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Set of probability distributions
probability and statistics, the class of exponential dispersion models (EDM), also called exponential dispersion family (EDF), is a set of probability distributions
Exponential_dispersion_model
Family of probability distributions
distributions are a special case of exponential dispersion models and are often used as distributions for generalized linear models. The Tweedie distributions
Tweedie_distribution
Class of statistical models
overdispersed exponential family (or exponential family with dispersion) is a generalization of an exponential family and the exponential dispersion model of distributions
Generalized_linear_model
diophantine equation Exponential dispersion model Exponential distribution Exponential error Exponential factorial Exponential family Exponential field Ordered
List_of_exponential_topics
Measure of goodness of fit for a statistical model
where model-fitting is achieved by maximum likelihood. It plays an important role in exponential dispersion models and generalized linear models. Deviance
Deviance_(statistics)
Family of probability distributions related to the normal distribution
regression models in statistics. Examples include logistic regression using the binomial family and Poisson regression. Exponential dispersion model Gibbs
Exponential_family
Normalized measure of the dispersion of a probability distribution
probability theory and statistics, the index of dispersion, dispersion index, coefficient of dispersion, relative variance, or variance-to-mean ratio (VMR)
Index_of_dispersion
British medical physicist and statistician
known as the Tweedie exponential dispersion models. As a consequence of these properties the Tweedie exponential dispersion models are characterized by
Maurice_Tweedie
Features that do not change if length or energy scales are multiplied by a common factor
special case of exponential dispersion models, a class of statistical models used to describe error distributions for the generalized linear model and characterized
Scale_invariance
Mathematical simulation of how air pollutants disperse in the ambient atmosphere
Atmospheric dispersion modeling is the mathematical simulation of how air pollutants disperse in the ambient atmosphere. It is performed with computer
Atmospheric dispersion modeling
Atmospheric_dispersion_modeling
factor analysis Exponential dispersion model Exponential distribution Exponential family Exponential-logarithmic distribution Exponential power distribution –
List_of_statistics_articles
System with multiple fractal dimensions
statistical distributions known as the Tweedie exponential dispersion models, as well as the geometric Tweedie models. The first convergence effect yields monofractal
Multifractal_system
Generates a forecast of future values of a time series
Exponential smoothing or exponential moving average (EMA) is a technique for smoothing time series data using the exponential window function. Whereas
Exponential_smoothing
Probability distribution
the gamma distribution is a member of the family of Tweedie exponential dispersion models. For the shape-scale parameterization x | θ ∼ Γ ( α , θ ) {\displaystyle
Gamma_distribution
Empirical law on the variance of species in a habitat
aggregation of the Colorado potato beetle described by an exponential dispersion model". Ecological Modelling. 151 (2–3): 261–269. Bibcode:2002EcMod.151..261K
Taylor's_law
Type of statistical measure over subsets of a dataset
2 → − ∞ {\displaystyle x_{1},x_{2}\to -\infty } . Sometimes, models that use exponential moving averages at multiple lags can be replaced by a single
Moving_average
or Rosin Rammler distribution, of which the exponential distribution is a special case, is used to model the lifetime of technical devices and is used
List of probability distributions
List_of_probability_distributions
Aspect of probability theory
X i {\displaystyle Y=\sum _{i=1}^{N}X_{i}} is a reproductive exponential dispersion model E D ( μ , σ 2 ) {\displaystyle ED(\mu ,\sigma ^{2})} with E
Compound_Poisson_distribution
Approximation method in statistics
purpose, Laplace used a symmetric two-sided exponential distribution we now call Laplace distribution to model the error distribution, and used the sum of
Least_squares
Model for tracing the history of genetic variation
samples under a Wright–Fisher neutral model. Bioinformatics 18:337–338 ^Kendal WS (2003) An exponential dispersion model for the distribution of human single
Coalescent_theory
Danish statistician
These models include both the proper dispersion models and the exponential dispersion models. He had an interest in a class of exponential dispersion models
Bent_Jørgensen_(statistician)
Probability of survival beyond any specified time
to be a good model of the complete lifespan of a living organism. As Efron and Hastie (p. 134) note, "If human lifetimes were exponential there wouldn't
Survival_function
Relaxation model
Schweidler law and the charge response corresponds to the stretched exponential function or the Kohlrausch–Williams–Watts (KWW) function, for small time
Cole–Cole_equation
Loudspeaker using an acoustic horn
and in some applications. A number of symmetrical, narrow dispersion, usually exponential horns can be combined in an array driven by a single driver
Horn_loudspeaker
Statistical property quantifying how much a collection of data is spread out
In statistics, dispersion (also called variability, scatter, or spread) is the extent to which a distribution is stretched or squeezed. Common examples
Statistical_dispersion
Type of mathematical model
A statistical model is a mathematical model that embodies a set of statistical assumptions concerning the generation of sample data (and similar data
Statistical_model
Atmospheric dispersion models are computer programs that use mathematical algorithms to simulate how pollutants in the ambient atmosphere disperse and
List of atmospheric dispersion models
List_of_atmospheric_dispersion_models
Function related to statistics and probability theory
likelihood) gives the relative merit of various statistical models for describing a data set. Often the models being compared are parameterized by a parameter, with
Likelihood_function
Class of statistical survival models
Proportional hazards models are a class of survival models in statistics. Survival models relate the time that passes, before some event occurs, to one
Proportional_hazards_model
Statistical model allowing for frequent zero values
In statistics, a zero-inflated model is a statistical model based on a zero-inflated probability distribution, i.e. a distribution that allows for frequent
Zero-inflated_model
Distinction between nominal, ordinal, interval and ratio variables
mode is also allowed, but not the mean), and the appropriate measure of dispersion is percentile or quartile (the standard deviation is not allowed). Those
Level_of_measurement
Parametric model in survival analysis
(including the exponential distribution as a special case) can be parameterised as either a proportional hazards model or an AFT model, and is the only
Accelerated failure time model
Accelerated_failure_time_model
Probability distribution
The normal distribution is a member of the family of Tweedie exponential dispersion models. Wrapped normal distribution – the normal distribution applied
Normal_distribution
Relative measure of dispersion expressed as the ratio of standard deviation to the mean
and relative standard deviation (RSD), is a standardized measure of dispersion of a probability distribution or frequency distribution. It is defined
Coefficient_of_variation
Continuous probability distribution on the unit interval
interval that belongs to an exponential dispersion family. It was introduced as a response distribution for generalized linear models for continuous proportional
Continuous binomial distribution
Continuous_binomial_distribution
Statistical model used in time series analysis
statistical analysis of time series, an autoregressive–moving-average (ARMA) model is used to represent a (weakly) stationary stochastic process by combining
Autoregressive moving-average model
Autoregressive_moving-average_model
Time series model
average (EWMA) is an alternative model in a separate class of exponential smoothing models. As an alternative to GARCH modelling it has some attractive properties
Autoregressive conditional heteroskedasticity
Autoregressive_conditional_heteroskedasticity
Risk measure estimating the average loss in the worst tail of the distribution
Emiliano (February 2004). "Tail Conditional Expectations for Exponential Dispersion Models" (PDF). Retrieved February 3, 2011. {{cite journal}}: Cite journal
Expected_shortfall
Smooth function in statistics
of the exponential family, a generalized linear model may be more appropriate to use, and moreover, when we wish not to force a parametric model onto our
Variance_function
Statistical model for a binary dependent variable
In statistics, a logistic model (or logit model) is a statistical model that models the log-odds of an event as a linear combination of one or more independent
Logistic_regression
Measure of covariance of components of a random vector
statistics, a covariance matrix (also known as auto-covariance matrix, dispersion matrix, variance matrix, or variance–covariance matrix) is a square matrix
Covariance_matrix
Form of causal modeling that fit networks of constructs to data
Structural equation modeling (SEM) is a diverse set of methods used by scientists for both observational and experimental research. SEM is used mostly
Structural_equation_modeling
Statistics term
and cannot be identically zero unless h is zero almost everywhere. The exponential is not zero, so this can only happen if g is zero almost everywhere.
Completeness_(statistics)
Family of continuous probability distributions
Gaussian distribution is a member of the family of Tweedie exponential dispersion models Stopping time Chhikara, Raj S.; Folks, J. Leroy (1989), The
Inverse_Gaussian_distribution
Interpretation of probability
variables, or more generally unknown quantities, to model all sources of uncertainty in statistical models including uncertainty resulting from lack of information
Bayesian_probability
Type of queue
process and service times are exponentially distributed is sometimes referred to as a Flatto–Hahn–Wright model or FHW model. On arrival at the fork point
Fork–join_queue
Statistical linear model
for a variety of other distributions from the exponential family for the residuals. The general linear model is a special case of the GLM in which the distribution
General_linear_model
Process of using data analysis for predicting population data from sample data
applications, especially with low-dimensional models with log-concave likelihoods (such as with one-parameter exponential families). For a given dataset that was
Statistical_inference
Concept in inferential statistics
Statistical model Model specification Lp space Parameter location scale shape Parametric family Likelihood (monotone) Location–scale family Exponential family
Statistical_significance
Concept in statistics
one-parameter models from the classical exponential family, and include 3 of the most important statistical regression models: the linear model, Poisson regression
Vector generalized linear model
Vector_generalized_linear_model
Distributional regression model
but not very flexible enough to model other characteristics of the distribution i.e tails. In GAMLSS the exponential family distribution assumption for
Generalized additive model for location, scale and shape
Generalized_additive_model_for_location,_scale_and_shape
Number of values in the final calculation of a statistic that are free to vary
fully determined). The term is most often used in the context of linear models (linear regression, analysis of variance), where certain random vectors
Degrees of freedom (statistics)
Degrees_of_freedom_(statistics)
Statistical method
of an estimator by resampling (often with replacement) one's data or a model which is estimated from the data. Bootstrapping assigns measures of accuracy
Bootstrapping_(statistics)
Type of average of a collection of numbers
0° (or 360°) is geometrically a better average value: there is lower dispersion about it (the points are both 1° from it and 179° from 180°, the putative
Arithmetic_mean
Model for generating observable data in probability and statistics
Generative models are a class of computational models frequently used for classification. In machine learning, it typically models the joint distribution
Generative_model
Statistical method for handling multiple comparisons
"Asymptotic minimaxity of false discovery rate thresholding for sparse exponential data". Annals of Statistics. 34 (6): 2980–3018. arXiv:math/0602311. Bibcode:2006math
False_discovery_rate
Statistical hypothesis test
the Pearson distribution to model the observation and performing a test of goodness of fit to determine how well the model really fits to the observations
Chi-squared_test
Statistic measuring inter-rater agreement for categorical items
account" chance agreement. To do this effectively would require an explicit model of how chance affects rater decisions. The so-called chance adjustment of
Cohen's_kappa
Summary statistic of variability
deviations from a central point. It is a summary statistic of statistical dispersion or variability. In the general form, the central point can be a mean,
Average_absolute_deviation
Graphical representation of the distribution of numerical data
preferred in applications, when their statistical properties need to be modeled. The correlated variation of a kernel density estimate is very difficult
Histogram
Statistical considerations on how many observations to make
Statistical model Model specification Lp space Parameter location scale shape Parametric family Likelihood (monotone) Location–scale family Exponential family
Sample_size_determination
Linear regression model with a single explanatory variable
In statistics, simple linear regression (SLR) is a linear regression model with a single explanatory variable. That is, it concerns two-dimensional sample
Simple_linear_regression
Statistical hypothesis test for forecasting
other lagged values of the variable jointly add explanatory power to the model according to an F-test. Then the null hypothesis of no Granger causality
Granger_causality
Model in electromagnetism
the dielectric dispersion curve. The model was first used to describe the dielectric relaxation of some polymers, by adding two exponential parameters to
Havriliak–Negami_relaxation
Statistical principle
on a sample dataset in relation to a parametric model of the dataset. A sufficient statistic for a model parameter contains all of the information that
Sufficient_statistic
Estimator for quality of a statistical model
quality of statistical models for a given set of data. Given a collection of models for the data, AIC estimates the quality of each model, relative to each
Akaike_information_criterion
Quality measure of a statistical method
the Fisher information matrix of the model at point θ. Generally, the variance measures the degree of dispersion of a random variable around its mean
Efficiency_(statistics)
Term in statistical hypothesis testing
Statistical model Model specification Lp space Parameter location scale shape Parametric family Likelihood (monotone) Location–scale family Exponential family
Power_(statistics)
Method of estimating the parameters of a statistical model, given observations
maximizing a likelihood function so that, under the assumed statistical model, the observed data is most probable. The point in the parameter space that
Maximum_likelihood_estimation
Statistical distribution for dependence between random variables
variable is uniform on the interval [0, 1]. Copulas are used to describe / model the dependence (inter-correlation) between random variables. Their name
Copula_(statistics)
Method of statistical inference
population are true by examining sample data. Typically, the population is modelled by a random variable whose distribution has unknown parameters. For example
Statistical_hypothesis_test
Statistical property
the linear exponential family and the conditional expectation function is correctly specified). Yet, in the context of binary choice models (Logit or Probit)
Homoscedasticity and heteroscedasticity
Homoscedasticity_and_heteroscedasticity
Sub-class of survival models
In statistics, first-hitting-time models are simplified models that estimate the amount of time that passes before some random or stochastic process crosses
First-hitting-time_model
Table that displays the frequency of variables
Correlation". 26 December 2019. Andersen, Erling B. 1980. Discrete Statistical Models with Social Science Applications. North Holland, 1980. Bishop, Y. M. M.;
Contingency_table
Covariance and correlation
Hezarkhani, Ardeshir; Sahimi, Muhammad (2012). "Multiple-point geostatistical modeling based on the cross-correlation functions". Computational Geosciences. 16
Cross-correlation
Mathematical model for stochastic processes
The generalized functional linear model (GFLM) is an extension of the generalized linear model (GLM) that allows one to regress univariate responses of
Generalized functional linear model
Generalized_functional_linear_model
Diagnostic plot of binary classifier ability
graphical plot that illustrates the performance of a binary classifier model (although it can be generalized to multiple classes) at varying threshold
Receiver operating characteristic
Receiver_operating_characteristic
Measure of the joint variability
producing the g factor. Another is to personality, with models like the five factor model being derived from principal component analysis. Algorithms
Covariance
Nonparametric test of the null hypothesis
sample and an observation in the second sample. Otherwise, if both the dispersions and shapes of the distribution of both samples differ, the Mann–Whitney
Mann–Whitney_U_test
Statistical test that compares goodness of fit
that involves comparing the goodness of fit of two competing statistical models, typically one found by maximization over the entire parameter space and
Likelihood-ratio_test
Task of selecting a statistical model from a set of candidate models
Model selection is the task of selecting a model from among various candidates on the basis of performance criterion to choose the best one. In the context
Model_selection
Statistics applied to risk in insurance and other financial products
and computer science. Historically, actuarial science used deterministic models in the construction of tables and premiums. The science has gone through
Actuarial_science
Branch of statistics
procedures. Here is a list of common models used in practice. Exponential families (e.g. normal distribution, exponential distribution, log-normal distribution
Parametric_statistics
Mathematical model used for classification or regression
Discriminative models, also referred to as conditional models, are a class of models frequently used for classification. In machine learning, it typically models the
Discriminative_model
Frequency with which an engineered system or component fails
( t ) = λ e − λ t , {\displaystyle f(t)=\lambda e^{-\lambda t},} an exponential function with scaling constant λ {\displaystyle \lambda } . As seen in
Failure_rate
Probabilistic problem-solving algorithm
to a degree of freedom. Monte Carlo methods provide a way out of this exponential increase in computation time. As long as the function in question is
Monte_Carlo_method
Statistical methods to build mathematical models of dynamical systems from measured data
experiments for efficiently generating informative data for fitting such models as well as model reduction. A common approach is to start from measurements of the
System_identification
Statistical model validation technique
rotation estimation or out-of-sample testing, is any of various similar model validation techniques for assessing how the results of a statistical analysis
Cross-validation_(statistics)
Experiment methodology
control mechanism. Adaptive control Between-group design experiment Choice modelling Multi-armed bandit Multivariate testing Randomized controlled trial Scientific
A/B_testing
Measure of statistical dispersion
statistics, the interquartile range (IQR) is a measure of statistical dispersion, which is the spread of the data. The IQR may also be called the midspread
Interquartile_range
Causal or moderating relationship between statistical variables
Since this quantity grows exponentially, it readily becomes impractically large. One method to limit the size of the model is to limit the order of interactions
Interaction_(statistics)
Comparison of two distributions
known. Q–Q plots are commonly used to compare a data set to a theoretical model. This can provide an assessment of goodness of fit that is graphical, rather
Q–Q_plot
Statistical property
size. In other words, the standard error of the mean is a measure of the dispersion of sample means around the population mean. In regression analysis, the
Standard_error
Statistical hypothesis test
two models, 1 and 2, where model 1 is 'nested' within model 2. Model 1 is the restricted model, and model 2 is the unrestricted one. That is, model 1 has
F-test
of a family of statistical distributions called the Tweedie exponential dispersion models. Much as the central limit theorem explains how certain types
Long-tail_traffic
Measure of linear correlation
sum of squares (RSS) over β0 and β1 are equal to 0 in the least squares model, where RSS = ∑ i ( Y i − Y ^ i ) 2 {\displaystyle {\text{RSS}}=\sum _{i}(Y_{i}-{\hat
Pearson correlation coefficient
Pearson_correlation_coefficient
Statistical modeling method
In statistics, linear regression is a model that estimates the relationship between a scalar response (dependent variable) and one or more explanatory
Linear_regression
Two different methods for presenting tabular data
transforming wide data into a long format. Wide and narrow: Common in database modeling. Wide, or unstacked data is presented with each different data variable
Wide_and_narrow_data
Ratio of competing statistical models
competing statistical models represented by their evidence, and is used to quantify the support for one model over the other. The models in question can have
Bayes_factor
Value that appears most often in a set of data
= find(diff([X, realmax]) > 0); % indices where repeated values change [modeL,i] = max (diff([0, indices])); % longest persistence length of repeated
Mode_(statistics)
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EXPONENTIAL DISPERSION-MODEL
EXPONENTIAL DISPERSION-MODEL
EXPONENTIAL DISPERSION-MODEL
EXPONENTIAL DISPERSION-MODEL
EXPONENTIAL DISPERSION-MODEL
EXPONENTIAL DISPERSION-MODEL
EXPONENTIAL DISPERSION-MODEL
EXPONENTIAL DISPERSION-MODEL
EXPONENTIAL DISPERSION-MODEL
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