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Log-Cauchy distribution

Index Log-Cauchy distribution

In probability theory, a log-Cauchy distribution is a probability distribution of a random variable whose logarithm is distributed in accordance with a Cauchy distribution. [1]

35 relations: Bayesian statistics, Cauchy distribution, Cumulative distribution function, Exponential function, Harold Jeffreys, Heavy-tailed distribution, HIV, Infinite divisibility (probability), Location parameter, Log-normal distribution, Logarithm, Logarithmic growth, MathWorld, Mean, Median, Median absolute deviation, Moment (mathematics), Natural logarithm, Outlier, Pareto distribution, Prior probability, Probability density function, Probability distribution, Random variable, Real number, Robust statistics, Sample (statistics), Scale parameter, Stable distribution, Standard deviation, Student's t-distribution, Survival analysis, Survival function, Weibull distribution, Zeros and poles.

Bayesian statistics

Bayesian statistics, named for Thomas Bayes (1701–1761), is a theory in the field of statistics in which the evidence about the true state of the world is expressed in terms of degrees of belief known as Bayesian probabilities.

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Cauchy distribution

The Cauchy distribution, named after Augustin Cauchy, is a continuous probability distribution.

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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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Exponential function

In mathematics, an exponential function is a function of the form in which the argument occurs as an exponent.

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Harold Jeffreys

Sir Harold Jeffreys, FRS (22 April 1891 – 18 March 1989) was a British mathematician, statistician, geophysicist, and astronomer.

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Heavy-tailed distribution

In probability theory, heavy-tailed distributions are probability distributions whose tails are not exponentially bounded: that is, they have heavier tails than the exponential distribution.

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HIV

The human immunodeficiency virus (HIV) is a lentivirus (a subgroup of retrovirus) that causes HIV infection and over time acquired immunodeficiency syndrome (AIDS).

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Infinite divisibility (probability)

In probability theory, a probability distribution is infinitely divisible if it can be expressed as the probability distribution of the sum of an arbitrary number of independent and identically distributed random variables.

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Location parameter

In statistics, a location family is a class of probability distributions that is parametrized by a scalar- or vector-valued parameter x_0, which determines the "location" or shift of the distribution.

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Log-normal distribution

In probability theory, a log-normal (or lognormal) distribution is a continuous probability distribution of a random variable whose logarithm is normally distributed.

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Logarithm

In mathematics, the logarithm is the inverse function to exponentiation.

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Logarithmic growth

In mathematics, logarithmic growth describes a phenomenon whose size or cost can be described as a logarithm function of some input.

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MathWorld

MathWorld is an online mathematics reference work, created and largely written by Eric W. Weisstein.

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Mean

In mathematics, mean has several different definitions depending on the context.

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Median

The median is the value separating the higher half of a data sample, a population, or a probability distribution, from the lower half.

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Median absolute deviation

In statistics, the median absolute deviation (MAD) is a robust measure of the variability of a univariate sample of quantitative data.

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Moment (mathematics)

In mathematics, a moment is a specific quantitative measure, used in both mechanics and statistics, of the shape of a set of points.

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Natural logarithm

The natural logarithm of a number is its logarithm to the base of the mathematical constant ''e'', where e is an irrational and transcendental number approximately equal to.

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Outlier

In statistics, an outlier is an observation point that is distant from other observations.

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Pareto distribution

No description.

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Prior probability

In Bayesian statistical inference, a prior probability distribution, often simply called the prior, of an uncertain quantity is the probability distribution that would express one's beliefs about this quantity before some evidence is taken into account.

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Probability density function

In probability theory, a probability density function (PDF), or density of a continuous random variable, is a function, whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) can be interpreted as providing a relative likelihood that the value of the random variable would equal that sample.

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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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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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Real number

In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.

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Robust statistics

Robust statistics are statistics with good performance for data drawn from a wide range of probability distributions, especially for distributions that are not normal.

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Sample (statistics)

In statistics and quantitative research methodology, a data sample is a set of data collected and/or selected from a statistical population by a defined procedure.

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Scale parameter

In probability theory and statistics, a scale parameter is a special kind of numerical parameter of a parametric family of probability distributions.

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Stable distribution

No description.

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Standard deviation

In statistics, the standard deviation (SD, also represented by the Greek letter sigma σ or the Latin letter s) is a measure that is used to quantify the amount of variation or dispersion of a set of data values.

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Student's t-distribution

In probability and statistics, Student's t-distribution (or simply the t-distribution) is any member of a family of continuous probability distributions that arises when estimating the mean of a normally distributed population in situations where the sample size is small and population standard deviation is unknown.

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Survival analysis

Survival analysis is a branch of statistics for analyzing the expected duration of time until one or more events happen, such as death in biological organisms and failure in mechanical systems.

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Survival function

The survival function is a function that gives the probability that a patient, device, or other object of interest will survive beyond any given specified time.

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Weibull distribution

No description.

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Zeros and poles

In mathematics, a zero of a function is a value such that.

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Log Cauchy, Log Cauchy distribution, Log-Cauchy, LogCauchy, LogCauchy distribution.

References

[1] https://en.wikipedia.org/wiki/Log-Cauchy_distribution

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