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Topic: Geometric distribution


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  Geometric distribution - Wikipedia, the free encyclopedia
In either case, the sequence of probabilities is a geometric sequence.
} and is a geometric distribution with p = 1/6.
The geometric distribution Y is a special case of the negative binomial distribution, with r = 1.
en.wikipedia.org /wiki/Geometric_distribution   (471 words)

  
 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   (1449 words)

  
 Log-normal distribution - Wikipedia, the free encyclopedia
The log-normal distribution, the geometric mean, and the geometric standard deviation are related.
In this case, the geometric mean is equal to exp(μ) and the geometric standard deviation is equal to exp(σ).
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/Log-normal_distribution   (475 words)

  
 Sebaran probabilitas - Wikipédia
A distribution is called discrete if its cumulative distribution function consists of a sequence of finite jumps, which means that it belongs to a discrete random variable X: a variable which can only attain values from a certain finite or countable set.
The Erlang distribution, which is a special case of the gamma distribution with integral shape parameter, developed to predict waiting times in queuing systems.
The Weibull distribution, of which the exponential distribution is a special case, is used to model the lifetime of technical devices.
su.wikipedia.org /wiki/Probability_distribution   (899 words)

  
 Geometric distribution: Facts and details from Encyclopedia Topic   (Site not responding. Last check: 2007-10-08)
The probability distribution of the number of times it is thrown is supported on the infinite set and is a geometric distribution with p = 1/6.
In probability theory, memorylessness is a property of certain probability distributions: the exponential distributions and the geometric distributions....
The geometric distribution Y is a special case of the negative binomial distribution negative binomial distribution quick summary:
www.absoluteastronomy.com /encyclopedia/g/ge/geometric_distribution.htm   (1273 words)

  
 PlanetMath: geometric random variable   (Site not responding. Last check: 2007-10-08)
The expected value of a geometric random variable is given by
The moment generating function of a geometric random variable is given by
This is version 8 of geometric random variable, born on 2001-10-26, modified 2005-08-12.
planetmath.org /encyclopedia/GeometricDistribution.html   (93 words)

  
 Geometric Distribution   (Site not responding. Last check: 2007-10-08)
The geometric distribution is similar to the binomial distribution in that the probability of occurrence is constant from trial to trial and the trials are independent.
The binomial distribution models situations where the number of trials is fixed, and the random variable is the number of successes.
The geometric distribution requires exactly 1 success, and the random variable is the number of trials required to obtain the first success.
www.engineeredsoftware.com /nasa/geometric.htm   (281 words)

  
 Distribution Fitting
To determine this underlying distribution, it is common to fit the observed distribution to a theoretical distribution by comparing the frequencies observed in the data to the expected frequencies of the theoretical distribution (i.e., a Chi-square goodness of fit test).
The major distributions that have been proposed for modeling survival or failure times are the exponential (and linear exponential) distribution, the Weibull distribution of extreme events, and the Gompertz distribution.
The logistic distribution is used to model binary responses (e.g., Gender) and is commonly used in logistic regression.
www.statsoft.com /textbook/stdisfit.html   (1769 words)

  
 Statistics Glossary - random variables and probability distributions
Typically, a Geometric random variable is the number of trials required to obtain the first failure, for example, the number of tosses of a coin untill the first 'tail' is obtained, or a process where components from a production line are tested, in turn, until the first defective item is found.
The Geometric distribution is related to the Binomial distribution in that both are based on independent trials in which the probability of success is constant and equal to p.
However, a Geometric random variable is the number of trials until the first failure, whereas a Binomial random variable is the number of successes in n trials.
www.stats.gla.ac.uk /steps/glossary/probability_distributions.html   (2101 words)

  
 No Title
Derive the formulae for the mean, variance and standard deviation for the discrete uniform distribution, for the binomial distribution, for the geometric distribution and for the Poisson distribution.
Graph the probability mass function and the distribution function for a random variable with a binomial distribution with expected value of 4 and variance of 2.
Graph the probability mass function and the distribution function for a random variable with a binomial distribution with expected value of 3 and variance of 2.
www.uwm.edu /~ericskey/361material/361F98/L07   (533 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 geometric distribution returns the probability density function of a geometric distribution, with parameter p, which is evaluated at the value m.
www.asu.edu /it/fyi/unix/helpdocs/statistics/sas/sasdoc/sashtml/lgref/z0270634.htm   (1051 words)

  
 Statistics:Distributions/Geometric - Wikibooks, collection of open-content textbooks
Geometric Distribution refers to the probability of the number of times needed to do something until getting a desired result.
If a random variable X is distributed with a Geometric Distribution with a parameter p we write its probability mass function as:
With a Geometric Distribution it is also pretty easy to calculate the probability of a "more than n times" case.
en.wikibooks.org /wiki/Statistics:Distributions/Geometric   (205 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 geometric distribution returns the probability that an obervation from a geometric distribution, with parameter p, is less than or equal to m.
www.asu.edu /it/fyi/dst/helpdocs/statistics/sas/sasdoc/sashtml/lgref/z0208980.htm   (1101 words)

  
 Probability Distributions   (Site not responding. Last check: 2007-10-08)
The Gamma Distribution is a general distribution covering many special cases, including the Chi-squared distribution and Exponential distribution.
The Log-Normal Distribution is useful when the raw data are highly skewed whereas the natural log of the data are normally distributed.
The Beta Distribution is a continuous distribution bounded between 0 and 1.
www.stat.vt.edu /~sundar/java/applets/Distributions.html#POISSON   (494 words)

  
 Poisson Distribution
The continuous analog of the geometric distribution is the poisson distribution.
Interpolate the geometric distribution, with finer and finer resolution, to obtain the poisson distribution.
In the geometric distribution, the standard deviation was often close to the mean.
www.mathreference.com /pr,pois.html   (1003 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 essential requirement for a random variable to have the geometric distribution is that it counts the number of trials to the first success in independent trials with the same probability p of success in each trial.
The binomial, geometric, hypergeometric, and negative binomial distributions are examples of discrete probability distributions.
www.stat.berkeley.edu /users/stark/SticiGui/Text/ch12.htm   (5742 words)

  
 Random Numbers
Like the geometric distribution, the sample space for the negative binomial distribution is the non-negative integers.
Uniform(a,b) The uniform distribution on the interval (a,b).
For the basic gamma distribution (with default scale equal to 1) the shape parameter `a' is also the mean.
www.reed.edu /~jones/141/sim1.html   (782 words)

  
 Geometric
Thus an alpha close to 1 yields a relatively flat distribution, whereas an alpha close to 0 yields a distribution that decays quickly.
The distribution is defined by: P(X = n) = (1 - alpha) alpha^n.
Returns a Geometric distribution with the given mean.
www.cs.berkeley.edu /~milch/blog/apidocs/blog/distrib/Geometric.html   (281 words)

  
 Zoology 500 D
Description: Similar to the geometric distribution, except that the negative binomial distribution describes the number of trials until the rth success.
Similarly, the Poisson distribution gives the number of events in a given area when the presence or absence of a point is independent of occurrences at other points (= Poisson random scatter).
The exponential distribution also approximates the geometric distribution when p is small (Note: they then have the same mean and variance).
www.zoology.ubc.ca /~otto/PopGen500/Lecture7/Overheads.html   (962 words)

  
 Distribution Form Frame   (Site not responding. Last check: 2007-10-08)
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   (1657 words)

  
 Math 235 Chapter 5   (Site not responding. Last check: 2007-10-08)
The probability distribution is simply and assignment of probabilities to the specific values of the random variable or to the range of value the random variable can take on.
To find the mean and standard deviation of a binomial distribution, we could use the formulas from section 5.1 that were for general discrete probability distributions; however, the special formulas that follow are easier to compute.
The geometric and Poisson probability distributions are further examples of discrete probability distributions.
www.lc.cc.il.us /gallaher.nsf/dd5cab6801f1723585256474005327c8/49348561f1be15978625696100614247?OpenDocument   (1397 words)

  
 Functions and CALL Routines : RAND Function
The hypergeometric distribution is a mathematical formalization of an experiment in which you draw n balls from an urn that contains N balls, R of which are red.
The hypergeometric distribution is the distribution of the number of red balls in the sample of n.
The negative binomial distribution is the distribution of the number of failures before k successes occur in sequential independent trials, all with the same probability of success, p.
support.sas.com /onlinedoc/913/getDoc/pl/lrdict.hlp/a001466748.htm   (752 words)

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