifies the distribution by looking at a system with replacement for large values of M and K. "hypergeometric random variable" is owned by mathcam. Cross-references: distribution, binomial random variable, approximation, variance, expected value, represents, syntax This is version 5 of hypergeometric random variable, born on 2001-10-26, modified 2005-04-14. planetmath.org /encyclopedia/HypergeometricDistribution.html   (100 words)

 Functions and CALL Routines : PDF The PDF function for the chi-squared distribution returns the probability density function of a chi-squared distribution, with df degrees of freedom and noncentrality parameter nc, which is evaluated at the value x. The PDF function for the F distribution returns the probability density function of an F distribution, with ndf numerator degrees of freedom, ddf denominator degrees of freedom, and noncentrality parameter nc, which is evaluated at the value x. The PDF function for the hypergeometric distribution returns the probability density function of an extended hypergeometric distribution, with population size m, number of items k, sample size n, and odds ratio r, which is evaluated at the value x. www.asu.edu /it/fyi/unix/helpdocs/statistics/sas/sasdoc/sashtml/lgref/z0270634.htm   (1051 words)

 Functions and CALL Routines : CDF The CDF function for the chi-squared distribution returns the probability that an observation from a chi-squared distribution, with df degrees of freedom and noncentrality parameter nc, is less than or equal to x. 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 noncentrality parameter nc, is less than or equal to x. The CDF function for the hypergeometric distribution returns the probability that an observation from an extended hypergeometric distribution, with population size m, number of items k, sample size n, and odds ratio r, is less than or equal to x. www.asu.edu /it/fyi/dst/helpdocs/statistics/sas/sasdoc/sashtml/lgref/z0208980.htm   (1101 words)

 Lecture Notes 5 A probability distribution is similar to the frequency distribution of a quantitative population because both provide a long-run frequency for outcomes. The graph of a binomial distribution can be constructed by using all the possible X values of a distribution and their associated probabilities. The hypergeometric distribution is used to determine the probability of a specified number of successes and/or failures when (1) a sample is selected from a finite population without replacement and/or (2) when the sample size, n, is greater than or equal to 5% of the population size, N, i.e., [ n>=5% N]. business.clayton.edu /arjomand/business/l5.html   (1466 words)

 [No title] The mean or expected value of a Hypergeometric random variable (as used in a sampling without replacement problem) is effectively the same as the mean of a Binomial random variable (used in a sampling with replacement problem). In the Bernoulli trials case, the Negative Binomial distribution is the distribution counting the number of trials required until a specified number (say k) of successes have been observed. The Negative Hypergeometric Distribution Let Y be a random variable counting the number of selections required until the kth success is obtained when sampling without replacement from a set of N objects of which M have a certain attribute (i.e. math.usask.ca /~oshaughn/103Hypergeometric.doc   (2833 words)

 Cdf (JMSL) The individual terms are calculated from the tails of the distribution to the mode of the distribution and summed. The hypergeometric random variable X can be thought of as the number of items of a given type in a random sample of size n that is drawn without replacement from a population of size l containing m items of this type. The gamma distribution is often defined as a two-parameter distribution with a scale parameter b (which must be positive), or even as a three-parameter distribution in which the third parameter c is a location parameter. www.vni.com /products/imsl/jmsl/v20/api/com/imsl/stat/Cdf.html   (2392 words)

 [No title] An exact p-value (as opposed to large-sample result) for the test of equal binomial probabilities is possible (appropriate for 2x2 tables in general) and is based on the distribution of the values in the table conditional on all fixed marginal totals. That is, the distribution of N_11 induced by the randomization is hypergeometric. The calculations for the hypergeometric probability distribution of n_11 under the null hypothesis of independence is shown in the following table. darkwing.uoregon.edu /~robinh/lec_05a.txt   (1363 words)

 ISE 162 Sec. 1, Class Notes, Class 7   (Site not responding. Last check: 2007-09-06) Don't be confused by N and n; the first is the size of the finite set from which the sample is drawn, the second the size of the sample. The hypergeometric distribution is a model for an engineering process where the population is finite. So, the negative binomial distribution is a model for an engineering process; k and p define the shape of the probability distribution, and X tells us what the values on the abscissa will be. www.engr.sjsu.edu /jgille/notes2005b07.html   (1162 words)

 [No title] This chapter introduces several other random variables and probability distributions that arise from drawing at random from a box of tickets numbered "0" or "1:" the geometric distribution, the negative binomial distribution, and the hypergeometric distribution. The binomial, geometric, hypergeometric, and negative binomial distributions are examples of discrete probability distributions. The hypergeometric distribution also can be used to calculate the probability that if WD had selected 31 firms from the CD-ROM at random, the 31 firms would contain as many of WBH's customers as it did, or even more. www.stat.berkeley.edu /users/stark/SticiGui/Text/ch12.htm   (5742 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 hypergeometric distribution returns the probability that an observation from an extended hypergeometric distribution, with population size N, number of items R, sample size n, and odds ratio o, 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. support.sas.com /91doc/getDoc/lrdict.hlp/a000208980.htm   (1109 words)

 2.3 Model Processes - DRAFT PSC Selective Fishery Evaluation   (Site not responding. Last check: 2007-09-06) The appropriate probability distribution to model the number of marked fish captured in a selective fishery depends upon the fate of the unmarked fish which are released. The multiple hypergeometric distribution is used in the SFM for the following reasons: (1) Harvest rates are likely to be less than 30% within the weekly time step of the model; (2) some reduced susceptibility to recapture within a week is likely; and (3) the probabilities are much more easily computed. Generate the theoretical frequency distribution of encounters per unit of effort in the absence of a bag limit using a negative binomial distribution. www.cqs.washington.edu /harvest/sfm/modsp.doc7.html   (1554 words)

 The Hypergeometric Distribution omline. For sampling without replication The hypergeometric distribution is used for calculating probabilities for samples drawn from relatively small populations and without replication. The hypergeometric distribution is often used in zoology to study small animal or plant populations. The hypergeometric procedure is a full integer procedure, the input is considered to consist of the number positive in the population, the number of positive observations in the sample, the sample size and the population size. home.clara.net /sisa/hypghlp.htm   (651 words)

 Hypergeometric Distribution: Probability Calculator In a hypergeometric experiment, a set of items are randomly selected from a finite population. In a hypergeometric experiment, each element in the population can be classified as a success or a failure. A cumulative hypergeometric probability refers to a sum of probabilities associated with a hypergeometric experiment. www.stattrek.com /Tables/Hypergeometric.aspx   (1053 words)

 lessonE Have students conjure other examples to which the hypergeometric distribution may be applied. The hypergeometric distribution is useful in many real-life contexts, not simply drawing chips from an urn. As long as there is a certain number selected from the total sample space with generally two types of objects in the sample, the hypergeometric distribution can be utilized. www.mste.uiuc.edu /courses/educ362sp04/folders/sala/lessonE.html   (654 words)

 The Hypergeometric Distribution Convergence of the Hypergeometric Distribution to the Binomial replacement, and hence the hypergeometric distribution should be well-approximated by the binomial. In the setting of Exercise 20, show that the mean and variance of the hypergeometric distribution converge to the mean and variance of the binomial distribution as as www.ds.unifi.it /VL/VL_EN/urn/urn2.html   (858 words)

 Distributions in Discrete Systems The binomial distribution, also known as Bernoulli distribution, describes the random sampling processes that all outcomes are either yes or no (success/failure) without ambiguity. The hypergeometric distribution describes the random sampling processes that once a sample has been chosen, it will NOT be placed back to the sampling pool (sampling without replacement). The Poisson distribution describes the random sampling process that the desired outcomes occur relatively infrequently but at a regular rate. www.efunda.com /math/distributions/dist_discrete.cfm   (190 words)

 [No title]   (Site not responding. Last check: 2007-09-06) A random variable X is defined to have a hypergeometric distribution, denoted by X~Hyp(n,M,K), if the pmf of X is given by: pX(x) = EMBED Equation.3 I{0,1,,min(n,K)}(x) where M is a positive integer, K is a nonnegative integer that is at most M, and n is a positive integer that is at most M. Theorem. This will require the evaluation of the expectation and variance of a linear function of random variables) A hypergeometric experiment consists of selecting a sample of size n using random sampling without replacement from a population of M elements, K of which may be classified as “success” and the remaining M-K as “failure”. Thus, the Binomial distribution is used in modeling the number of successes in a random sample of size n when the sample size is small relative to the size of the population even if sampling is done without replacement. www.upd.edu.ph /~stat/faculty/tgc/Stat121Ch_3.doc   (3310 words)

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