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Measure of income inequality
In statistics and econometrics, the mean log deviation (MLD) is a measure of income inequality. The MLD is zero when everyone has the same income, and
Mean_log_deviation
Statistical measure
the geometric standard deviation (GSD) describes how spread out are a set of numbers whose preferred average is the geometric mean. For such data, it may
Geometric_standard_deviation
Relative measure of dispersion expressed as the ratio of standard deviation to the mean
variation (CV), also known as normalized root-mean-square deviation (NRMSD), and relative standard deviation (RSD), is a standardized measure of dispersion
Coefficient_of_variation
N-th root of the product of n numbers
Arithmetic-geometric mean Generalized mean Geometric mean theorem Geometric standard deviation Harmonic mean Heronian mean Heteroscedasticity Log-normal distribution
Geometric_mean
Measure of variation in statistics
variance being the average of the squared deviations from the mean). A useful property of the standard deviation is that, unlike the variance, it is expressed
Standard_deviation
Probability distribution
} Specifically, the arithmetic mean, expected square, arithmetic variance, and arithmetic standard deviation of a log-normally distributed variable X
Log-normal_distribution
Statistical error measure
related to the mean squared error, the equivalent for mean absolute error is least absolute deviations. MAE is not identical to root-mean square error (RMSE)
Mean_absolute_error
Summary statistic of variability
related to the given data set. AAD includes the mean absolute deviation and the median absolute deviation (both abbreviated as MAD). Several measures of
Average_absolute_deviation
Statistical measure of variability
data set than the standard deviation. In the standard deviation, the distances from the mean are squared, so large deviations are weighted more heavily
Median_absolute_deviation
Type of average of a collection of numbers
number for which the residuals (deviations from the estimate) sum to zero. This can also be interpreted as saying that the mean is translationally invariant
Arithmetic_mean
Measured values that are relatively normal for a particular medical test
arithmetic mean in this case, the parameters μlog and σlog can be estimated from the arithmetic mean (m) and standard deviation (s.d.) as: μ log = ln (
Reference_range
Measure of prediction accuracy of a forecast
The mean absolute percentage error (MAPE), also known as mean absolute percentage deviation (MAPD), is a measure of prediction accuracy of a forecasting
Mean absolute percentage error
Mean_absolute_percentage_error
Inverse of the average of the inverses of a set of numbers
only. The harmonic mean is the reciprocal of the arithmetic mean of the reciprocals of the numbers, that is, the generalized f-mean with f ( x ) = 1 x
Harmonic_mean
Probability distribution
standard deviation away from the mean, namely at x = μ − σ {\textstyle x=\mu -\sigma } and x = μ + σ . {\textstyle x=\mu +\sigma .} Its density is log-concave
Normal_distribution
Probability distribution
mean) by the range (c − a), linearly for the mean deviation and nonlinearly for the variance: (mean deviation around mean) ( Y ) = ( (mean deviation around
Beta_distribution
Index to measure economic inequality
the lower end of the distribution. It is also referred to as the mean log deviation measure. GE(1) = Theil's T and is more sensitive to differences at
Theil_index
Measure of inequality of a statistical distribution
entropy measures are frequently used (e.g. or the Theil Index and Mean log deviation as special cases of the generalized entropy index, or equivalently
Gini_coefficient
Procedure to estimate standard deviation from a sample
estimation of a standard deviation is the calculation from a statistical sample of an estimated value of the standard deviation (a measure of statistical
Unbiased estimation of standard deviation
Unbiased_estimation_of_standard_deviation
Statistical property
standard deviation of its sampling distribution. It is the square root of the variance of an estimator of a parameter, as in the standard error of the mean. The
Standard_error
Branch of probability theory
In probability theory, the theory of large deviations concerns the asymptotic behaviour of remote tails of sequences of probability distributions. While
Large_deviations_theory
Bound on probability of a random variable being far from its mean
deviation of a random variable (with finite variance) from its mean. More specifically, the probability that a random variable deviates from its mean
Chebyshev's_inequality
Measure of income inequality
income inequality metrics as special cases. For example, GE(0) is the mean log deviation a.k.a. Theil L index, GE(1) is the Theil T index, and GE(2) is half
Generalized_entropy_index
Topics referred to by the same term
genetic condition Masking Level Difference, see Auditory masking Mean log deviation in statistics and econometrics Mixed layer depth in hydrography Multicast
MLD
Test statistic
extensively in goodness of fit testing. It is also known as mean squared weighted deviation (MSWD) in isotopic dating and variance of unit weight in the
Reduced_chi-squared_statistic
Statistics concept
observation is the deviation of the observed value from the true value of a quantity of interest (for example, a population mean). The residual is the
Errors_and_residuals
Statistical phenomenon
where it's below its mean, when t < 0), is rt standard deviations above the mean of Y. Since |r| ≤ 1, Y is no farther from the mean than X is, as measured
Regression_toward_the_mean
Generalization of means
numbers, and f ( x ) = log ( x ) , {\displaystyle \ f(x)\ =\ \log(x)\ ,} then the f mean corresponds to the geometric mean. (The result is the same
Quasi-arithmetic_mean
Statistical measure of the magnitude of a phenomenon
group, M denotes the sample mean, μ the population mean, SD the sample's standard deviation, σ the population's standard deviation, and n is the sample size
Effect_size
Number taken as representative of a list of numbers
distributions. Thus standard deviation about the mean is lower than standard deviation about any other point, and the maximum deviation about the midrange is
Average
Value that appears most often in a set of data
has standard deviation σ = 0.25, the distribution of Y is weakly skewed. Using formulas for the log-normal distribution, we find: mean = e μ + σ 2 /
Mode_(statistics)
Statistical property quantifying how much a collection of data is spread out
Standard deviation Interquartile range (IQR) Range Mean absolute difference (also known as Gini mean absolute difference) Median absolute deviation (MAD)
Statistical_dispersion
Statistical measure of effect size
the strictly standardized mean difference (SSMD) is a measure of effect size. It is the mean divided by the standard deviation of a difference between two
Strictly standardized mean difference
Strictly_standardized_mean_difference
How many standard deviations apart from the mean an observed datum is
number of standard deviations by which the value of a raw score (i.e., an observed value or data point) is above or below the mean value of what is being
Standard_score
Transforming data by taking the logarithm
median or the mean, by transforming back to the original scale using exponent (with some adjustments for CI for the mean), the inverse of the log transformation
Log transformation (statistics)
Log_transformation_(statistics)
Ratio of the desired signal to the background noise
standard deviation σN. The signal and the noise must be measured the same way, for example, as voltages across the same impedance. Their root mean squares
Signal-to-noise_ratio
Statistical quantity
{\displaystyle S={\frac {\mu -\nu }{\sigma }}} where the mean (μ), median (ν) and standard deviation (σ) of the population have their usual meanings. The
Nonparametric_skew
Normalized measure of the dispersion of a probability distribution
{t_{a}}{t_{b}}}\right)\right]\right)}}\right)}} where tj is the mean absolute deviation of the jth sample and zα is the confidence interval length for
Index_of_dispersion
Shorthand used in statistics
distributed random variable, μ (mu) is the mean of the distribution, and σ (sigma) is its standard deviation: Pr ( μ − 1 σ ≤ X ≤ μ + 1 σ ) ≈ 68.27 % Pr
68–95–99.7_rule
Probability distribution
1853. Poisson noted that if the mean of observations following such a distribution were taken, the standard deviation did not converge to any finite number
Cauchy_distribution
Unbiased statistical estimator minimizing variance
the sample standard deviation is not unbiased for the population standard deviation – see unbiased estimation of standard deviation. Further, for other
Minimum-variance unbiased estimator
Minimum-variance_unbiased_estimator
Mathematical function, inverse of an exponential function
formula: log b x = log 10 x log 10 b = log e x log e b . {\displaystyle \log _{b}x={\frac {\log _{10}x}{\log _{10}b}}={\frac {\log _{e}x}{\log _{e}b}}
Logarithm
Fourth standardized moment in statistics
kurtosis corresponds to greater extremity of deviations (or outliers), and not the configuration of data near the mean. The widespread misunderstanding of kurtosis
Kurtosis
Type of mathematical function
distribution with specified mean μ and Deviation risk measure D. As it happens, many common probability distributions are log-concave. Some examples: the
Logarithmically concave function
Logarithmically_concave_function
Middle quantile of a data set or probability distribution
variability: the range, the interquartile range, the mean absolute deviation, and the median absolute deviation. For practical purposes, different measures of
Median
Statistical hypothesis test
{n}}}},} where x ¯ {\displaystyle {\bar {x}}} is the sample mean, s is the sample standard deviation and n is the sample size. The degrees of freedom used in
Student's_t-test
Graphical representation of the distribution of numerical data
which is less sensitive than the standard deviation to outliers in data. This approach of minimizing integrated mean squared error from Scott's rule can be
Histogram
Probability distribution that has the most entropy of a class
result). Every distribution with log-concave density is a maximal entropy distribution with specified mean μ and deviation risk measure D . In particular
Maximum entropy probability distribution
Maximum_entropy_probability_distribution
Statistical indicators of the deviation of a sample
conventional or non-robust measures of scale, such as sample standard deviation, which are greatly influenced by outliers. The most common such robust
Robust_measures_of_scale
Sampling from a population which can be partitioned into subpopulations
measurements within strata have a lower standard deviation (as compared to the overall standard deviation in the population), stratification gives a smaller
Stratified_sampling
preserving spread Mean reciprocal rank Mean signed difference Mean square quantization error Mean square weighted deviation Mean squared error Mean squared prediction
List_of_statistics_articles
Averages of repeated trials converge to the expected value
will tend toward zero (standard deviation asymptotic to 1 / 2 log log log n {\textstyle 1/{\sqrt {2\log \log \log n}}} ), but for a given ε, there
Law_of_large_numbers
Statistical test
the population standard deviation. Next calculate the z-score, which is the distance from the sample mean to the population mean in units of the standard
Z-test
Type of statistics
distribution, and 5% a normal distribution with the same mean but significantly higher standard deviation (representing outliers). Robust parametric statistics
Robust_statistics
Type of statistics
tendency, such as the arithmetic mean a measure of statistical dispersion like the standard mean absolute deviation a measure of the shape of the distribution
Summary_statistics
Class of statistical models
log(μ) be a linear model. This produces the "cloglog" transformation log ( − log ( 1 − p ) ) = log ( μ ) . {\displaystyle \log(-\log(1-p))=\log(\mu
Generalized_linear_model
Formal IT practice
Infrastructure or the delivery of IT service and evaluation of the impact a deviation might cause to the services. Events are typically notifications created
Event_management_(ITIL)
Data visualization
samples independently from their mean values, it is more appropriate to look at the ratio of the pairs of measurements. Log transformation (base 2) of the
Bland–Altman_plot
Measure of statistical dispersion
median of some common distributions are shown below The IQR, mean, and standard deviation of a population P can be used in a simple test of whether or
Interquartile_range
Measure of the deviation of position over time
squared displacement, or mean square fluctuation, is a measure of the deviation of the position of a particle with respect to a reference position over
Mean_squared_displacement
Statistical measure of how far values spread from their average
defined as the expected value of the squared deviation from the mean of a random variable. The standard deviation is the square root of the variance. Technically
Variance
Linear regression model with a single explanatory variable
\Delta y_{i}} as the deviations in xi and yi with respect to their respective means. The above equations are efficient to use if the mean of the x and y variables
Simple_linear_regression
Comparisons in quantitative sciences
F_{0}} and log change is F 1 {\displaystyle F_{1}} . Approximation error Errors and residuals in statistics Relative standard deviation Logarithmic
Relative_change
Probability distribution
(N\alpha -m)}{\Gamma (N\alpha )}}y^{m}} which shows that the mean ± standard deviation estimate of the posterior distribution for θ is y N α − 1 ± y
Gamma_distribution
Tool to assess control of a manufacturing process
line is drawn at the value of the mean or median of the statistic The standard deviation (e.g., sqrt(variance) of the mean) of the statistic is calculated
Control_chart
Statistical distance measure
standard deviations away P {\displaystyle P} is from the mean of D {\displaystyle D} . This distance is zero for P {\displaystyle P} at the mean of D {\displaystyle
Mahalanobis_distance
Type of radio propagation model
distribution with σ {\displaystyle \sigma } standard deviation in decibels, resulting in a log-normal distribution of the received power in watts. In
Log-distance_path_loss_model
Non-informative prior distribution
the Jeffreys prior for the standard deviation σ > 0 {\textstyle \sigma >0} is p ( σ ) ∝ I ( σ ) = E [ ( d d σ log f ( x ∣ σ ) ) 2 ] = E [ ( ( x − μ
Jeffreys_prior
Probability distribution
log-Cauchy distribution are finite. The mean is a moment so the log-Cauchy distribution does not have a defined mean or standard deviation. The log-Cauchy
Log-Cauchy_distribution
Particular case of the generalized extreme value distribution
-\ln(\ln(2))\approx 0.3665} , the mean is γ ≈ 0.5772 {\displaystyle \gamma \approx 0.5772} (the Euler–Mascheroni constant), and the standard deviation is π / 6 ≈ 1.2825
Gumbel_distribution
Concept in signal processing
n]\right|^{2}}{\sum _{m=0}^{M-1}\sum _{n=0}^{N-1}\left|x[m,n]\right|^{2}}}} Root-mean-square deviation is derived from MSE by taking the square root of the MSE. It downscale
Similarity (signal processing)
Similarity_(signal_processing)
Probability distribution of the possible sample outcomes
separately used to compute one value of a statistic (for example, the sample mean or sample variance) per sample, the sampling distribution is the probability
Sampling_distribution
Functional relationship between two quantities
terms that are constant, log, and log-squared. When the mean is small and variance is large, the constant in front of the log-squared term is very small
Power_law
Measure of the asymmetry of random variables
{\displaystyle \mu } is the mean, ν {\displaystyle \nu } is the median, and σ {\displaystyle \sigma } is the standard deviation, the skewness is defined
Skewness
Probability distribution
\right){\frac {\sqrt {n}}{s}},} which differs from Z in that the exact standard deviation σ is replaced by the sample standard error s, has a Student's t-distribution
Student's_t-distribution
Measure of linear correlation
standard deviations. The formal definition involves a "product moment", that is, the mean (the first moment about the origin) of the product of the mean-adjusted
Pearson correlation coefficient
Pearson_correlation_coefficient
Quantity that indexes a parametrized family of probability distributions
summarizes or describes an aspect of the population, such as a mean or a standard deviation. If a population exactly follows a known and defined distribution
Statistical_parameter
Data clustering algorithm
to minimize each class's average square deviation from the class mean, while maximizing each class's deviation from the means of the other classes. In
Jenks natural breaks optimization
Jenks_natural_breaks_optimization
Observation that in many real-life datasets, the leading digit is likely to be small
1 if log 1 ≤ log x < log 2, or starts with 9 if log 9 ≤ log x < log 10. The interval [log 1, log 2] is much wider than the interval [log 9, log 10] (0
Benford's_law
Measure of the joint variability
-1 and 1 by dividing by the geometric mean of the total variances (i.e., the product of the standard deviations) for the two random variables. A distinction
Covariance
Detailed record of borehole contents
exponent) for a pressure pack log. Other information that is normally notated on a mud log include directional data (deviation surveys), weight on bit, rotary
Well_logging
Function related to statistics and probability theory
with: log L ( α , β ∣ x ) = α log β − log Γ ( α ) + ( α − 1 ) log x − β x . {\displaystyle \log {\mathcal {L}}(\alpha ,\beta \mid x)=\alpha \log \beta
Likelihood_function
Statistical model for count data
offset(log(exposure)) + x, family=poisson(link=log) ) A characteristic of the Poisson distribution is that its mean is equal to its variance. In certain circumstances
Poisson_regression
Statistical accuracy measure
The symmetric mean absolute percentage error (SMAPE or sMAPE) is an accuracy measure based on percentage (or relative) errors. It is usually defined[citation
Symmetric mean absolute percentage error
Symmetric_mean_absolute_percentage_error
Variable used for specification
base-b logarithm by the formula log b ( x ) = log ( x ) log ( b ) {\displaystyle \log _{b}(x)={\frac {\log(x)}{\log(b)}}} where b is a parameter that
Parameter
Set of quantities in probability theory
⋯ + X m ( t ) = log E [ e t ( X 1 + ⋯ + X m ) ] = log ( E [ e t X 1 ] ⋯ E [ e t X m ] ) = log E [ e t X 1 ] + ⋯ + log E [ e t X m ]
Cumulant
Method for generating pseudo-random numbers
* math.log(w) / w) z2 = u2 * math.sqrt(-2 * math.log(w) / w) return z1, z2 Simple implementation in Java using the mean and standard deviation: private
Marsaglia_polar_method
Type of statistical measure over subsets of a dataset
a moving average (rolling average or running average or moving mean or rolling mean) is a calculation to analyze data points by creating a series of
Moving_average
Probability distribution
around the mean and the tail behavior are of particular interest. Other families of distributions can be used if the focus is on other deviations from normality
Generalized normal distribution
Generalized_normal_distribution
Problem in statistical estimation
m+{\frac {m\ln(2)}{k-1}}} and the following approximations for the mean and standard deviation: N ≈ μ ± σ = 89 ± 50 , μ = ( m − 1 ) k − 1 k − 2 , σ = ( k −
German_tank_problem
Statistical modeling method
variable that follows a Gaussian distribution, where the standard deviation is fixed and the mean is a linear combination of x → {\displaystyle {\vec {x}}} :
Linear_regression
Distinction between nominal, ordinal, interval and ratio variables
also allowed, but not the mean), and the appropriate measure of dispersion is percentile or quartile (the standard deviation is not allowed). Those restrictions
Level_of_measurement
Statistical property
squared-error loss function (among mean-unbiased estimators), as observed by Gauss. A minimum-average absolute deviation median-unbiased estimator minimizes
Bias_of_an_estimator
Measure of distance to normality
J(Y)=h(Y_{G})-h(Y),} where h ( Y G ) = 1 2 log ( 2 π e ⋅ σ 2 ) {\displaystyle h(Y_{G})={\tfrac {1}{2}}\log \left(2\pi \mathrm {e} \cdot \sigma ^{2}\right)}
Negentropy
Fundamental theorem in probability theory and statistics
appropriate conditions, the distribution of a normalized version of the sample mean converges to a standard normal distribution. This holds even if the original
Central_limit_theorem
Mathematical function of two positive real arguments
In mathematics, the arithmetic–geometric mean (AGM or agM) of two positive real numbers x and y is the mutual limit of a sequence of arithmetic means and
Arithmetic–geometric_mean
Type of statistical probability
{\displaystyle {\bar {X}}} and S {\displaystyle S} denote the sample mean and standard deviation of the log-transformed data for a sample of size n, a 95% confidence
Tolerance_interval
Probability distribution with more than one mode
constant and x and y are distributed as normal variables with a mean of 0 and a standard deviation of 1. R has a known density that can be expressed as a confluent
Multimodal_distribution
Probability distribution
\operatorname {Var} [X]={\frac {1}{\lambda ^{2}}},} so the standard deviation is equal to the mean. The moments of X, for n ∈ N {\displaystyle n\in \mathbb {N}
Exponential_distribution
= log S D Q T 2 / ( Q T m e a n ) 2 S D H R 2 / ( H R m e a n ) 2 {\displaystyle QTVi=\log {\frac {SDQT^{2}/(QT_{mean})^{2}}{SDHR^{2}/(HR_{mean})^{2}}}}
QT_interval_variability
Variable capable of taking on a limited number of possible values
low levels assigning 1 standard deviation above the mean, at the mean, and at one standard deviation below the mean respectively). In our categorical
Categorical_variable
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MEAN LOG-DEVIATION
MEAN LOG-DEVIATION
MEAN LOG-DEVIATION
MEAN LOG-DEVIATION
MEAN LOG-DEVIATION
MEAN LOG-DEVIATION
MEAN LOG-DEVIATION
MEAN LOG-DEVIATION
MEAN LOG-DEVIATION
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