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- Logarithmic_distribution abstract "In probability and statistics, the logarithmic distribution (also known as the logarithmic series distribution or the log-series distribution) is a discrete probability distribution derived from the Maclaurin series expansion From this we obtain the identityThis leads directly to the probability mass function of a Log(p)-distributed random variable:for k ≥ 1, and where 0 < p < 1. Because of the identity above, the distribution is properly normalized.The cumulative distribution function iswhere B is the incomplete beta function.A Poisson compounded with Log(p)-distributed random variables has a negative binomial distribution. In other words, if N is a random variable with a Poisson distribution, and Xi, i = 1, 2, 3, ... is an infinite sequence of independent identically distributed random variables each having a Log(p) distribution, thenhas a negative binomial distribution. In this way, the negative binomial distribution is seen to be a compound Poisson distribution.R.A. Fisher described the logarithmic distribution in a paper that used it to model relative species abundance.Recurrence relation".
- Logarithmic_distribution thumbnail Logarithmicpmf.svg?width=300.
- Logarithmic_distribution wikiPageID "1119231".
- Logarithmic_distribution wikiPageRevisionID "604821957".
- Logarithmic_distribution cdfImage "300".
- Logarithmic_distribution hasPhotoCollection Logarithmic_distribution.
- Logarithmic_distribution name "Logarithmic".
- Logarithmic_distribution pdfImage "300".
- Logarithmic_distribution title "Log-Series Distribution".
- Logarithmic_distribution type "mass".
- Logarithmic_distribution urlname "Log-SeriesDistribution".
- Logarithmic_distribution subject Category:Discrete_distributions.
- Logarithmic_distribution subject Category:Logarithms.
- Logarithmic_distribution subject Category:Probability_distributions.
- Logarithmic_distribution type Abstraction100002137.
- Logarithmic_distribution type Arrangement105726596.
- Logarithmic_distribution type Cognition100023271.
- Logarithmic_distribution type Communication100033020.
- Logarithmic_distribution type DiscreteDistributions.
- Logarithmic_distribution type Distribution105729036.
- Logarithmic_distribution type Exponent106812417.
- Logarithmic_distribution type Logarithm106812631.
- Logarithmic_distribution type Logarithms.
- Logarithmic_distribution type MathematicalNotation106808720.
- Logarithmic_distribution type Notation106808493.
- Logarithmic_distribution type PsychologicalFeature100023100.
- Logarithmic_distribution type Structure105726345.
- Logarithmic_distribution type Writing106359877.
- Logarithmic_distribution type WrittenCommunication106349220.
- Logarithmic_distribution comment "In probability and statistics, the logarithmic distribution (also known as the logarithmic series distribution or the log-series distribution) is a discrete probability distribution derived from the Maclaurin series expansion From this we obtain the identityThis leads directly to the probability mass function of a Log(p)-distributed random variable:for k ≥ 1, and where 0 < p < 1.".
- Logarithmic_distribution label "Distribución logarítmica".
- Logarithmic_distribution label "Distribuzione logaritmica".
- Logarithmic_distribution label "Logarithmic distribution".
- Logarithmic_distribution label "Logarithmische Verteilung".
- Logarithmic_distribution label "Loi logarithmique".
- Logarithmic_distribution label "Логарифмическое распределение".
- Logarithmic_distribution label "对数分布".
- Logarithmic_distribution sameAs Logarithmische_Verteilung.
- Logarithmic_distribution sameAs Distribución_logarítmica.
- Logarithmic_distribution sameAs Loi_logarithmique.
- Logarithmic_distribution sameAs Distribuzione_logaritmica.
- Logarithmic_distribution sameAs m.047pms.
- Logarithmic_distribution sameAs Q1867999.
- Logarithmic_distribution sameAs Q1867999.
- Logarithmic_distribution sameAs Logarithmic_distribution.
- Logarithmic_distribution wasDerivedFrom Logarithmic_distribution?oldid=604821957.
- Logarithmic_distribution depiction Logarithmicpmf.svg.
- Logarithmic_distribution isPrimaryTopicOf Logarithmic_distribution.
