Q-exponential distribution - Revision history

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2014-10-06T21:04:34Z

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	~~{{Probability distribution~~		Tarnish does occur since surface molecules of the silver react with sulphur in the air, or certain foodstuffs including eggs, to form a compound called silver sulphide. When you polish it off, you"re actually removing a number of the gold. For silver-plated items, this means that with repeated polishing over many years there is a risk of exposing the bottom metal and wearing completely through the plating. The sole s-olution then is to have that re-plated. <br><br>So a much better idea would be to eliminate the tarnish by converting the silver sulphide back to silver. That is really simple to do and does not require any sophisticated equipment. You"ll just desire a pan large enough to allow the piece to become entirely immersed, some aluminum foil, some hot water and some baking soda. <br><br>Line the bottom of the bowl with aluminium foil and devote the gold piece, making sure it"s in touch with the foil. Boil enough water to dip them and put it over. Sprinkle the baking soft drink to the water, using about 1 tablespoon for every single pint of water. It"ll froth and foam and might spill over the top-of the pan, so best try this in the drain. Dig up more on our favorite related web page - Click here: [http://www.indyarocks.com/blog/1748548/Silver ipas2 gold membership]. [http://www.feedbooks.com/user/1301111/profile Ipas2] includes supplementary info about where to see about it. Immediately, you must see the tarnish commence to disappear. For carefully damaged items, it will all be gone in a couple of minutes. Get more on an affiliated wiki - Browse this webpage: [http://about.me/onlineadvertisingrvu Hedrick Bank - Work at home Effectively through the Web and Network Marketing \| about]. For seriously damaged things, you might need to re-heat the water when it"s started to cool and repeat the therapy. <br><br>So just how does it work? <br><br>Well, it"s an electrochemical reaction. Within the heated water and baking soda solution a little electric current is made between the aluminum and silver. The electric energy causes a chemical reaction between the aluminium and the sulphur than silver has since aluminium has a higher affinity with sulphur. The sulphur in the tarnish is drawn into the solution and towards the aluminium, leaving the silver behind, where it belongs. The effect occurs faster when the solution is hot. The compound formed when aluminium and sulphur react is named aluminium sulphide and that is what you will find hanging in the bottom of the bowl or stuck to the foil when you"re done. And your silver will be bright and shiny..<br><br>When you loved this information and you would love to receive more info about [http://longtact8510.page.tl emotional health] generously visit our web-site.
	~~\| name =Lomax~~
	~~\| type =density~~
	~~\| pdf_image =~~
	~~\| cdf_image =~~
	~~\| parameters =~~
	~~<math>\lambda >0 </math> [[scale parameter\|scale]] (real)<br />~~
	~~<math>\alpha > 0 </math> [[shape parameter\|shape]] (real)~~
	~~\| support =<math> x \ge 0 </math>~~
	~~\| pdf =<math> {\alpha \over \lambda} \left[{1+ {x \over \lambda}}\right]^{~~-~~(\alpha+1)}</math>~~
	~~\| cdf =<math> 1- \left[{1+ {x \~~over ~~\lambda}}\right]^{~~-~~\alpha}</math>~~
	~~\| mean =<math> {\lambda \over {\alpha~~ -~~1}} \text{ for } \alpha > 1</math>~~<br ~~/> Otherwise undefined~~
	~~\| median =<math>\lambda (\sqrt[\alpha]{2} - 1)</math>~~
	~~\| mode = 0~~
	~~\| variance =<math> {{\lambda^2 \alpha} \over {(\alpha-1)^2(\alpha-2)}} \text{ for } \alpha > 2 </math~~><br />~~<math> \infty \text{ for } 1 < \alpha \le 2 </math> <br /> Otherwise undefined~~
	~~\| skewness =<math>\frac{2(1+\alpha)}{\alpha-3}\,\sqrt{\frac{\alpha-2}{\alpha}}\text{ for }\alpha>3\,</math>~~
	~~\| kurtosis =<math>\frac{6(\alpha^3+\alpha^2-6\alpha-2)}{\alpha(\alpha-3)(\alpha-4)}\text{ for }\alpha>4\,</math>~~
	~~\| entropy =~~
	~~\| mgf =~~
	~~\| char =~~
	}}

	~~The '''Lomax distribution''', conditionally also called~~ the ~~'''[[Pareto_distribution#Pareto types I–IV\|Pareto Type II distribution]]''',~~ is ~~a [[heavy tail\|heavy-tail]] [[probability distribution]] often used in business, economics,~~ and ~~actuarial modeling~~.~~<ref>Lomax, K. S. (1954) "Business Failures~~; ~~Another example of~~ the ~~analysis of failure data". ''[[Journal of the American Statistical Association]]''~~, 49, ~~847–852~~. ~~{{jstor\|2281544}}~~<~~/ref~~><~~ref~~>~~Johnson~~, N.L., ~~Kotz, S., Balakrishnan, N. (1994) ''Continuous Univariate Distributions, Volume~~ 1~~'', 2nd Edition, Wiley~~. ~~ISBN 0-471-58495-9 (pages 575, 602)</ref>~~ It ~~is named after K.~~&~~nbsp~~;~~S. Lomax. It is essentially a [[Pareto distribution]] that has been shifted~~ so ~~that its support begins at zero.<ref>Van Hauwermeiren M and Vose D (2009)~~. [http://www.~~vosesoftware~~.com/~~content~~/~~ebook~~.~~pdf '' A Compendium of Distributions'']~~ [~~ebook]. Vose Software, Ghent, Belgium. Available at~~ www.~~vosesoftware~~.com~~. Accessed 07~~/07/~~11<~~/~~ref>~~

	~~== Characterization ==~~
	~~=== Probability density function ===~~
	~~The [[probability density function~~]~~] for~~ the ~~Lomax distribution is given by~~
	~~:<math> p(x) = {\alpha \over \lambda} \left[{1+ {x \over \lambda}}\right]^{-(\alpha+1)}, \qquad x \geq 0~~,
	~~</math>~~
	~~with shape parameter α>0 and scale parameter λ>0. The density can~~ be ~~rewritten~~ in ~~such~~ a ~~way that~~ more ~~clearly shows the relation to the~~ [~~[Pareto distribution\|Pareto Type I distribution]]. That is~~:
	~~:<math> p(x) = {{\alpha \lambda^\alpha} \over { (x+\lambda)^{\alpha+1}}}~~.</~~math>~~

	~~== Relation to~~ the ~~Pareto distribution ==~~
	~~The Lomax distribution is a [[Pareto distribution~~\|~~Pareto Type I distribution]~~] ~~shifted so that its support begins at zero~~. ~~Specifically:~~
	~~:<math>\text{If } Y \sim \mbox{Pareto}(x_m = \lambda~~, ~~\alpha), \text{ then } Y~~ - ~~x_m \sim \mbox{Lomax}(\lambda,\alpha)~~.<~~/math~~>

	~~The Lomax distribution is a [[Pareto_distribution#Pareto types I–IV\|Pareto Type II distribution]] with ''x''~~<~~sub~~>m<~~/sub~~>~~=λ and μ=0:{{cn\|date=October 2012}}~~
	:<~~math~~>
	~~\text{If } X \sim \mbox{Lomax}(\lambda~~,~~\alpha) \text{ then } X \sim \text{P(II)}(x_m = \lambda, \alpha, \mu=0)~~.~~</math>~~

	~~== Relation to generalized Pareto distribution ==~~
	The ~~Lomax distribution is~~ a ~~special case of~~ the ~~[[generalized Pareto distribution]]~~. ~~Specifically:~~

	~~:<math> \mu = 0~~,~~~ \xi = {1 \over \alpha}~~,~~~ \sigma = {\lambda \over \alpha}~~ .~~</math>~~

	~~== Relation to q-exponential distribution ==~~
	The ~~Lomax distribution~~ is ~~a special case~~ of the ~~[[q-exponential distribution]]~~. ~~The q-exponential extends this distribution to support on a bounded interval~~. ~~The Lomax parameters are given by:~~

	~~:<math> \alpha = { {2-q} \over {q-1}}, ~ \lambda = {1 \over \lambda_q (q-1)}~~ .<~~/math~~>

	~~== Non-central moments ==~~

	~~The~~ <~~math~~>~~\nu</math>th non-central moment <math>E~~[~~X^\nu]</math> exists only if the shape parameter <math>\alpha</math> strictly exceeds <math>\nu</math>, when the moment has the value~~
	:~~<math> E(X^\nu) = \frac{ \lambda^\nu \Gamma(\alpha-\nu)\Gamma(1+\nu)}{\Gamma(\alpha)}<~~/~~math>~~

	~~== See also ==~~
	*[[Power law]]

	~~==References==~~
	~~<references~~ />
	~~{{ProbDistributions\|continuous-semi-infinite}}~~
	~~[[Category:Continuous distributions~~]]
	~~[[Category:Probability distributions with non~~-~~finite variance]]~~
	~~[[Category:Probability distributions]]~~

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2013-12-10T04:08:05Z

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