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Logarithmic distribution

Index Logarithmic distribution

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 identity This leads directly to the probability mass function of a Log(p)-distributed random variable: for k ≥ 1, and where 0 F(k). [1]

13 relations: Beta function, Compound Poisson distribution, Cumulative distribution function, Negative binomial distribution, Poisson distribution, Probability, Probability distribution, Probability mass function, Random variable, Relative species abundance, Ronald Fisher, Statistics, Taylor series.

Beta function

In mathematics, the beta function, also called the Euler integral of the first kind, is a special function defined by for.

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Compound Poisson distribution

In probability theory, a compound Poisson distribution is the probability distribution of the sum of a number of independent identically-distributed random variables, where the number of terms to be added is itself a Poisson-distributed variable.

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Cumulative distribution function

In probability theory and statistics, the cumulative distribution function (CDF, also cumulative density function) of a real-valued random variable X, or just distribution function of X, evaluated at x, is the probability that X will take a value less than or equal to x. In the case of a continuous distribution, it gives the area under the probability density function from minus infinity to x. Cumulative distribution functions are also used to specify the distribution of multivariate random variables.

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Negative binomial distribution

In probability theory and statistics, the negative binomial distribution is a discrete probability distribution of the number of successes in a sequence of independent and identically distributed Bernoulli trials before a specified (non-random) number of failures (denoted r) occurs.

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Poisson distribution

In probability theory and statistics, the Poisson distribution (in English often rendered), named after French mathematician Siméon Denis Poisson, is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant rate and independently of the time since the last event.

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Probability

Probability is the measure of the likelihood that an event will occur.

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Probability distribution

In probability theory and statistics, a probability distribution is a mathematical function that provides the probabilities of occurrence of different possible outcomes in an experiment.

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Probability mass function

In probability and statistics, a probability mass function (pmf) is a function that gives the probability that a discrete random variable is exactly equal to some value.

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Random variable

In probability and statistics, a random variable, random quantity, aleatory variable, or stochastic variable is a variable whose possible values are outcomes of a random phenomenon.

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Relative species abundance

Relative species abundance is a component of biodiversity and refers to how common or rare a species is relative to other species in a defined location or community.

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Ronald Fisher

Sir Ronald Aylmer Fisher (17 February 1890 – 29 July 1962), who published as R. A. Fisher, was a British statistician and geneticist.

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Statistics

Statistics is a branch of mathematics dealing with the collection, analysis, interpretation, presentation, and organization of data.

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Taylor series

In mathematics, a Taylor series is a representation of a function as an infinite sum of terms that are calculated from the values of the function's derivatives at a single point.

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Redirects here:

Fisher logseries, Log-series distribution, Logarithmic series distribution, Logseries distribution.

References

[1] https://en.wikipedia.org/wiki/Logarithmic_distribution

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