Proof of knowledge - Revision history

213.65.138.54: Clarify 'it'

2014-12-04T08:13:05Z

Clarify 'it'

← Older revision		Revision as of 10:13, 4 December 2014
Line 1:		Line 1:
	~~{{Probability distribution \|~~		The title of the writer is Nestor. Bookkeeping is what she does. One of my preferred hobbies is camping and now I'm attempting to earn cash with it. I presently reside in Alabama.<br><br>Here is my web site :: extended car warranty, [http://www.team.trustfactory.ch/index.php?mod=users&action=view&id=4832 please click the next internet page],
	~~name =variance-gamma distribution\|~~
	~~type =density\|~~
	~~pdf_image =\|~~
	~~cdf_image =\|~~
	parameters =<math>\mu</math> [[location parameter\|location]] ([[real number\|real]])<br/><math>\alpha</math> <!--to do--> (real)<br/><math>\beta</math> asymmetry parameter (real)<br/><math>\lambda > 0</math><br/><math>\gamma = \sqrt{\alpha^2 - \beta^2} > 0 </math>\|
	~~support =<math>x \in (-\infty; +\infty)\!</math>\|~~
	pdf =<math>\frac{\gamma^{2\lambda} \| x - \mu\|^{\lambda-1/2} K_{\lambda-1/2} \left(\alpha\|x - \mu\|\right)}{\sqrt{\pi} \Gamma (\lambda)(2 \alpha)^{\lambda-1/2}} \; e^{\beta (x - \mu)}</math> <br/><br/><math>K_\lambda</math> denotes a modified Bessel function of the ~~second kind<br/><math>\Gamma</math> denotes the Gamma function\|~~
	~~cdf =<!-- to do -->\|~~
	~~mean =<math>\mu + 2 \beta \lambda/ \gamma^2</math>\|~~
	~~median =<!-- to do -->\|~~
	~~mode =\|~~
	~~variance =<math>2\lambda(1 + 2 \beta^2/\gamma^2)/\gamma^2</math>\|~~
	~~skewness =<!-- to do -->\|\|~~
	~~kurtosis =<!-- to do -->\|\|~~
	~~entropy =<!-- to do -->\|~~
	~~mgf =<math>e^{\mu z} \left(\gamma/\sqrt{\alpha^2 -(\beta+z)^2}\right)^{2\lambda}</math>\|~~
	~~char =<!-- to do -->\|~~
	}}
	~~The '''variance-gamma distribution''', '''generalized Laplace distribution'''<ref name=laplace>{{cite book\|title=The Laplace Distribution and Generalizations\|author=Kotz, S~~. et al\|page=180\|year=2001\|publisher=Birkhauser\|isbn=0-8176-4166-1}}</ref> or '''Bessel function distribution'''<ref name=laplace/> is a [[continuous probability distribution]] that is defined as the [[normal variance-mean mixture]] where the [[mixture density\|mixing density]] is ~~the [[gamma distribution]]~~. ~~The tails~~ of ~~the distribution decrease more slowly than the [[normal distribution]]. It is therefore suitable to model phenomena where numerically large values are more probable than~~ is the case for the normal distribution. Examples are returns from financial assets and turbulent wind speeds. The distribution was introduced in the financial literature by Madan and Seneta.<ref>D.B. Madan and ~~E. Seneta (1990): The variance gamma (V.G.) model for share market returns,~~ '~~'Journal of Business'', 63, pp. 511–524.</ref> The variance-gamma distributions form a subclass of the [[generalised hyperbolic distribution]]s~~.

	The fact that there is a simple expression for the [[moment generating function]] implies that simple expressions for all [[moment (mathematics)\|moments]] are available. The class of variance-gamma distributions is closed under [[convolution]] in ~~the following sense~~. If <~~math~~>~~X_1~~</math> and <math>X_2</math> are [[statistical independence\|independent]] [[random variable]]s that are variance-gamma distributed with the same values of the parameters <math>\alpha</math> and <math>\beta</math>, but possibly different values of the other parameters, <math>\lambda_1</math>, <math>\mu_1</math> and <math>\lambda_2,</math> <math>\mu_2</math>, respectively, then <math>X_1 + X_2</math> is ~~variance-gamma distributed with parameters <math>\alpha~~, </~~math> <math>\beta, <~~/~~math><math>\lambda_1+\lambda_2</math> and <math>\mu_1 + \mu_2~~.~~</math>~~

	~~The Variance Gamma distribution can also be expressed in terms of three inputs parameters (C,G,M) denoted after the initials of its founders~~. ~~If the "C" ,<math>\lambda <~~/~~math> here, parameter is integer then the distribution has a closed form 2-EPT distribution. See [[2-EPT probability density function\|2-EPT Probability Density Function]]~~. ~~Under this restriction closed form option prices can be derived.~~

	~~See also [[Variance gamma process]].~~

	== ~~Notes~~ ==
	~~<references/>~~

	~~{{ProbDistributions\|continuous-infinite}}~~

	~~{{DEFAULTSORT:Variance-Gamma Distribution}}~~
	~~[[Category:Continuous distributions]]~~
	~~[[Category:Probability distributions]~~]

en>BG19bot: WP:CHECKWIKI error fix for #61. Punctuation goes before References. Do general fixes if a problem exists. - using AWB (8855)

2013-01-16T08:58:25Z

WP:CHECKWIKI error fix for #61. Punctuation goes before References. Do general fixes if a problem exists. - using AWB (8855)

← Older revision		Revision as of 10:58, 16 January 2013
Line 1:		Line 1:
	I'~~m Yoshiko Oquendo~~. ~~Playing crochet~~ is a ~~thing~~ that I'~~m completely addicted to~~. ~~Interviewing~~ is ~~what she does~~. ~~Her family life~~ in ~~Delaware~~ but ~~she needs to transfer simply because~~ of ~~her family members.~~<br><br>~~My web~~-~~site :: extended car warranty ([http:~~//~~Www~~.~~Sceltic~~.at/~~index~~.~~php?mod~~=~~users&action~~=~~view&id~~=~~19873 mouse click the up coming document~~])		{{Probability distribution \|
			name =variance-gamma distribution\|
			type =density\|
			pdf_image =\|
			cdf_image =\|
			parameters =<math>\mu</math> [[location parameter\|location]] ([[real number\|real]])<br/><math>\alpha</math> <!--to do--> (real)<br/><math>\beta</math> asymmetry parameter (real)<br/><math>\lambda > 0</math><br/><math>\gamma = \sqrt{\alpha^2 - \beta^2} > 0 </math>\|
			support =<math>x \in (-\infty; +\infty)\!</math>\|
			pdf =<math>\frac{\gamma^{2\lambda} \| x - \mu\|^{\lambda-1/2} K_{\lambda-1/2} \left(\alpha\|x - \mu\|\right)}{\sqrt{\pi} \Gamma (\lambda)(2 \alpha)^{\lambda-1/2}} \; e^{\beta (x - \mu)}</math> <br/><br/><math>K_\lambda</math> denotes a modified Bessel function of the second kind<br/><math>\Gamma</math> denotes the Gamma function\|
			cdf =<!-- to do -->\|
			mean =<math>\mu + 2 \beta \lambda/ \gamma^2</math>\|
			median =<!-- to do -->\|
			mode =\|
			variance =<math>2\lambda(1 + 2 \beta^2/\gamma^2)/\gamma^2</math>\|
			skewness =<!-- to do -->\|\|
			kurtosis =<!-- to do -->\|\|
			entropy =<!-- to do -->\|
			mgf =<math>e^{\mu z} \left(\gamma/\sqrt{\alpha^2 -(\beta+z)^2}\right)^{2\lambda}</math>\|
			char =<!-- to do -->\|
			}}
			The '''variance-gamma distribution''', '''generalized Laplace distribution'''<ref name=laplace>{{cite book\|title=The Laplace Distribution and Generalizations\|author=Kotz, S. et al\|page=180\|year=2001\|publisher=Birkhauser\|isbn=0-8176-4166-1}}</ref> or '''Bessel function distribution'''<ref name=laplace/> is a [[continuous probability distribution]] that is defined as the [[normal variance-mean mixture]] where the [[mixture density\|mixing density]] is the [[gamma distribution]]. The tails of the distribution decrease more slowly than the [[normal distribution]]. It is therefore suitable to model phenomena where numerically large values are more probable than is the case for the normal distribution. Examples are returns from financial assets and turbulent wind speeds. The distribution was introduced in the financial literature by Madan and Seneta.<ref>D.B. Madan and E. Seneta (1990): The variance gamma (V.G.) model for share market returns, ''Journal of Business'', 63, pp. 511–524.</ref> The variance-gamma distributions form a subclass of the [[generalised hyperbolic distribution]]s.

			The fact that there is a simple expression for the [[moment generating function]] implies that simple expressions for all [[moment (mathematics)\|moments]] are available. The class of variance-gamma distributions is closed under [[convolution]] in the following sense. If <math>X_1</math> and <math>X_2</math> are [[statistical independence\|independent]] [[random variable]]s that are variance-gamma distributed with the same values of the parameters <math>\alpha</math> and <math>\beta</math>, but possibly different values of the other parameters, <math>\lambda_1</math>, <math>\mu_1</math> and <math>\lambda_2,</math> <math>\mu_2</math>, respectively, then <math>X_1 + X_2</math> is variance-gamma distributed with parameters <math>\alpha, </math> <math>\beta, </math><math>\lambda_1+\lambda_2</math> and <math>\mu_1 + \mu_2.</math>

			The Variance Gamma distribution can also be expressed in terms of three inputs parameters (C,G,M) denoted after the initials of its founders. If the "C" ,<math>\lambda </math> here, parameter is integer then the distribution has a closed form 2-EPT distribution. See [[2-EPT probability density function\|2-EPT Probability Density Function]]. Under this restriction closed form option prices can be derived.

			See also [[Variance gamma process]].

			== Notes ==
			<references/>

			{{ProbDistributions\|continuous-infinite}}

			{{DEFAULTSORT:Variance-Gamma Distribution}}
			[[Category:Continuous distributions]]
			[[Category:Probability distributions]]

en>Noamz: /* Sigma protocols */ insert "letter"

2012-05-07T12:35:11Z

Sigma protocols: insert "letter"

New page

I'm Yoshiko Oquendo. Playing crochet is a thing that I'm completely addicted to. Interviewing is what she does. Her family life in Delaware but she needs to transfer simply because of her family members.<br><br>My web-site :: extended car warranty ([http://Www.Sceltic.at/index.php?mod=users&action=view&id=19873 mouse click the up coming document])

← Older revision		Revision as of 10:13, 4 December 2014
Line 1:		Line 1:
	~~{{Probability distribution \|~~		The title of the writer is Nestor. Bookkeeping is what she does. One of my preferred hobbies is camping and now I'm attempting to earn cash with it. I presently reside in Alabama.<br><br>Here is my web site :: extended car warranty, [http://www.team.trustfactory.ch/index.php?mod=users&action=view&id=4832 please click the next internet page],
	~~name =variance-gamma distribution\|~~
	~~type =density\|~~
	~~pdf_image =\|~~
	~~cdf_image =\|~~
	parameters =<math>\mu</math> [[location parameter\|location]] ([[real number\|real]])<br/><math>\alpha</math> <!--to do--> (real)<br/><math>\beta</math> asymmetry parameter (real)<br/><math>\lambda > 0</math><br/><math>\gamma = \sqrt{\alpha^2 - \beta^2} > 0 </math>\|
	~~support =<math>x \in (-\infty; +\infty)\!</math>\|~~
	pdf =<math>\frac{\gamma^{2\lambda} \| x - \mu\|^{\lambda-1/2} K_{\lambda-1/2} \left(\alpha\|x - \mu\|\right)}{\sqrt{\pi} \Gamma (\lambda)(2 \alpha)^{\lambda-1/2}} \; e^{\beta (x - \mu)}</math> <br/><br/><math>K_\lambda</math> denotes a modified Bessel function of the ~~second kind<br/><math>\Gamma</math> denotes the Gamma function\|~~
	~~cdf =<!-- to do -->\|~~
	~~mean =<math>\mu + 2 \beta \lambda/ \gamma^2</math>\|~~
	~~median =<!-- to do -->\|~~
	~~mode =\|~~
	~~variance =<math>2\lambda(1 + 2 \beta^2/\gamma^2)/\gamma^2</math>\|~~
	~~skewness =<!-- to do -->\|\|~~
	~~kurtosis =<!-- to do -->\|\|~~
	~~entropy =<!-- to do -->\|~~
	~~mgf =<math>e^{\mu z} \left(\gamma/\sqrt{\alpha^2 -(\beta+z)^2}\right)^{2\lambda}</math>\|~~
	~~char =<!-- to do -->\|~~
	}}
	~~The '''variance-gamma distribution''', '''generalized Laplace distribution'''<ref name=laplace>{{cite book\|title=The Laplace Distribution and Generalizations\|author=Kotz, S~~. et al\|page=180\|year=2001\|publisher=Birkhauser\|isbn=0-8176-4166-1}}</ref> or '''Bessel function distribution'''<ref name=laplace/> is a [[continuous probability distribution]] that is defined as the [[normal variance-mean mixture]] where the [[mixture density\|mixing density]] is ~~the [[gamma distribution]]~~. ~~The tails~~ of ~~the distribution decrease more slowly than the [[normal distribution]]. It is therefore suitable to model phenomena where numerically large values are more probable than~~ is the case for the normal distribution. Examples are returns from financial assets and turbulent wind speeds. The distribution was introduced in the financial literature by Madan and Seneta.<ref>D.B. Madan and ~~E. Seneta (1990): The variance gamma (V.G.) model for share market returns,~~ '~~'Journal of Business'', 63, pp. 511–524.</ref> The variance-gamma distributions form a subclass of the [[generalised hyperbolic distribution]]s~~.

	The fact that there is a simple expression for the [[moment generating function]] implies that simple expressions for all [[moment (mathematics)\|moments]] are available. The class of variance-gamma distributions is closed under [[convolution]] in ~~the following sense~~. If <~~math~~>~~X_1~~</math> and <math>X_2</math> are [[statistical independence\|independent]] [[random variable]]s that are variance-gamma distributed with the same values of the parameters <math>\alpha</math> and <math>\beta</math>, but possibly different values of the other parameters, <math>\lambda_1</math>, <math>\mu_1</math> and <math>\lambda_2,</math> <math>\mu_2</math>, respectively, then <math>X_1 + X_2</math> is ~~variance-gamma distributed with parameters <math>\alpha~~, </~~math> <math>\beta, <~~/~~math><math>\lambda_1+\lambda_2</math> and <math>\mu_1 + \mu_2~~.~~</math>~~

	~~The Variance Gamma distribution can also be expressed in terms of three inputs parameters (C,G,M) denoted after the initials of its founders~~. ~~If the "C" ,<math>\lambda <~~/~~math> here, parameter is integer then the distribution has a closed form 2-EPT distribution. See [[2-EPT probability density function\|2-EPT Probability Density Function]]~~. ~~Under this restriction closed form option prices can be derived.~~

	~~See also [[Variance gamma process]].~~

	== ~~Notes~~ ==
	~~<references/>~~

	~~{{ProbDistributions\|continuous-infinite}}~~

	~~{{DEFAULTSORT:Variance-Gamma Distribution}}~~
	~~[[Category:Continuous distributions]]~~
	~~[[Category:Probability distributions]~~]

← Older revision		Revision as of 10:58, 16 January 2013
Line 1:		Line 1:
	I'~~m Yoshiko Oquendo~~. ~~Playing crochet~~ is a ~~thing~~ that I'~~m completely addicted to~~. ~~Interviewing~~ is ~~what she does~~. ~~Her family life~~ in ~~Delaware~~ but ~~she needs to transfer simply because~~ of ~~her family members.~~<br><br>~~My web~~-~~site :: extended car warranty ([http:~~//~~Www~~.~~Sceltic~~.at/~~index~~.~~php?mod~~=~~users&action~~=~~view&id~~=~~19873 mouse click the up coming document~~])		{{Probability distribution \|
			name =variance-gamma distribution\|
			type =density\|
			pdf_image =\|
			cdf_image =\|
			parameters =<math>\mu</math> [[location parameter\|location]] ([[real number\|real]])<br/><math>\alpha</math> <!--to do--> (real)<br/><math>\beta</math> asymmetry parameter (real)<br/><math>\lambda > 0</math><br/><math>\gamma = \sqrt{\alpha^2 - \beta^2} > 0 </math>\|
			support =<math>x \in (-\infty; +\infty)\!</math>\|
			pdf =<math>\frac{\gamma^{2\lambda} \| x - \mu\|^{\lambda-1/2} K_{\lambda-1/2} \left(\alpha\|x - \mu\|\right)}{\sqrt{\pi} \Gamma (\lambda)(2 \alpha)^{\lambda-1/2}} \; e^{\beta (x - \mu)}</math> <br/><br/><math>K_\lambda</math> denotes a modified Bessel function of the second kind<br/><math>\Gamma</math> denotes the Gamma function\|
			cdf =<!-- to do -->\|
			mean =<math>\mu + 2 \beta \lambda/ \gamma^2</math>\|
			median =<!-- to do -->\|
			mode =\|
			variance =<math>2\lambda(1 + 2 \beta^2/\gamma^2)/\gamma^2</math>\|
			skewness =<!-- to do -->\|\|
			kurtosis =<!-- to do -->\|\|
			entropy =<!-- to do -->\|
			mgf =<math>e^{\mu z} \left(\gamma/\sqrt{\alpha^2 -(\beta+z)^2}\right)^{2\lambda}</math>\|
			char =<!-- to do -->\|
			}}
			The '''variance-gamma distribution''', '''generalized Laplace distribution'''<ref name=laplace>{{cite book\|title=The Laplace Distribution and Generalizations\|author=Kotz, S. et al\|page=180\|year=2001\|publisher=Birkhauser\|isbn=0-8176-4166-1}}</ref> or '''Bessel function distribution'''<ref name=laplace/> is a [[continuous probability distribution]] that is defined as the [[normal variance-mean mixture]] where the [[mixture density\|mixing density]] is the [[gamma distribution]]. The tails of the distribution decrease more slowly than the [[normal distribution]]. It is therefore suitable to model phenomena where numerically large values are more probable than is the case for the normal distribution. Examples are returns from financial assets and turbulent wind speeds. The distribution was introduced in the financial literature by Madan and Seneta.<ref>D.B. Madan and E. Seneta (1990): The variance gamma (V.G.) model for share market returns, ''Journal of Business'', 63, pp. 511–524.</ref> The variance-gamma distributions form a subclass of the [[generalised hyperbolic distribution]]s.

			The fact that there is a simple expression for the [[moment generating function]] implies that simple expressions for all [[moment (mathematics)\|moments]] are available. The class of variance-gamma distributions is closed under [[convolution]] in the following sense. If <math>X_1</math> and <math>X_2</math> are [[statistical independence\|independent]] [[random variable]]s that are variance-gamma distributed with the same values of the parameters <math>\alpha</math> and <math>\beta</math>, but possibly different values of the other parameters, <math>\lambda_1</math>, <math>\mu_1</math> and <math>\lambda_2,</math> <math>\mu_2</math>, respectively, then <math>X_1 + X_2</math> is variance-gamma distributed with parameters <math>\alpha, </math> <math>\beta, </math><math>\lambda_1+\lambda_2</math> and <math>\mu_1 + \mu_2.</math>

			The Variance Gamma distribution can also be expressed in terms of three inputs parameters (C,G,M) denoted after the initials of its founders. If the "C" ,<math>\lambda </math> here, parameter is integer then the distribution has a closed form 2-EPT distribution. See [[2-EPT probability density function\|2-EPT Probability Density Function]]. Under this restriction closed form option prices can be derived.

			See also [[Variance gamma process]].

			== Notes ==
			<references/>

			{{ProbDistributions\|continuous-infinite}}

			{{DEFAULTSORT:Variance-Gamma Distribution}}
			[[Category:Continuous distributions]]
			[[Category:Probability distributions]]