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| {{Probability distribution
| | Charge card providers will always would rather lend to established debtors than first-timers. The reason being first-time borrowers don't have a past history of dealing with credit and paying down debt.<br><br>I've usually known my credit was Okay” rather than worried about attempting to actively improve it. I take advantage of my credit card for several my purchases unless there's literally no option for transaction via CC and spend the balance off about once weekly. Year ago We purchased a fresh car and could get 1 about a.70% interest on my mortgage therefore i assumed my credit was still OK. I JUST had to get into my bank to change my checking account to a new type because my financial institution was discontinuing their free looking at accounts.<br><br>I have done a substantial amount of churning - I'm not in to the manufactured spend game (an excessive amount of work, much threat of changing rules too, and it feels dishonest if you ask me), but beyond that, I play the charge card game quite a bit. MMM mentions it above in this article, but you certainly usually do not wish to be doing ANY charge card churning in the six months prior to using for a mortgage. If you want to be cautious or your credit isn't pristine really, a year or 24 months make that period.<br><br>For those who have any kind of queries concerning wherever along with how to make use of [http://generateurcartebancaire.fr/ generateur de carte bancair], you can email us with our own web-page. The data source furthermore feeds into an interactive device on the FCAC website. 59 The interactive tool uses various interview-type [http://www.guardian.co.uk/search?q=questions questions] to create a user profile of the user's charge card usage routines and needs, eliminating unsuitable options based on the profile, so the consumer is offered with a small amount of bank cards and the capability to perform detailed comparisons of features, incentive programs, interest levels, etc. |
| | name =Log-Cauchy
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| | type =density
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| | box_width =300px
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| | pdf_image = [[File:Logcauchypdf.svg|275px|Log-Cauchy density function for values of <math>(\mu, \sigma)</math>]]
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| | cdf_image = [[File:Logcauchycdf.svg|275px|Log-Cauchy cumulative distribution function for values of <math>(\mu, \sigma)</math>]]
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| | parameters =<math>\mu</math> ([[real number|real]])<br><math>\displaystyle \sigma > 0\!</math> (real)
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| | support =<math>\displaystyle x \in (0, +\infty)\!</math>
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| | pdf =<math>{ 1 \over x\pi } \left[ { \sigma \over (\ln x - \mu)^2 + \sigma^2 } \right], \ \ x>0</math>
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| | cdf =<math>\frac{1}{\pi} \arctan\left(\frac{\ln x-\mu}{\sigma}\right)+\frac{1}{2}, \ \ x>0</math>
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| | qf =
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| | qdf =
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| | mean =does not exist
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| | median =<math>e^{\mu}\,</math>
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| | mode =
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| | variance =infinite
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| | skewness =does not exist
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| | kurtosis =does not exist
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| | entropy =
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| | mgf =does not exist
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| | char =
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| }}
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| In probability theory, a '''log-Cauchy distribution''' is a [[probability distribution]] of a [[random variable]] whose [[logarithm]] is distributed in accordance with a [[Cauchy distribution]]. If ''X'' is a random variable with a Cauchy distribution, then ''Y'' = exp(''X'') has a log-Cauchy distribution; likewise, if ''Y'' has a log-Cauchy distribution, then ''X'' = log(''Y'') has a Cauchy distribution.<ref name=robust/>
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| ==Characterization==
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| ===Probability density function===
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| The log-Cauchy distribution has the [[probability density function]]:
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| :<math>\begin{align}
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| f(x; \mu,\sigma)
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| & = \frac{1}{x\pi\sigma \left[1 + \left(\frac{\ln x - \mu}{\sigma}\right)^2\right]}, \ \ x>0 \\
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| & = { 1 \over x\pi } \left[ { \sigma \over (\ln x - \mu)^2 + \sigma^2 } \right], \ \ x>0
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| \end{align}</math>
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| where <math> \mu</math> is a [[real number]] and <math> \sigma >0</math>.<ref name=robust>{{cite web|title=Applied Robust Statistics|url=http://www.math.siu.edu/olive/run.pdf|author=Olive, D.J.|date=June 23, 2008|publisher=Southern Illinois University|page=86|accessdate=2011-10-18}}</ref><ref name=stochastic>{{cite book|title=Statistical analysis of stochastic processes in time|author=Lindsey, J.K.|pages=33, 50, 56, 62, 145|year=2004|publisher=Cambridge University Press|isbn=978-0-521-83741-5}}</ref> If <math>\sigma</math> is known, the [[scale parameter]] is <math>e^{\mu}</math>.<ref name=robust/> <math> \mu</math> and <math> \sigma</math> correspond to the [[location parameter]] and [[scale parameter]] of the associated Cauchy distribution.<ref name=robust/><ref name=hiv>{{cite book|title=Stochastic processes in epidemiology: HIV/AIDS, other infectious diseases|author=Mode, C.J. & Sleeman, C.K.|pages=29–37|year=2000|publisher=World Scientific|isbn=978-981-02-4097-4}}</ref> Some authors define <math> \mu</math> and <math> \sigma</math> as the [[location parameter|location]] and scale parameters, respectively, of the log-Cauchy distribution.<ref name=hiv/>
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| For <math>\mu = 0</math> and <math>\sigma =1</math>, corresponding to a standard Cauchy distribution, the probability density function reduces to:<ref name=life/>
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| :<math> f(x; 0,1) = \frac{1}{x\pi (1 + (\ln x)^2)}, \ \ x>0</math>
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| ===Cumulative distribution function===
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| The cumulative distribution function ([[cdf]]) when <math>\mu = 0</math> and <math>\sigma =1</math> is:<ref name=life/>
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| :<math>F(x; 0, 1)=\frac{1}{2} + \frac{1}{\pi} \arctan(\ln x), \ \ x>0</math>
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| ===Survival function===
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| The [[survival function]] when <math>\mu = 0</math> and <math>\sigma =1</math> is:<ref name=life/>
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| :<math>S(x; 0, 1)=\frac{1}{2} - \frac{1}{\pi} \arctan(\ln x), \ \ x>0</math>
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| ===Hazard rate===
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| The [[hazard rate]] when <math>\mu = 0</math> and <math>\sigma =1</math> is:<ref name=life/>
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| :<math> \lambda(x; 0,1) = \left(\frac{1}{x\pi \left(1 + \left(\ln x\right)^2\right)} \left(\frac{1}{2} - \frac{1}{\pi} \arctan(\ln x)\right)\right)^{-1}, \ \ x>0</math>
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| The hazard rate decreases at the beginning and at the end of the distribution, but there may be an interval over which the hazard rate increases.<ref name=life/>
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| ==Properties==
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| The log-Cauchy distribution is an example of a [[heavy-tailed distribution]].<ref name=small>{{cite book|title=Laws of Small Numbers: Extremes and Rare Events|author=Falk, M., Hüsler, J. & Reiss, R.|page=80|year=2010|publisher=Springer|isbn=978-3-0348-0008-2}}</ref> Some authors regard it as a "super-heavy tailed" distribution, because it has a heavier tail than a [[Pareto distribution]]-type heavy tail, i.e., it has a [[logarithmic growth|logarithmically decaying]] tail.<ref name=small/><ref>{{cite web|title=Statistical inference for heavy and super-heavy tailed distributions|url=http://docentes.deio.fc.ul.pt/fragaalves/SuperHeavy.pdf|author=Alves, M.I.F., de Haan, L. & Neves, C.|date=
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| March 10, 2006}}</ref> As with the Cauchy distribution, none of the non-trivial [[moment (mathematics)|moments]] of the log-Cauchy distribution are finite.<ref name=life>{{cite book|title=Life distributions: structure of nonparametric, semiparametric, and parametric families|author=Marshall, A.W. & Olkin, I.|pages=443–444|year=2007|publisher=Springer|isbn=978-0-387-20333-1}}</ref> The [[mean]] is a moment so the log-Cauchy distribution does not have a defined mean or [[standard deviation]].<ref>{{cite web|title=Moment|url=http://mathworld.wolfram.com/Moment.html|publisher=[[Mathworld]]|accessdate=2011-10-19}}</ref><ref>{{cite web|title=
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| Trade, Human Capital and Technology Spillovers: An Industry Level Analysis|author=Wang, Y.|page=14|publisher=Carleton University|accessdate=2011-10-19}}</ref>
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| The log-Cauchy distribution is [[Infinite divisibility (probability)|infinitely divisible]] for some parameters but not for others.<ref>{{cite journal|title=On the Lévy Measure of the Lognormal and LogCauchy Distributions|url=http://resources.metapress.com/pdf-preview.axd?code=gn16hw202rxh4q1g&size=largest|accessdate=2011-10-18|author=Bondesson, L.|journal=Methodology and Computing in Applied Probability|year=2003|pages=243–256|publisher=Kluwer Academic Publications}}</ref> Like the [[lognormal distribution]], [[log-t distribution|log-t or log-Student distribution]] and [[Weibull distribution]], the log-Cauchy distribution is a special case of the [[generalized beta distribution of the second kind]].<ref>{{cite book|title=Return distributions in finance|author=Knight, J. & Satchell, S.|page=153|year=2001|publisher=Butterworth-Heinemann|isbn=978-0-7506-4751-9}}</ref><ref>{{cite book|title=Market consistency: model calibration in imperfect markets|author=Kemp, M.|page=|year=2009|publisher=Wiley|isbn=978-0-470-77088-7}}</ref> The log-Cauchy is actually a special case of the log-t distribution, similar to the Cauchy distribution being a special case of the [[Student's t distribution]] with 1 degree of freedom.<ref>{{cite book|title=Statistical distributions in scientific work: proceedings of the NATO Advanced Study Institute|author=MacDonald, J.B.|chapter=Measuring Income Inequality|page=169|editor=Taillie, C., Patil, G.P. & Baldessari, B.|year=1981|publisher=Springer|isbn=978-90-277-1334-6}}</ref><ref name=kleiber>{{cite book|title=Statistical Size Distributions in Economics and Actuarial Science|author=Kleiber, C. & Kotz, S.|pages=101–102, 110|year=2003|publisher=Wiley|isbn=978-0-471-15064-0}}</ref>
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| Since the Cauchy distribution is a [[stable distribution]], the log-Cauchy distribution is a logstable distribution.<ref>{{cite journal|title=Distribution function values for logstable distributions|url=http://www.sciencedirect.com/science/article/pii/089812219390128I|doi=10.1016/0898-1221(93)90128-I|author=Panton, D.B.|accessdate=2011-10-18|date=May 1993|pages=17–24|volume=25|issue=9|journal=Computers & Mathematics with Applications}}</ref> Logstable distributions have [[pole (complex analysis)|poles]] at x=0.<ref name=kleiber/>
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| ==Estimating parameters==
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| The [[median]] of the [[natural logarithm]]s of a [[sample (statistics)|sample]] is a [[robust estimator]] of <math> \mu</math>.<ref name=robust/> The [[median absolute deviation]] of the natural logarithms of a sample is a robust estimator of <math>\sigma</math>.<ref name=robust/>
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| ==Uses==
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| In [[Bayesian statistics]], the log-Cauchy distribution can be used to approximate the [[improper prior|improper]] [[Harold Jeffreys|Jeffreys]]-Haldane density, 1/k, which is sometimes suggested as the [[prior distribution]] for k where k is a positive parameter being estimated.<ref>{{cite book|title=Good thinking: the foundations of probability and its applications|author=Good, I.J.|page=102|year=1983|publisher=University of Minnesota Press|isbn=978-0-8166-1142-3}}</ref><ref>{{cite book|title=Frontiers of Statistical Decision Making and Bayesian Analysis|page=12|author=Chen, M.|year=2010|publisher=Springer|isbn=978-1-4419-6943-9}}</ref> The log-Cauchy distribution can be used to model certain survival processes where significant [[outlier]]s or extreme results may occur.<ref name=stochastic/><ref name=hiv/><ref>{{cite journal|title=Some statistical issues in modelling pharmacokinetic data|author=Lindsey, J.K., Jones, B. & Jarvis, P.|url=http://onlinelibrary.wiley.com/doi/10.1002/sim.742/abstract|doi = 10.1002/sim.742|journal=Statistics in Medicine|date=September 2001|volume=20|issue=17-18|pages=2775–278|accessdate=2011-10-19|doi=10.1002/sim.742}}</ref> An example of a process where a log-Cauchy distribution may be an appropriate model is the time between someone becoming infected with [[HIV virus]] and showing symptoms of the disease, which may be very long for some people.<ref name=hiv/> It has also been proposed as a model for species abundance patterns.<ref>{{cite journal|title=LogCauchy, log-sech and lognormal distributions of species abundances in forest communities|url=http://www.sciencedirect.com/science/article/pii/S0304380004005587|author=Zuo-Yun, Y. et al|journal=Ecological Modelling|volume=184|issue=2-4|doi=10.1016/j.ecolmodel.2004.10.011|date=June 2005|accessdate=2011-10-18|pages=329–340}}</ref>
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| ==References==
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| {{reflist|colwidth=33em}}
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| {{ProbDistributions|continuous-semi-infinite}}
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| [[Category:Continuous distributions]]
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| [[Category:Probability distributions with non-finite variance]]
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| [[Category:Probability distributions]]
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Charge card providers will always would rather lend to established debtors than first-timers. The reason being first-time borrowers don't have a past history of dealing with credit and paying down debt.
I've usually known my credit was Okay” rather than worried about attempting to actively improve it. I take advantage of my credit card for several my purchases unless there's literally no option for transaction via CC and spend the balance off about once weekly. Year ago We purchased a fresh car and could get 1 about a.70% interest on my mortgage therefore i assumed my credit was still OK. I JUST had to get into my bank to change my checking account to a new type because my financial institution was discontinuing their free looking at accounts.
I have done a substantial amount of churning - I'm not in to the manufactured spend game (an excessive amount of work, much threat of changing rules too, and it feels dishonest if you ask me), but beyond that, I play the charge card game quite a bit. MMM mentions it above in this article, but you certainly usually do not wish to be doing ANY charge card churning in the six months prior to using for a mortgage. If you want to be cautious or your credit isn't pristine really, a year or 24 months make that period.
For those who have any kind of queries concerning wherever along with how to make use of generateur de carte bancair, you can email us with our own web-page. The data source furthermore feeds into an interactive device on the FCAC website. 59 The interactive tool uses various interview-type questions to create a user profile of the user's charge card usage routines and needs, eliminating unsuitable options based on the profile, so the consumer is offered with a small amount of bank cards and the capability to perform detailed comparisons of features, incentive programs, interest levels, etc.