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Discrete probability distribution
the logarithmic distribution (also known as the logarithmic series distribution or the log-series distribution) is a discrete probability distribution derived
Logarithmic_distribution
Family of lifetime distributions with decreasing failure rate
Exponential-Logarithmic (EL) distribution is a family of lifetime distributions with decreasing failure rate, defined on the interval [0, ∞). This distribution is
Exponential-logarithmic distribution
Exponential-logarithmic_distribution
Probability distribution
"the local-mean power expressed in logarithmic values, such as dB or neper, has a normal (i.e., Gaussian) distribution." Also, the random obstruction of
Log-normal_distribution
Topics referred to by the same term
to describe measurements Logarithmic spiral, Logarithmic growth Logarithmic distribution, a discrete probability distribution Natural logarithm This disambiguation
Logarithmic
Hermite distribution The logarithmic (series) distribution The mixed Poisson distribution The negative binomial distribution or Pascal distribution, a generalization
List of probability distributions
List_of_probability_distributions
Mathematical function, inverse of an exponential function
scaled by a constant factor. This gives rise to a logarithmic spiral. Benford's law on the distribution of leading digits can also be explained by scale
Logarithm
Probability distribution
and put into a parametrized family with the logarithmic distribution and the negative binomial distribution by H.U. Gerber. For a natural number m ≥ 1
Extended negative binomial distribution
Extended_negative_binomial_distribution
Measurement scale based on orders of magnitude
A logarithmic scale (or log scale) is a method used to display numerical data that spans a broad range of values, especially when there are significant
Logarithmic_scale
Measure for evaluating probabilistic forecasts
probability as p, then one can write the logarithmic scoring rule as x ln(p) + (1 − x) ln(1 − p). Note that any logarithmic base may be used, since strictly proper
Scoring_rule
Observation that in many real-life datasets, the leading digit is likely to be small
the following distribution: The quantity P ( d ) {\displaystyle P(d)} is proportional to the space between d and d + 1 on a logarithmic scale. Therefore
Benford's_law
Probability distribution and special case of gamma distribution
logarithmic transform removes much of the asymmetry. Other functions of the chi-squared distribution converge more rapidly to a normal distribution.
Chi-squared_distribution
Mathematical operation in calculus
In mathematics, specifically in calculus and complex analysis, the logarithmic derivative of a function f is defined by the formula f ′ f {\displaystyle
Logarithmic_derivative
Probability distribution
incorrectly referred to as the log-gamma distribution. Formulas for its mean and variance are in the section #Logarithmic expectation and variance. If X ~ Gamma(α
Gamma_distribution
Probability distribution
\ln(1-X)]}\end{aligned}}} For a beta distribution, higher order logarithmic moments can be derived by using the representation of a beta distribution as a proportion of
Beta_distribution
In mathematics, many logarithmic identities exist. The following is a compilation of the notable of these, many of which are used for computational purposes
List of logarithmic identities
List_of_logarithmic_identities
Scale of numbers with a fixed ratio
magnitude one. Logarithmic distributions are common in nature and considering the order of magnitude of values sampled from such a distribution can be more
Order_of_magnitude
Term in probability theory
values of k: for example the logarithmic distribution and the discrete uniform distribution. The (a, b, 0) class of distributions has important applications
(a,b,0) class of distributions
(a,b,0)_class_of_distributions
Probability distribution
The Pareto distribution, named after the Italian polymath Vilfredo Pareto, is a probability distribution in the form of a power law that is used to describe
Pareto_distribution
Psychophysics of varying the intensity of a stimulus
arXiv:1405.4209. doi:10.1093/mnras/stu992. Scheler G. (2017). "Logarithmic distributions prove that intrinsic learning is Hebbian". F1000Research. 6: 1222
Weber–Fechner_law
Finance term; profit on an investment
to a logarithmic return of 40.55%, while an arithmetic return of −50% is equivalent to a logarithmic return of −69.31%. Advantages of logarithmic return:
Rate_of_return
Distribution of an uncertain quantity
logarithmic prior on the positive reals (uniform distribution on log scale).[citation needed] These functions, interpreted as uniform distributions,
Prior_probability
differentiation Logarithmic distribution Logarithmic form Logarithmic graph paper Logarithmic growth Logarithmic identities Logarithmic mean Logarithmic number
Index_of_logarithm_articles
Distribution of a country's total GDP amongst its population
In economics, income distribution covers how a country's total GDP is distributed amongst its population. Economic theory and economic policy have long
Income_distribution
Probability distribution
consider the logarithmic marginals, log x k 1 − x k {\displaystyle \log {\frac {x_{k}}{1-x_{k}}}} , which follow the logistic-beta distribution, B σ ( α
Dirichlet_distribution
British polymath (1890–1962)
abundance where he developed the log series distribution (sometimes called the logarithmic distribution) to fit two different abundance data sets. In
Ronald_Fisher
2D graphic with logarithmic scales on both axes
log–log plot is a two-dimensional graph of numerical data that uses logarithmic scales on both the horizontal and vertical axes. Power functions – relationships
Log–log_plot
Spread of wealth in a society
economic heterogeneity. The distribution of wealth differs from the income distribution in that it looks at the economic distribution of ownership of the assets
Distribution_of_wealth
Probability distribution
This is because the negative binomial distribution can be derived from a Poisson-stopped sum of logarithmic random variables. The decimal digits of
Geometric_distribution
Probability distribution
identically distributed random variables, each one having the logarithmic series distribution Log(p), with probability mass function f ( k ; r , p ) = −
Negative binomial distribution
Negative_binomial_distribution
Functional relationship between two quantities
identified using bundle plots. In general, power-law distributions are plotted on doubly logarithmic axes, which emphasizes the upper tail region. The most
Power_law
Fourth standardized moment in statistics
densities, on a linear scale and logarithmic scale: D: Laplace distribution, also known as the double exponential distribution, red curve (two straight lines
Kurtosis
Probability distribution
exhibits logarithmic decay producing a heavier tail than the Pareto distribution. Those that are two-tailed include: The Cauchy distribution, itself a
Heavy-tailed_distribution
Branch of statistics
distribution Exponential-logarithmic distribution Gamma distribution Generalized gamma distribution Hypertabastic distribution Lindley distribution Log-logistic
Survival_analysis
regression Log-log plot Log-logistic distribution Logarithmic distribution Logarithmic mean Logistic distribution Logistic function Logistic regression
List_of_statistics_articles
Number of occurrences in an experiment or study
class intervals are preferred in frequency distribution, while unequal class intervals (for example logarithmic intervals) may be necessary in certain situations
Frequency_(statistics)
Materials' resistance to heat transfer
obtain The logarithmic distribution of the temperature is sketched in the inset of the thumbnail figure. Assuming that the temperature distribution, equation
Thermal conductance and resistance
Thermal_conductance_and_resistance
For generation of random factorized numbers
{\displaystyle x} with logarithmic distribution over the desired range; rejection sampling is then used to get a uniform distribution. Bach, Eric (1988).
Bach's_algorithm
also suggested in 1781 two other distributions for errors – a raised cosine distribution and a logarithmic distribution. Laplace gave (1781) a formula for
History_of_statistics
Probability of shared birthdays
the other people in the group. For independent birthdays, a uniform distribution of birthdays minimizes the probability of two people in a group having
Birthday_problem
North American standard for electrical-wire diameters
American Wire Gauge (AWG) is a logarithmic stepped standardized wire gauge system used since 1857, predominantly in North America, for the diameters of
American_wire_gauge
Generalization of the one-dimensional normal distribution to higher dimensions
statistics, the multivariate normal distribution, multivariate Gaussian distribution, or joint normal distribution is a generalization of the one-dimensional
Multivariate normal distribution
Multivariate_normal_distribution
Type of mathematical function
In convex analysis, a non-negative function f: Rn → R+ is logarithmically concave (or log-concave for short) if its domain is a convex set, and if it
Logarithmically concave function
Logarithmically_concave_function
Method of mathematical differentiation
calculus, logarithmic differentiation or differentiation by taking logarithms is a method used to differentiate functions by employing the logarithmic derivative
Logarithmic_differentiation
Transforming data by taking the logarithm
In statistics, the log transformation is the application of the logarithmic function to each point in a data set—that is, each data point zi is replaced
Log transformation (statistics)
Log_transformation_(statistics)
Search algorithm used in sorted arrays
computer science, binary search, also known as half-interval search, logarithmic search, or binary chop, is a search algorithm that finds the position
Binary_search
Statistical distribution
statistics, the reciprocal distribution, also known as the log-uniform distribution, is a continuous probability distribution. It is characterised by its
Reciprocal_distribution
Wind model
the vertical distribution of horizontal mean wind speed within the lowest portion of the planetary boundary layer (PBL). The logarithmic profile of wind
Log_wind_profile
Statistical quantity
0.31 {\displaystyle S=1-\log _{e}(2)\approx 0.31} Exponential-logarithmic distribution S = − p o l y l o g ( 2 , 1 − p ) + ln ( 1 + p ) ln p − [ 2
Nonparametric_skew
Mathematical statistics distance measure
P(x)\right){\text{.}}} In other words, it is the expectation of the logarithmic difference between the probabilities P and Q, where the expectation is
Kullback–Leibler_divergence
Measurement system to quantify intensity of rainfall
The raindrop size distribution (DSD), or granulometry of rain, is the distribution of the number of raindrops according to their diameter (D). Three processes
Raindrop_size_distribution
Hypothetical invisible cosmic material
theorem, together with the measured velocity distribution, can be used to measure the mass distribution in a bound system, such as elliptical galaxies
Dark_matter
Mathematical concept
customary to transform data logarithmically to fit symmetrical distributions (like the normal and logistic) to data obeying a distribution that is positively skewed
Probability distribution fitting
Probability_distribution_fitting
Family of continuous probability distributions
The Pearson distribution is a family of continuous probability distributions. It was first published by Karl Pearson in 1895 and subsequently extended
Pearson_distribution
Name for several different families of probability distributions
_{k}{\stackrel {iid}{\sim }}{\text{Exp}}(1)} . By using the logarithmic expectations of the gamma distribution, the mean and variance can be derived as: E [ x ]
Generalized logistic distribution
Generalized_logistic_distribution
Characterization of how many integers are prime
Gustav Lejeune Dirichlet came up with his own approximating function, the logarithmic integral li(x) (under the slightly different form of a series, which
Prime_number_theorem
Operation in calculus
Differentiation notation Second derivative Implicit differentiation Logarithmic differentiation Related rates Taylor's theorem Rules and identities Sum
Integral
List of values of a mathematical function
approximations of logarithmic functions — that is, to compute large logarithmic tables. This was motivated mainly by errors in logarithmic tables made by
Mathematical_table
Degree of variation of a trading price series over time
price series over time, usually measured by the standard deviation of logarithmic returns. Historic volatility measures a time series of past market prices
Volatility_(finance)
they do not. As with all magnitude systems in astronomy, the scale is logarithmic and inverted, i.e., lower/more negative numbers are brighter. Most stars
List_of_brightest_stars
S-shaped curve
"logistic" (French: logistique), but it is presumably in contrast to the logarithmic curve, and by analogy with arithmetic and geometric. His growth model
Logistic_function
Compound probability distribution
Poisson distribution where mean and variance are the same. In practice, almost only densities of gamma distributions, logarithmic normal distributions and
Mixed_Poisson_distribution
Measurement of radiant electromagnetic power emitted by an object
magnitude (Mbol) of an object is a logarithmic measure of its total energy emission rate, while absolute magnitude is a logarithmic measure of the luminosity within
Luminosity
Unit of measure used in weather radar
dBZ is a logarithmic dimensionless technical unit used in radar. It is mostly used in weather radar, to compare the equivalent reflectivity factor (Z)
DBZ_(meteorology)
Probability distribution on the circle
statistics, a wrapped normal distribution is a wrapped probability distribution that results from the "wrapping" of the normal distribution around the unit circle
Wrapped_normal_distribution
Formula for the derivative of a ratio of functions
x ) | . {\displaystyle \ln |h(x)|=\ln |f(x)|-\ln |g(x)|.} Taking the logarithmic derivative of both sides, h ′ ( x ) h ( x ) = f ′ ( x ) f ( x ) − g ′
Quotient_rule
Fundamental result in the theory of large deviations
version of this result was first shown by Harald Cramér in 1938. The logarithmic moment generating function (which is the cumulant-generating function)
Cramér's theorem (large deviations)
Cramér's_theorem_(large_deviations)
Probability distribution
, it has a logarithmically decaying tail. As with the Cauchy distribution, none of the non-trivial moments of the log-Cauchy distribution are finite.
Log-Cauchy_distribution
Mathematical function having a characteristic "bell"-shaped curve
+ x 2 ) 3 / 2 {\displaystyle f(x)={\frac {1}{(1+x^{2})^{3/2}}}} Some logarithmic functions. For example f ( x ) = log x 2 + e x 2 + 1 . {\displaystyle
Bell-shaped_function
Topics referred to by the same term
Arcsine law of Deshouillers–Dress–Tenenbaum, concerning divisors and their logarithmic ratios. This disambiguation page lists mathematics articles associated
Arcsine_law
Statistical dispersion in nominal distributions
Fowlkes–Mallows index Goodman and Kruskal's gamma Information entropy Logarithmic distribution PERMANOVA Robinson–Foulds metric Statistical dispersion Variation
Qualitative_variation
Generating pseudo-random numbers that follow a probability distribution
generating pseudo-random numbers (PRN) that follow a given probability distribution. Methods are typically based on the availability of a uniformly distributed
Non-uniform random variate generation
Non-uniform_random_variate_generation
Analog graphical calculator
also include labeled reference values. These scales may be linear or logarithmic, or have some other more complex relationship. The sample isopleth shown
Nomogram
Replacing a number with a simpler value
is also named rounding to a logarithmic scale, is a variant of rounding to a specified power. Rounding on a logarithmic scale is accomplished by taking
Rounding
Polish mathematician (1931–1967)
cybersecurity. There is no formula to calculate prime numbers. However, the distribution of primes can be statistically modelled. The prime number theorem, which
Stanisław_Knapowski
Information-theoretic measure
the given distribution q i {\displaystyle q_{i}} is the predicted value of the current model. This is also known as the log loss (or logarithmic loss or
Cross-entropy
oval window than did lower ones. Frequency values approximate a logarithmic distribution with distance. Early mechanical and electrical analog ears were
Analog_ear
Multivariate derivative (mathematics)
Differentiation notation Second derivative Implicit differentiation Logarithmic differentiation Related rates Taylor's theorem Rules and identities Sum
Gradient
(1:D) Dirichlet distribution / (F:C) Discrete phase-type distribution / (1:D) Erlang distribution / (1:C) Exponential-logarithmic distribution / (1:C) Exponential
Catalog of articles in probability theory
Catalog_of_articles_in_probability_theory
Magnitude or dimension of a thing
the magnitude of brightness or intensity of a star is measured on a logarithmic scale. Such a scale is also used to measure the intensity of an earthquake
Size
Concept in network science
of connections it has to other nodes and the degree distribution is the probability distribution of these degrees over the whole network. The degree of
Degree_distribution
Probability distribution
the maximum entropy distribution for a fixed first inverse moment ( E ( 1 / X ) ) {\displaystyle (E(1/X))} and first logarithmic moment ( E ( ln ( X
Scaled inverse chi-squared distribution
Scaled_inverse_chi-squared_distribution
The inequality of wealth (i.e., inequality in the distribution of assets) has substantially increased in the United States since the late 1980s. Wealth
Wealth inequality in the United States
Wealth_inequality_in_the_United_States
Type of radio propagation model
modelled as a random variable with exponential distribution). This corresponds to the following non-logarithmic gain model: P Rx P Tx = c 0 F g d γ , {\displaystyle
Log-distance_path_loss_model
Function of the observed sample results
The S-value, also known as the surprisal value, has been defined as a logarithmic transformation of the p-value: S-value = - log2(p-value). The transformation
P-value
Matrix of partial derivatives of a vector-valued function
Differentiation notation Second derivative Implicit differentiation Logarithmic differentiation Related rates Taylor's theorem Rules and identities Sum
Jacobian matrix and determinant
Jacobian_matrix_and_determinant
Statistical parameter of random process evolution
{\bar {\tau }}(y_{0})=\operatorname {E} [\tau (y_{0})\mid y_{0}].} The logarithmic residence time is a dimensionless variation of the residence time. It
Residence_time_(statistics)
Differential operator in mathematics
gravitational potential due to a given mass density distribution is a constant multiple of that density distribution. Solutions of Laplace's equation Δf = 0 are
Laplace_operator
Property of a thermodynamic system
to the macroscopically observable behaviour, in the form of a simple logarithmic law, with a proportionality constant, the Boltzmann constant, which has
Entropy
Fourteenth letter in the Greek alphabet
in atomic physics. The Killing vector in general relativity. Average logarithmic energy decrement per collision (neutron calculations in nuclear physics)
Xi_(letter)
4%, 16.6%, and 12.5%, respectively. Income growth since 1970 Income distribution can be assessed using a variety of income definitions. Adjustments are
Income inequality in the United States
Income_inequality_in_the_United_States
Probability distribution used in multivariate hypothesis testing
In statistics, Wilks' lambda distribution (named for Samuel S. Wilks), is a probability distribution used in multivariate hypothesis testing, especially
Wilks's_lambda_distribution
Extension of the factorial function
function for the factorial, defined over the positive reals, which is logarithmically convex, meaning that y = log f ( x ) {\displaystyle y=\log f(x)}
Gamma_function
Formula in calculus
Differentiation notation Second derivative Implicit differentiation Logarithmic differentiation Related rates Taylor's theorem Rules and identities Sum
Chain_rule
Formula for the derivative of a product
logarithmic derivative provides a simpler expression of the last form, as well as a direct proof that does not involve any recursion. The logarithmic
Product_rule
Risk measure estimating the average loss in the worst tail of the distribution
x {\displaystyle \mathrm {li} (x)=\int {\frac {dx}{\ln x}}} is the logarithmic integral function. If the loss of a portfolio L {\displaystyle L} follows
Expected_shortfall
Method of estimating the parameters of a statistical model, given observations
Conveniently, most common probability distributions – in particular the exponential family – are logarithmically concave. While the domain of the likelihood
Maximum_likelihood_estimation
Function in statistics
one most often used. The choice of base corresponds to the choice of logarithmic unit for the value: base 2 corresponds to a shannon, base e to a nat
Logit
Model in electromagnetism
(1-(\omega \tau )^{2\alpha })^{\beta }}} The first logarithmic moment of this distribution, the average logarithmic relaxation time is ⟨ ln τ D ⟩ = ln τ +
Havriliak–Negami_relaxation
Relative measure of dispersion expressed as the ratio of standard deviation to the mean
transformation. (In the event that measurements are recorded using any other logarithmic base, b, their standard deviation s b {\displaystyle s_{b}\,} is converted
Coefficient_of_variation
Generalized chain rule in calculus
Differentiation notation Second derivative Implicit differentiation Logarithmic differentiation Related rates Taylor's theorem Rules and identities Sum
Faà_di_Bruno's_formula
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