Q-EXPONENTIAL DISTRIBUTION

Exponential Distribution Application Exponential Distribution Example Exponential Distribution Calculator Exponential Distribution Excel Exponential Form Exponential Probability Exponential Functions Q Distribution Table




Cloud:

| Exponential Distribution Application | Exponential Distribution Example | Exponential Distribution Calculator | Exponential Distribution Excel | Exponential Form | Exponential Probability | Exponential Functions | Q Distribution Table |

| Q-exponential_distribution | Q-Logarithm | Tsallis_distribution | Lomax_distribution | Laplace_distribution | Hyper-exponential_distribution | Chi-squared_distribution | Maximum_entropy_probability_distribution | Differential_entropy | Q-Gaussian_distribution | Phase-type_distribution | Stochastic_simulation | Power_law_distribution | Normal_distribution | Tsallis_entropy | Gamma_distribution | Poisson_distribution | Binomial_distribution | Weibull_distribution | Beta_distribution | Variational_Bayesian_methods | Gumbel_distribution | Geometric_distribution | Logistic_distribution | Normal-gamma_distribution | List_of_statistics_articles | Conjugate_distribution | Rayleigh_distribution | Gaussian_minus_exponential_distribution | Generalized_beta_distribution | Symmetric_probability_distribution | Uniform_distribution_(continuous) | Generalized_extreme_value_distribution | Matrix_exponential | Q-analog | List_of_exponential_topics | Inverse_distribution_function | Gaussian_q-distribution | Exponential_average | Exponentially_modified_Gaussian_distribution | Exponential_generating_function | Rotation_matrix | Relationships_among_probability_distributions | Exponential-logarithmic_distribution | Stable_distribution | Logarithm | Non-extensive_self-consistent_thermodynamical_theory | Nonparametric_skew |



[ Link Deletion Request ]



q-exponential distribution


q-exponential distribution
Probability density function
Probability density plots of q-exponential distributions
Parameters q<2 shape (real)
\lambda >0 rate (real)
Support x\in [0;+\infty )\!{\text{ for }}q\geq 1
x\in [0;{1 \over {\lambda (1-q)}}){\text{ for }}q<1
pdf {(2-q)\lambda e_{q}^{{-\lambda x}}}
CDF {1-e_{{q'}}^{{-\lambda x \over q'}}}{\text{ where }}q'={1 \over {2-q}}
Mean {1 \over \lambda (3-2q)}{\text{ for }}q<{3 \over 2}
Otherwise undefined
Median {{-q'{\text{ ln}}_{{q'}}({1 \over 2})} \over {\lambda }}{\text{ where }}q'={1 \over {2-q}}
Mode 0
Variance {{q-2} \over {(2q-3)^{2}(3q-4)\lambda ^{2}}}{\text{ for }}q<{4 \over 3}
Skewness {2 \over {5-4q}}{\sqrt  {{3q-4} \over {q-2}}}{\text{ for }}q<{5 \over 4}
Ex. kurtosis 6{{-4q^{3}+17q^{2}-20q+6} \over {(q-2)(4q-5)(5q-6)}}{\text{ for }}q<{6 \over 5}

The q-exponential distribution is a probability distribution arising from the maximization of the Tsallis entropy under appropriate constraints, including constraining the domain to be positive. It is one example of a Tsallis distribution. The q-exponential is a generalization of the exponential distribution in the same way that Tsallis entropy is a generalization of standard Boltzmann–Gibbs entropy or Shannon Entropy.[1] The exponential distribution is recovered as q\rightarrow 1.


Q-exponential distribution Characterization



Q-exponential distribution Probability density function

The q-exponential distribution has the probability density function

{(2-q)\lambda e_{q}^{{-\lambda x}}}

where

e_{q}(x)=[1+(1-q)x]^{{1 \over 1-q}}

is the q-exponential.


Q-exponential distribution Derivation


In a similar procedure to how the exponential distribution can be derived using the standard Boltzmann–Gibbs entropy or Shannon entropy and constraining the domain of the variable to be positive, the q-exponential distribution can be derived from a maximization of the Tsallis Entropy subject to the appropriate constraints.


Q-exponential distribution Relationship to other distributions


The q-exponential is a special case of the Generalized Pareto distribution where

\mu =0~,~\xi ={{q-1} \over {2-q}}~,~\sigma ={1 \over {\lambda (2-q)}}

The q-exponential is the generalization of the Lomax distribution (Pareto Type II), as it extends this distribution to the cases of finite support. The Lomax parameters are:

\alpha ={{2-q} \over {q-1}}~,~\lambda _{{lomax}}={1 \over {\lambda (q-1)}}

As the Lomax distribution is a shifted version of the Pareto distribution, the q-exponential is a shifted reparameterized generalization of the Pareto. When q > 1, the q-exponential is equivalent to the Pareto shifted to have support starting at zero. Specifically:

{\text{If }}X\sim {\mbox{qExp}}(q,\lambda ){\text{ and }}Y\sim \left[{\text{Pareto}}\left(x_{m}={1 \over {\lambda (q-1)}},\alpha ={{2-q} \over {q-1}}\right)-x_{m}\right],{\text{ then }}X\sim Y\,

Q-exponential distribution Generating random deviates


Random deviates can be drawn using Inverse transform sampling. Given a variable U that is uniformly distributed on the interval (0,1), then

X={{-q'{\text{ ln}}_{{q'}}(U)} \over \lambda }\sim {\mbox{qExp}}(q,\lambda )

where {\text{ln}}_{{q'}} is the q-logarithm and q'={1 \over {2-q}}


Q-exponential distribution Applications



Q-exponential distribution Economics (econophysics)

The q-exponential distribution has been used to describe the distribution of wealth (assets) between individuals.[2]


Q-exponential distribution See also



Q-exponential distribution Notes


  1. ^ Tsallis, C. Nonadditive entropy and nonextensive statistical mechanics-an overview after 20 years. Braz. J. Phys. 2009, 39, 337–356
  2. ^ Adrian A. Dragulescu Applications of physics to economics and finance: Money, income, wealth, and the stock market arXiv:cond-mat/0307341v2

Q-exponential distribution Further reading



Q-exponential distribution External links




Exponential Distribution Application Exponential Distribution Example Exponential Distribution Calculator Exponential Distribution Excel Exponential Form Exponential Probability Exponential Functions Q Distribution Table

| Exponential Distribution Application | Exponential Distribution Example | Exponential Distribution Calculator | Exponential Distribution Excel | Exponential Form | Exponential Probability | Exponential Functions | Q Distribution Table | Q-exponential_distribution | Q-Logarithm | Tsallis_distribution | Lomax_distribution | Laplace_distribution | Hyper-exponential_distribution | Chi-squared_distribution | Maximum_entropy_probability_distribution | Differential_entropy | Q-Gaussian_distribution | Phase-type_distribution | Stochastic_simulation | Power_law_distribution | Normal_distribution | Tsallis_entropy | Gamma_distribution | Poisson_distribution | Binomial_distribution | Weibull_distribution | Beta_distribution | Variational_Bayesian_methods | Gumbel_distribution | Geometric_distribution | Logistic_distribution | Normal-gamma_distribution | List_of_statistics_articles | Conjugate_distribution | Rayleigh_distribution | Gaussian_minus_exponential_distribution | Generalized_beta_distribution | Symmetric_probability_distribution | Uniform_distribution_(continuous) | Generalized_extreme_value_distribution | Matrix_exponential | Q-analog | List_of_exponential_topics | Inverse_distribution_function | Gaussian_q-distribution | Exponential_average | Exponentially_modified_Gaussian_distribution | Exponential_generating_function | Rotation_matrix | Relationships_among_probability_distributions | Exponential-logarithmic_distribution | Stable_distribution | Logarithm | Non-extensive_self-consistent_thermodynamical_theory | Nonparametric_skew

Copyright:
Dieser Artikel basiert auf dem Artikel http://en.wikipedia.org/wiki/Q-exponential_distribution aus der freien Enzyklopaedie http://en.wikipedia.org bzw. http://www.wikipedia.org und steht unter der Doppellizenz GNU-Lizenz fuer freie Dokumentation und Creative Commons CC-BY-SA 3.0 Unported. In der Wikipedia ist eine Liste der Autoren unter http://en.wikipedia.org/w/index.php?title=Q-exponential_distribution&action=history verfuegbar. Alle Angaben ohne Gewähr.

Dieser Artikel enthält u.U. Inhalte aus dmoz.org : Help build the largest human-edited directory on the web. Suggest a Site - Open Directory Project - Become an Editor






Search: deutsch english español français русский

| deutsch | english | español | français | русский |




[ Privacy Policy ] [ Link Deletion Request ] [ Imprint ]