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{{Probability distribution
会議に関する情報を読んで、
| name      = Gamma/Gompertz distribution
ルビーの宝石を購入する傾向を求めるの外観。 [http://www.cosmopolitancarpetcleaning.com/data/images1/gaga.html �����ߥ�� �rӋ ��� �˚�] アクセサリーガーメント地区地区地区ペニンシュラブティックコンセプトストア、
| type      = density
このデザインはスーツスタイルを兼ね備えた、
| pdf_image  =[[File:Gamma Gompertz probability distribution.png|325px|Gamma Gompertz cumulative distribution]]<br><small>Note: b=0.4, &beta;=3</small>
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| cdf_image  =[[File:Gamma Gompertz cumulative distribution function.png|325px|Gamma Gompertz cumulative distribution]]
チャネルが結晶と結晶と他の関連するプレゼンテーションや知識の外観から識別する方法など、
| parameters =<math>b, s, \beta  > 0\,\!</math>
私たちは不可解な悲しみ山の皇帝日です:2013-8から24十時15分32秒比Guanya四半期は重慶でより快適に見えた...........[http://special-education-soft.com/images/photoalbum/gaga.html �����ߥ�� �rӋ ���n] 企業の資金調達の難しさに応じて、
| support    =<math>x \in [0, \infty)\!</math>
2012ブランドの売上高は、
| pdf        =<math>bse^{bx}\beta^{s}/\left(\beta-1+e^{bx}\right)^{s+1} \text{where } b,s,\beta > 0</math>
東南アジアなどの国と地域に輸出されています。
| cdf        =<math>1-\beta^{s}/\left(\beta-1+e^{bx}\right)^{s}, x>0, b,s,\beta>0</math><br><math>1-e^{-bsx}, \beta=1</math>
子供(ケリー·リン)本当に控えめな結婚式はまた、 [http://citruscontrols.com/Consulting/converse.html ����Щ`��<br><br>����å� ��]
| mean      =<math>=\left(1/b\right)\left(1/s\right){_2\text{F}_1}\left(s,1;s+1;\left(\beta-1\right)/\beta\right),</math><br>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;<math> b,s>0, \beta\ne1</math><br><math>=\left(1/b\right)\left[\beta/\left(\beta-1\right)\right]\ln\left(\beta\right),</math><br>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;<math> b>0,s=1,\beta\ne1</math><br><math>=1/\left(bs\right),\quad b,s>0,\beta=1</math>
| median    =<math>\left(1/b\right)\ln\{\beta\left[\left(1/2\right)^{-1/s}-1\right]+1\}</math>
| mode      =<math>\begin{align}x^*& = (1/b)\ln\left[(1/s)(\beta-1)\right], \\&\text{with } 0<\text{F}(x^*)<1-(\beta s)^s/\left[(\beta-1)(s+1)\right]^s<0.632121,\\& \beta > s+1\\& = 0, \quad \beta\le s+1\\\end{align}</math>
| variance  =<math>=2(1/b^{2})(1/s^{2})\beta^{s} {_3\text{F}_2}(s,s,s;s+1,s+1;1-\beta) </math><br>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;<math>- \text{E}^{2}(\tau|b,s,\beta), \quad \beta \ne 1</math><br><math>=(1/b^{2})(1/s^{2}), \quad \beta = 1</math><br><br><math>\text{with}</math><br><br><math>{_3\text{F}_2}(a,b,c;d,e;z) = \sum_{k=0}^\infty\{(a)_k(b)_k(c)_k/[(d)_k(e)_k]\}z^k/k!</math><br><br><math>\text{and}</math><br><br><math>(a)_k=\Gamma(a+k)/\Gamma(a)</math>
| skewness  =
| kurtosis  =
| entropy    =
| mgf        =<math>\text{E}(e^{-tx})</math><br><math>=\beta^{s}[sb/(t+sb)]{_2\text{F}_1}(s+1,(t/b)+s;(t/b)+s+1;1-\beta), </math><br><math>\quad \beta \ne 1</math><br><math>= sb/(t+sb), \quad \beta =1</math><br><math>\text{with }{_2\text{F}_1}(a,b;c;z) = \sum_{k=0}^\infty[(a)_k(b)_k/(c)_k]z^k/k!</math>
| char      =
}}


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In [[probability and statistics]], the '''Gamma/Gompertz distribution''' is a [[continuous probability distribution]]. It has been used as an aggregate-level model of customer lifetime and a model of mortality risks.
 
== Specification ==
 
===Probability density function===
 
The [[probability density function]] of the Gamma/Gompertz distribution is:
 
:<math>f(x;b,s,\beta) = \frac{bse^{bx}\beta^{s}}{\left(\beta-1+e^{bx}\right)^{s+1}}</math>
 
where <math>b > 0</math> is the [[scale parameter]] and <math>\beta, s > 0\,\!</math> are the [[shape parameter]]s of the Gamma/Gompertz distribution.
 
===Cumulative distribution function===
 
The [[cumulative distribution function]] of the Gamma/Gompertz distribution is:
 
:<math>\begin{align}F(x;b,s,\beta)& = 1 - \frac{\beta^s}{\left(\beta-1+e^{bx}\right)^s}, {\ }x>0, {\ } b,s,\beta>0 \\[6pt]
& = 1-e^{-bsx}, {\ }\beta=1\\\end{align}</math>
 
===Moment generating function===
The moment generating function is given by:
:<math>\begin{align}
\text{E}(e^{-tx})=
\begin{cases}\displaystyle
\beta^s \frac{sb}{t+sb}{\ } {_2\text{F}_1}(s+1,(t/b)+s;(t/b)+s+1;1-\beta), & \beta \ne 1; \\
\displaystyle
\frac{sb}{t+sb},& \beta =1.
\end{cases}
\end{align}</math>
where <math> {_2\text{F}_1}(a,b;c;z) = \sum_{k=0}^\infty[(a)_k(b)_k/(c)_k]z^k/k!</math> is a [[Hypergeometric function]].
 
== Properties ==
The Gamma/Gompertz distribution is a flexible distribution that can be skewed to the right and to the left.
 
== Related distributions ==
*When &beta; = 1, this reduces to an [[Exponential distribution]] with parameter ''sb''.
*The [[gamma distribution]] is a natural [[conjugate prior]] to a Gompertz likelihood with known , scale parameter <math>b \,\!.</math><ref name=BG/>
* When the shape parameter <math>\eta\,\!</math> of a [[Gompertz distribution]] varies according to a [[gamma distribution]] with shape parameter <math>\alpha\,\!</math> and scale parameter <math>\beta\,\!</math> (mean = <math>\alpha/\beta\,\!</math>), the distribution of <math>x</math> is Gamma/Gompertz.<ref name=BG/>
 
== See also ==
*[[Gompertz distribution]]
*[[Customer lifetime value]]
 
==Notes==
{{reflist|refs=
 
<ref name=BG>Bemmaor, A.C.; Glady, N. (2012)</ref>
 
}}
 
==References==
*{{cite journal|last=Bemmaor|first=Albert C.|coauthors=Glady, Nicolas|title=Modeling Purchasing Behavior With Sudden 'Death': A Flexible Customer Lifetime Model|volume = 58|issue=5|pages = 1012–1021|journal=Management Science|year=2012|doi=10.1287/mnsc.1110.1461|url=http://www.essec.edu/faculty/showDeclFileRes.do?declId=9971&key=Publication-Content}}
*{{cite web|last=Bemmaor|first=Albert C. |last2=Glady|first2=Nicolas| year = 2011 |title=Implementing the Gamma/Gompertz/NBD Model in MATLAB|url=http://dl.dropbox.com/u/7097708/gg_nbd_MATLAB.pdf| publisher = ESSEC Business School|location = Cergy-Pontoise }}
*{{Cite journal | last=Gompertz | first=B. | year= 1825 |pages=513–583| title=On the Nature of the Function Expressive of the Law of Human Mortality, and on a New Mode of Determining the Value of Life Contingencies  | journal =[[Philosophical Transactions of the Royal Society of London]]|
volume = 115 |jstor=107756}}
*{{Cite journal | last=Johnson | first=Norman L.| last2=Kotz | first2=Samuel| last3=Balakrishnan | first3=N. |year= 1995 | title=Continuous Univariate Distributions  |volume=2 |edition=2nd| publisher=John Wiley & Sons  | location=New York |isbn=0-471-58494-0|pages=25&ndash;26}}
*{{Cite journal | last=Manton | first=K. G.| last2=Stallard | first2=E.| last3=Vaupel | first3=J. W. |year= 1986 | title=Alternative Models for the Heterogeneity of Mortality Risks Among the Aged| journal=[[Journal of the American Statistical Association]]  |volume=81 |pages=635–644}}
 
{{ProbDistributions|continuous-semi-infinite}}
 
{{DEFAULTSORT:Gamma Gompertz distribution}}
[[Category:Continuous distributions]]
[[Category:Probability distributions]]
 
[[hu:Gompertz-eloszlás]]

Latest revision as of 22:42, 24 September 2012

Template:Probability distribution

In probability and statistics, the Gamma/Gompertz distribution is a continuous probability distribution. It has been used as an aggregate-level model of customer lifetime and a model of mortality risks.

Specification

Probability density function

The probability density function of the Gamma/Gompertz distribution is:

where is the scale parameter and are the shape parameters of the Gamma/Gompertz distribution.

Cumulative distribution function

The cumulative distribution function of the Gamma/Gompertz distribution is:

Moment generating function

The moment generating function is given by:

where is a Hypergeometric function.

Properties

The Gamma/Gompertz distribution is a flexible distribution that can be skewed to the right and to the left.

Related distributions

See also

Notes

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References

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    Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

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    A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

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  • Template:Cite web
  • One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

    In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

    Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

    Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

    A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

    There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
  • One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

    In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

    Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

    Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

    A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

    There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
  • One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

    In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

    Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

    Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

    A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

    There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang

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  1. 1.0 1.1 Cite error: Invalid <ref> tag; no text was provided for refs named BG